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[Hiori Kino](https://orcid.org/0000-0002-8912-686X), Hieu Chi Dam, Takashi Miyake, Riichiro Mizoguchi

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[Function Decomposition Tree with Causality-First Perspective and Systematic Description of Problems in Materials Informatics](https://mdr.nims.go.jp/datasets/c8aabae9-426a-4fcd-a480-6826b1d5016a)

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arXiv:2205.00829v1  [cs.AI]  26 Apr 2022Function Decomposition Tree with Causality-First Perspectiveand Systematic Description of Problems in Materials InformaticsHiori KinoResearch and Services Division of Materials Data and Integrated System,National Institute for Materials Science,1-1 Namiki, Tsukuba, Ibaraki 315-0044, JapanHieu-Chi DamJapan Advanced Institute of Science and Technology,1-1 Asahidai, Nomi, Ishikawa 923- 1292, Japan andInternational Center for Synchrotron RadiationInnovation Smart Cross Fertilization Division,Tohoku University, Katahira 2-1-1,Aoba-ku, Sendai, Miyagi, 980-8577, JapanTakashi MiyakeResearch Center for Computational Design of Advanced Functional Materials,National Institute of Advanced Industrial Science and Technology,1-1-1 Umezono, Tsukuba, Ibaraki 315-8568, JapanRiichiro MizoguchiJapan Advanced Institute of Science and Technology,1-1 Asahidai, Nomi, Ishikawa 923- 1292, Japan(Dated: May 3, 2022)1http://arxiv.org/abs/2205.00829v1AbstractAs interdisciplinary science is flourishing because of materials informatics and additional factors;a systematic way is required for expressing knowledge and facilitating communication betweenscientists in various fields. A function decomposition tree is such a representation, but domainscientists face difficulty in constructing it. Thus, this study cites the general problems encounteredby beginners in generating function decomposition trees and proposes a new function decomposi-tion representation method based on a causality-first perspective for resolution of these problems.The causality-first decomposition tree was obtained from a workflow expressed according to theprocessing sequence. Moreover, we developed a program that performed automatic conversion us-ing the features of the causality-first decomposition trees. The proposed method was applied tomaterials informatics to demonstrate the systematic representation of expert knowledge and itsusefullness.I. INTRODUCTIONIn general, useful information can be obtained by relating and organizing the components(entities) of things with each other, and there are many examples in materials informatics,the area of application of this study. The most familiar example for material informatics isthat of representing a molecule as a graph. By representing an entity (molecular structure)as a graph of molecular bonds [1] and analyzing it using machine learning methods, it ispossible not only to regress the physical properties but also to construct molecular genera-tive models.[2–4] In inorganic materials, the definition of neighboring atoms is ambiguous;however, by representing the 3D atomic structure as a graph, explanatory variables can beobtained from data by regressing the total energy [5]. Explanatory variables can also beobtained from data using supervised learning of the time evolution of the glass simulationfrom the initial atomic positions.[6]The prediction of physical properties using graphs as basic data includes the use ofknowledge graphs.[7] In polymers, there is a high dependence of electrical conduction onimpurities, therefore it is difficult to identify and quantify the type of impurity and thechanges in electronic state caused by the impurity.[8] In such cases, graphs, which directlyrelate the dependence of preparation conditions to electrical conduction have been created,can perform missing problems to infer unmeasured conditions, values.2There is another stream of research using knowledge graphs. The relationship betweenentities itself is sometimes useful information. Studies on a citation map [9] have consideredother entities, such as material properties, as well as the citation relationship.[10] One studyaimed to understand the correlation of entities (properties) from the data [11] which makesit easy to understand the relationship between properties.Some studies use ontologies to organize relationships. Research in this direction includeswork on inferring chemical reaction kinetics and reaction mechanisms[12] which is similarto IBM Watson [13]. Ontologies give concepts, attributes, and a network of relationships(TBox) and generate instances to embody the chemical or reaction of interest. Next, exper-imental data are taken in to create a database, and Q&A (reasoning) is exactly the same asdatabase searching, but the ontology (conceptual structure) allows for high-level searchingwhile reasoning.To reasonably infer and predict the knowledge of physical properties and mechanisms, itis, of course, necessary to accurately describe the relationships. In recent years, studies haveaimed to obtain relations (summarizing knowledge) by natural language processing[14] butthe most accurate property values are still obtained by humans or modified by humans.[15]Therefore, human assistance is still important for knowledge compilation. However, no oneperson knows everything in the domain, and even if one did, it would be impossible for oneperson to obtain all the values from the literature. To obtain a reasonable experimentalphysical property value from the literature, it is necessary to know, for example, the dimen-sion of the values (scalar or vector), the type of values (median or not), and the unit inwhich the value can be expressed. In addition, due to the isotropic nature of crystals, thereare cases in which an originally vector quantity is treated as a scalar quantity. These canbe classified in the ontology, but generally we cannot assume everything in the conceptualhierarchy structure of the initial ontology; thus, we notice flaws in the hierarchy during dataacquisition. Therefore, having knowledge of not only the results of the ontology but also thereasons why it was constructed allows us to summarize and share knowledge among researchgroups efficiently in a limited amount of time and budget.Function decomposition tree can be used for this purpose. It has been proposed asa method to represent the relationships among entities as a diagram assuming that it ismainly used by humans to visualize the relationships among entities themselves for the pur-pose of conceptual design, understanding, and idea support, and their usefulness has been3recognized.[16] (Diagrams are defined as general visualization techniques that include theflowchart and the function decomposition tree.) Although the function decomposition treewas initially proposed for the decomposition of functions of artefacts, it can also be appliedto the decomposition of (human) actions due to the similarity between the functions ofartefacts and actions.[17] Therefore, the scope of the function decomposition trees includesnot only the principle of the artificial device to be specifically executed, but also the pro-cedures and calculation methods to solve the problem (algorithms) and the action. Theusefulness of diagrammatic representation on knowledge is also discussed in physics educa-tion. The relationship between reinterpretation of physics problems and the organizationof physics knowledge has been investigated by means of diagrammatic representations forexperts and novices. Experts and novices can start their problem representations from dif-ferent problem categories, but the completeness of the representation depends on the domainknowledgeREFExpertsandNovices suggesting that the difference in the domain knowledge isthe main factor distinguishing experts and novices in their problem-solving abilities.[19] Per-haps for this reason, it is not effective for novices to create diagrammatic representations ofeven simple problem,[20] but on the other hand, diagrammatic methods that convey expertknowledge to novices can also contribute significantly to improving their problem-solvingabilities. For example, it is reported that novices can select almost the same methods asthose of experts by using the function decomposition tree prepared by experts in nanoma-terial domain.[21] One might think that purpose-based decomposition algorithms, whichthe function decomposition trees use, requests high a cognitive load for humans, becauseit requires a large amount of memory when exactly solved by a computer. However, theuse of external memory in the form of diagrammatic representations compiled in the formthat humans can efficiently understand may help to reduce the cognitive load for humansgreatly.[19]The function decomposition is summarized in this paragraph.[16] It is a visualization ofan algorithm or a sequence of actions emphasizing what it does rather than how it runs.i.1) Contrary to ordinary chronological descriptions of sequence of actions, it explicatesthe intermediate goals to be achieved (purpose-based decomposition algorithm).i.2) It makes the hidden intermediate goals explicit as well as final goals that even theactors (inventors of the algorithm) themselves are not aware of.4i.3) A single (sub)goal can be achieved in multiple ways. A decomposition tree allows usto draw them in a single tree so that one can capture the whole picture of a familyof related procedures with many possible variants, which is enabled by decomposinga function into what to achieve from how to achieve. This contributes to the in-depthunderstanding of algorithms/procedures.i.4) This is not an ontology, but it is one of the most valuable results derived from theontology engineering research. Furthermore, it provides a ”point of view” to ”under-stand” algorithms ontologically (to explicate their essentials).Thus, the following benefits are expected in practice.ii.1) Even people who are not familiar with algorithms can understand the essence of thealgorithms.ii.2) Multiple algorithms sharing the same final goal can be superimposed on a single func-tion decomposition tree (general purpose function decomposition tree), so that mutualsimilarities and differences can be made explicit.ii.3) It can predict the spillover effects of algorithm modifications, which is useful whenimproving procedures.Function decomposition trees have been studied outside of the field where ontology-relatedresearch was originally conducted, for example, in collaboration with researchers who areexperts in lifestyle research [22–24]. On the other hand, in fields where ontology-relatedresearch is minor, it is not easy for the domain experts to create function decompositiontrees. Therefore, as stated in the first paragraph, this study is written assuming that theprimary target audience is materials informatics researchers.The function decomposition tree is one of the top-down methods, and another example isConcept Map.[25] The latter differs from the former in that it uses verbs, prepositions, andspecializations to decompose the relationships between concepts, and it has been proposedas an educational tool and used as a knowledge integration tool. The drawback of the top-down methods is that they require a lot of explanation and examples for proficiency, and ithas been reported that the learning cost for creating the concept map is not low. Even withthese drawbacks, the function decomposition tree and the concept map have been studiedand have applied in other domains because they offer sufficient returns.5Function decomposition trees in this manuscript may seem obvious to experts who havealready understood the algorithms in materials informatics. If the explanation by the func-tion decomposition seems natural and plain to an expert, then a novice can expect tounderstand the important points in a logical manner, thus demonstrating the usefulness offunction decomposition as an explanatory tool.Some readers may think that the idea of the function decomposition tree is so-calledmeans-ends analysis.[26] However, the difference is that the latter is at the level of strategyor algorithm, whereas the former is based on the results of ontology engineering and givesconcrete ways to realize it through a simple strategy of the function decomposition.This study applies the function decomposition to the conversion algorithm from atomicdescriptors to crystal descriptors in materials informatics, which suggests that there areconversion methods that have not been used so far. (It will be discussed in Section VC) Webelieve that this research will help to demonstrate the usefulness of function decompositionof existing algorithms.In this study, Section II briefly introduces the conventional function decomposition treeand highlights the problems that hinder its application for beginners. In Section IIIC, wedefine the most basic verbs used in function decomposition in the field of materials scienceand materials informatics. In Section IV, we present a novel function decomposition methodthat compensates for its shortcomings. In addition, the novel function decomposition methodallows for direct mapping to a time-series description (sequential algorithm), and a simpleprogram is introduced for this conversion. In Sections V and V, function decompositionwas applied for material search algorithms and a Python package. Section VII contains adiscussion, and Section VII summarizes this work.II. SEQUENTIAL ALGORITHM AND PURPOSE-BASED DECOMPOSITIONALGORITHMThe basics of the conventional function decomposition trees described in [16] are brieflyexplained in this section. First, devices, behaviors, and functions in sequential algorithmsand actions are introduced.6A. Devices, Behaviors, and Functions in Sequential AlgorithmsThe sequential algorithm is described with its accompanying concepts using heat transferas an example. The device (an artefact) is defined as entity that converts the input object(s)into output object(s). In the following, devices that exchange heat are considered concretely.Devices that use heat are useful; for example, materials with low thermal conductivity [27]and high-performance thermoelectric materials that convert heat into electricity [28] arebeing explored through machine learning techniques. Radiant coolersREFAdiativeCoolingwhich radiate heat directly with no object to exchange, are also attracting attention. Thefollowing paragraphs use an example of these heat exchanger to illustrate its behavior andfunction and related issues.A contact heat exchanger is depicted in Figure 1 (a), where the ”warm substance 1 andcold substance 2” is the input and the ”cold substance 1 and warm substance 2” is theoutput. All pairs of inputs and outputs are termed as the behavior of the device action.Thus, the number of input and output pairs corresponds to that of the behaviors of thedevice. However, in practice, the behavior of the device will be represented by a pair ofattentions. Thus, the behavior of the heat exchanger (device 1) shown in Figure 1 (a) isrepresented by the contact of the substance 1 and substance 2, which transfers heat andseparates both the substances.A device is the most basic entity that acts on the object(s) to alter the object-attribute(s) by converting the input to the output of the device.[30] Moreover, devicescan be virtual. The entire process can be considered in terms of the sequential change inobject-attribute(s), and the device can be interpreted as acting in the sequence: contact,transfer heat, and separate, as shown in Figure 1 (b). Consequently, the attributes ofboth substances become contacted substances, heat exchanged substances, and separatedsubstances, respectively. (Although contact and heat transfer occur simultaneously, wealigned the sequence based on the cause-effect principle of the two processes, i.e., contactprecedes heat transfer.) Hereafter, the diagram, such as Figure 1 (b), is referred to as theobject-attribute flowchart.The term function is defined as the role played by the behavior of the device underdesigner’s intention.[31] If the design intention of the device is to obtain a cold substance,the function would change warm substance 1 into cold substance 1, i.e., cool substance 17FIG. 1. Figure 1: (a) A contact heat exchanger with ”warm substance 1 and cold substance 2”as input, ”cold substance 1 and warm substance 2” as output, and its internal process procedures,which are converted to the object-attribute flowchart presented in (b). (c) depicts a device exhibit-ing a cooling function (converting warm material into cold material). (d) denotes a device and itsinternal processing procedures that cools via thermal radiation.as shown in Figure 1 (c). The same cooling function of the various devices can be clearlydiscussed on the same footing by narrowing down the action of the device to its function.Another cooling device is described in the object-attribute flowchart as device 1’ in Figure 1(d), which exposes the surface of a material to radiate heat.8III. FUNCTION DECOMPOSITION TREE IN PURPOSE-BASED DECOMPO-SITION ALGORITHMThe way how to achieve the function considered in this section. Any artefact creationproblem, such as device design, can be distinguished in three tiers: i) a (parent) function asa requirement, ii) a device that realizes and determines the behavior, and iii) furthermore,a (concrete internal) structure that realizes the behavior (inside the device) is determined.Once a device is selected under the designer’s intention, the behavior inside the device isa mechanism for realizing the function using a sequence of children functions. In addition,the device and its implementation way may be considered the same depending on thecontext, because a device embodies a single implementation, regardless of being conceptuallydifferent from other devices. The conventional function decomposition was defined with thefollowing two ways:#1. The parent function is decomposed into multiple child-functions via the implementa-tion way. This may be done hierarchically as parent function −→ parent implemen-tation way −→ child function −→ child implementation way −→ grandchild function−→ grandchild implementation way −→ and so forth. This is called the (function)decomposition way. The specific structure of the device has been described later.#2. The substitution of a function with a specialized function positioned at a level lowerthan the (parent) function in the is-a hierarchy is termed as the specialization way.Although this operation is not ”decomposition”, it can be regarded as a type of decom-position, considering that the essential purpose of the function decomposition bringsfunctions closer to the implementation level by reducing the granularity of the func-tions.The two function decomposition methods are explained in Table I. Note that the term”decomposition way” is used instead of the term ”implementation way” to represent thecontext contrary to the object-attribute flowchart.The function decomposition employs the black-box model to prohibit access to the be-haviors inside the device. The access to the inside of the device is allowed only for childfunctions. Although the decomposition of the parent function into multiple children func-tions apparently allows us to access the inside of the device — turning the black box to9TABLE I. Two function decomposition methods.#1. Decomposition by Decomposition Way1a. Select a decomposition way for the decomposition of a parent function.1b. Decompose into a series of child functions with a specific sequence of processes accordingto the decomposition scheme.#2. Decomposition by Specialization Way2a. Replace a parent function with a child function that is a specialization of the parentfunction (specialization via is-a relation).the white box — this access is allowed at the function level rather than the behavior level.Thus, the black box model is maintained. The nested structure for black-boxing of schemesat higher level functions and the corresponding white-boxing with function decompositionof those schemes continues until the function decomposition has been exhausted.In the conventional function decomposition trees, the decomposition way and the spe-cialization way are combined to form ways for function decomposition, where functions arewritten as oval functional nodes, the ways are indicated with squares, and the relation-ship between the functions and ways are represented with connecting lines, as depicted inFigure 2 (a). In addition, the execution (achievement) of child functions obtained from adecomposition proceeds from left to right in the function decomposition tree.The difference between the two decomposition methods explained in Table I are furtherexplained: the decomposition method #1 exhibits a corresponding implementation, whereasthe #2 does not. In the decomposition tree, the #1 decomposes the parent function intomultiple functional nodes, whereas #2 replaces the parent function with a single specializedfunctional node based on the is-a relation. Therefore, the two methods are significantlydifferent from each other, as shown in Figure 2 (a).The resulting diagram is a hierarchical pyramidal decomposition tree structure that de-composed the parent function into multiple subfunctions. This decomposition expression is10FIG. 2. Figure 2: (a) The parent function is achieved in the decomposition way by processing childfunction 1 and child function 2 in sequence. In specialization, ways 1’ and 2’ are accomplished bychild functions 1’ and 2’, respectively. (b) (c) Function decomposition tree of the cooling system.Although the devices are conceptually different, they can be equated with the way in the functiondecomposition tree. (b) is the function-first perspective and (c) is the way-first perspective.known as a function decomposition tree.The parent function can be decomposed by multiple ways. A function decompositiontree comprising the decomposition of the parent function by multiple ways is called a gen-eral function decomposition tree, where each decomposition corresponds to a design-alternative representing how to achieve the parent function. In this study, the generaldecomposition tree has been referred to as the function decomposition tree, as the decom-position of functions by multiple ways is common.Function decomposition trees of the device presented in Figure 1 are depicted in Figure 2(b) or (c), which use the methods explained in Table I #1 to achieve ”cool a warm substance”11by two different implementation ways: the contact heat exchanger uses the heat conductionway as its implementation way, and the thermal radiator uses the thermal radiation way asits implementation way. To illustrate the expression of function decomposition in line withFigure 2 (b). The heat conduction way is achieved by ”Make the warm substance existent”,”Make the cold substance existent”, ”Contact these substances”, and ”Transfer heat”. Sim-ilarly, the thermal radiation way is achieved by ”Make a warm substance existent”, ”Exposethe surface”, and ”Radiate heat”, as shown in Figure 2 (b).A. Function and action decompositionIn actions, an action decomposition tree [17, 22–24] were developed because a virtualdevice acting on object attributes can be considered to obtain the desired results. Thefunctions and actions can be connected without any gaps because both are expressed inthe decomposition trees. Henceforth, we will refer to both decomposition trees as functiondecomposition trees without distinguishing between them.Function and action decomposition trees significantly expand the scope of applicationof the function decomposition. For instance, computer programs are methods for problemsolving. They can be considered as artefact devices to imitate the functions of artefactswith equations initiated from principles, or action procedures such as solving equations asdirected by humans. Either way, the computer programs can be systematically expressedwith a function and action decomposition tree that renders the objective structure explicit.B. Perspectives and issues in conventional function decompositionThe perspectives and problems are explained with the conventional function decomposi-tion prior to proposing the new method.1. Two perspectives of conventional function decompositionIn the conventional function decomposition tree, the schemes of function decompositioncan be divided into two major perspectives, which will be explained as follows using Figure 2(b) and (c) as an example. Figure 2 (b) initially places the way nodes and places the12functional nodes underneath the way nodes from left to right in the processing sequence.This is referred as the way-first perspective. Figure 2 (c) initially arranges the functionalnodes from left to right according to the processing sequence shown in Figure 1. This isreferred as the function-first perspective. (Thereafter the figure arranges the nodes ofpossible ways.) There are multiple ways of representing the function decomposition tree,even for schemes as simple as that presented in Figure 1. In the traditional approach, theskilled personnel take advantage of this representational flexibility and select a systematicrepresentation from those shown in Figure 2 for easy comprehension.2. Problems with conventional function decomposition treesThough the usefulness of the function decomposition tree has been extensively evalu-ated through real-world applications[17, 30, 32], describing a proper decomposition tree ischallenging for domain experts. The present authors believe that the conventional functiondecomposition trees have the following drawbacks.a. Unfamiliarity with function decomposition trees In general, researchers aren’t accus-tomed in creating a purpose-based decomposition algorithm. Additionally, novices are oftenunsure of wording the sentence describing the functions.b. Too much emphasis on the action of the device Because the function decompositionis white-boxing, the emphasis is placed on the action of the device though of the way node.Thus, there is no direct relationship between the object-attribute flowchart and the functiondecomposition trees, and there can be an overlap between the representations of the higher-level functions and the lower-level functions.c. Processing sequence The functional nodes that have no processing sequence amongthem cannot be described. Although there is always a processing sequence from left toright for functional nodes in the function decomposition trees, there is often no processingsequence in decomposing functions in case of multiple inputs to the device, as depicted inFigure 1 (b) and (c). Thus, as shown in Figure 2 (b) and (c), the creator of the decompositiontree must ”generate” the processing sequence, where the warm material is introduced priorto the cold material. These issues significantly challenge novices to generate function de-composition trees. However, the problems caused by the proficiency level can be solved withthe automatic conversion of the object-attribute flowcharts to the function decomposition13trees.C. The verb ”obtain”As functions are expressed using verbs, there must be a common understanding of themeaning of the verbs; otherwise, communication will not be possible. A systematic study ofvocabulary was conducted in previous research for functional expression (function vocabu-lary) in [33]. This section describes (defines) the verb ”obtain” and the related verbs mostoften used to describe the attributes of objects, which are the outputs of devices (ways).This allows a clear distinction between modifications in the attributes of the objects andthat in the objects itself. ”Obtain” is used to mean ”to make an object (attribute) satisfy arequirement that was not at hand before”. For instance, the function of Figure 1 (c) ”cool (awarm substance)” could be rendered as ”obtain a cold substance (from a warm substance)”.As shown in Table II, the function ”obtain” can be defined recursively using the functions”select,” ”construct,” and ”generate.”Subsequently, the parts are defined herein. For artefacts, the parts refer to gears, screws,and pipes that pass through a medium. For algorithms, parts refer to function subroutinesas parts to be combined.Both ”select” and ”construct” are used to ”obtain” a new part from an existing part.”Select” means picking up an object from the candidates at random or according to theselection criteria that could be selected from the candidates finding a recursion. ”Construct”refers to obtaining parts (operable objects) by transforming or disassembling them, andsubsequently transforming, decomposing, and combining them to obtain a new part forthe purpose. For instance, several sub-parts can be combined into a complete part with”construct”.Let us illustrate the word ”generate” with another example. Optimization of the efficiencyof GaN LEDs is done using machine learning [34]. ”Generate” means to essentially createsomething out of nothing in one view and is used to bring forth a new object of differenttypes from the input. The meaning of different types from the input is explained below interms of the artefact function. LED lights are artefacts and devices that convert electricalenergy into visible light. (Although a portion of the electrical energy is converted into heatas well, heat generation was not considered as a function as it was not the purpose of the14TABLE II. ”Obtain” is defined cyclically from ”Select”, ”Construct”, and ”Generate.”• Obtain– Select∗ No evaluation way1. Randomly select one candidate∗ Evaluation way1. Select or construct evaluation criteria <recursion> and evaluate (correspond-ing to generate evaluation values).2. Select one with reference to the evaluation value.– Construct (parts = operable objects)∗ Creation way1. Obtain parts <recursion>2. ”Deform” or ”disassemble” the part3. Combine parts (select only one)– Generate∗ Generation way1. Obtain the output of the constructed partsdevice herein.) The input object of this device is electrical energy, and the output object isvisible light. In the perspective of existence or non-existence in the category of visible light,something is created out of nothing through the device, and this type of transformation isdescribed as ”generate (light)”.Next, we will provide an example of a regression model.[35] The linear model with anintercept is written as f(x) =∑icixi + c0 and is ”constructed” because they are made ofalready existing parts, xi and ci, which are explanatory variables and scalars. In contrast,the values of coefficients ci are ”generated” as a result of training based on training data.It is because the values of coefficients in the trained model have different types from the15training data and do not exist before training. Note that the selection of ”construct” or”create” depends on the context of describing algorithms. For example, LASSO, whichemploys the L1 penalty term, was newly discovered in 1986,[36] i.e. was ”created”, butit was ”constructed” in the sense that the power of the penalty term in the optimizationfunction was changed from the Ridge regression, which uses the L2 penalty term in 1977.[37]Lastly, note that ”construct a part and generating an output from the part” may becollectively described as ”obtain”, expecting that there will be no misunderstanding as thedecomposition tree would become redundant. The above minimal definitions will allow usto express ”obtain” and the changes in attribute without any misunderstanding.IV. NEW FUNCTION DECOMPOSITION METHODA. Decomposition methods with new types of functional nodesIn this section, a new function decomposition way is proposed. Revisit the correspondencebetween the object/attribute flowchart and the function decomposition tree. Although thechanged attributes constitute the purpose (output) of the object-attribute flowchart, thefunction generally represents the changes in attributes as well as the action that causes thechange. For instance, the objective (object-attribute) in Figure 1 (c) is the cold substance1,whereas the main purpose in Figure 2 (b) is to ”cool (warm) substance”. The ”cool” actionmakes the warm state cold. This would be the main cause of difficulty and confusion faced bybeginners during the creation of decomposition trees. The current study solves this problemby introducing a new perspective.1. Two Types of Functional NodesIn contrast to the single type of functional node present in the conventional functiondecomposition trees, the current study introduces two types of functional nodes that can bedistinguished based on their roles in the object-attribute flowchart. As shown in Figure 3,the ellipsoidal attribute-functional node indicates the change in the object-attribute, andthe hexagonal way-application functional node indicates the effect of the device on theobject-attribute. The attribute-functional node of the function decomposition corresponds16FIG. 3. (a) Object-attribute flowchart consisting of object-attribute i?1, device i, and theobject-attribute i. (b) Causality-first function decomposition corresponding to (a) is shown us-ing attribute-functional nodes and way-application functional nodes. The devices in the object-attribute flowchart correspond to the decomposition way in the function decomposition.to the object-attribute of the device, which was converted from the object-attribute to ”ob-tain the object-attribute”. On the contrary, the way-application functional node correspondsto the action of the device and was converted using the decomposition way to ”apply thedecomposition way” (the device and way are detailed in Section III).2. Decomposition into Sub-function Sequences in Decomposition WayThe object-attribute flowchart in Figure 3 (a) was converted to that in Figure 3 (b) withthe following steps. The object-attribute i was converted to the attribute-functional node”obtain object-attribute i”, where i indicates the i-th term. The device i was converted tothe decomposition way i, and the object-attribute functional node ”obtain object-attributei” was achieved by the decomposition way i. The decomposition way i was achieved bythe attribute-functional node ”obtain the object-attribute i − 1” and the way-applicationfunctional node ”apply the decomposition way i”, which corresponds to the action of devicei and was repeated with respect to i.As represented in Figure 3 (b), ”obtain” and ”apply” are the most common forms of17verbs used in this study because an appropriate automatic conversion in natural languageis almost impossible for authors. However, the text can be modified to make the concretedescriptions more natural.How can we observe this function decomposition translating for the sequence of object-attributes and devices shown in Figure 4 (a)? This function decomposition can be regardedas forming a nested structure with object-attributes, where devices and ways were cate-gorized as large, medium, and small. In particular, the medium object-attribute depictedin Figure 4 (a) was converted into the large object-attribute using the large device, corre-sponding to the large decomposition way. The medium object-attribute exhibited an in-ternal structure, whereas the small object-attribute exhibited a structure transformed intothe object-attribute b in the medium device, corresponding to the medium decompositionway. This can be considered as a perspective that clearly depicts the present attribute(denoted as large object-attribute) as a result of attribute changes involving the nestedpast, i.e., the result of a causal chain. Thus, this new proposed method was termed ascausality-first perspective of function decomposition (or causality-first function decom-position). Additionally, this sequence of function decomposition can be stated as functiondecomposition chain.This decomposition scheme constructs a network of chains rather than a decompositiontree. Thus, we will call it a causality-first function decomposition network (for simplicity, afunction decomposition network).3. Specialization Way DecompositionThe conversion corresponding to the specialization way decomposition (#2 in Table I)was performed according to the conventional function decomposition trees. The functionalnodes used in this decomposition were only attribute-functional nodes. In addition, there areno way-application functional nodes in this conversion (the same as Figure 2 (a)), becausethere is no corresponding device for the specialization way.In conventional function decomposition trees, the distinction between the decompositionway and the specialization way is ambiguous. Because those who write function decomposi-tion trees also understand ontology, these distinctions have been made implicitly, but theyshould be explained explicitly, especially for novices.18FIG. 4. The object-attribute flowchart showing (a) small device to large object-attributes and(b) its causality-first function decomposition.B. Features of function decomposition tree in causality-first perspective1. Role Assignments for Functional NodesAlthough the conventional function decomposition is always aware of the conversion of theinput to the output object-attributes for the device, the conversion of function decompositiontrees decomposed in terms of paraphrased functions. On the contrary, the expression ofthe device action in the causality-first perspective is represented by the role of the way-application functional node, and the attribute-functional nodes describe only the object-attributes achieved by the ways.2. White-boxing of Decomposition WayThe way-application functional nodes are not functionally decomposed in the causality-first perspective. Instead, white-boxing of the decomposition way was achieved in thecausality-first function decomposition by inserting function decomposition chains in the19FIG. 5. White-boxing of decomposition way 1 in (a) was conducted with the insertion of thefunction decomposition chain in (b).longitudinal (causal) direction, as depicted in Figure 5.3. Network Connection of Function decomposition ChainsThe object-attribute flowcharts in Figure 2 (b) and (d) can be converted according to thecausality-first conversion rules in Figure 3. An example of the transformation of Figure 1(b) (d) into a function decomposition network is shown in Figure 6.The relationship between the function decomposition chain and the function decomposi-tion network is equivalent to the relationship between the function decomposition tree andthe general function decomposition tree.[16] In addition, the same multiple ways (referringto both decomposition and specialization ways) were represented as design alternatives alongwith a relationship that depicts a function achieved by satisfying at least one way.4. Uniqueness of Function Decomposition NetworkThe object-attribute function flowchart was uniquely converted to the function decom-position network. Therefore, how to connect function and way nodes are also determineduniquely. Existing decomposition network is preserved when new decomposition chains is20FIG. 6. Function decomposition network with the causality-first perspective corresponding toFigure 2 (b) and (d).added. In other words, new decomposition chains can be added at any position. This isexemplified in the Electronegativity portion of Section VB.5. Description of Independently Achievable ProceduresThe processing sequence only executes the way-application functional node after all theattribute-functional nodes have been achieved. In this context, the achievement of allattribute-functional nodes serves as a trigger for the execution (execution trigger) ofthe way-application functional nodes. Thus, the rules of processing sequence in the functiondecomposition tree (left to right) were able to be abolished in the function decompositionnetwork, and the only sequence of processing immediately below the way i was to performthe way-application functional node i at the end.21C. Computer-aided generation of causality-first function decomposition networksWith the explanations given so far, the conversion rules from the object-attributeflowchart to the function decomposition network should be obvious without the furtherexplanation. This sub-section introduces a software to automatically generate functiondecomposition networks.As beginners face difficulty in directly performing function decomposition, the sequentialalgorithms are first prepared with Cytoscape GUI-based network visualization software.[38]Then, it is converted into a function decomposition network using the Python computerprogram we developed.[39] The output network is in the Graphviz or Cytoscape CX formatand the latter can be edited with Cytoscape GUI.We explain how to describe an object-attribute flowchart based on the sample/descrip-torTarget in the repository.[39] Figure 7 shows a device-based workflow associated withElectronegativity. The object-attribute function nodes are shown as ovals, the device namesare represented as squares, and their input-output relationships are represented by arrows.In addition, the ”is-a” label is added to the arrows to express the is-a relationship betweenthe attribute function nodes at the same time. The former corresponds to Table I, #1 andthe latter to Table I, #2.After saving in a CX JSON file in Cytoscape, the command,$ python cx_network_main.py --graphviz_FDN file1 file2 ...is used to create the function decomposition network using graphviz [41], where file1, file2,...are the Cytoscape CX JSON format files. The command,$ python cx_network_main.py --cx_FDN file1 file2 ...,creates the function decomposition network in Cytoscape CX format. It is noted that arrowsare added to correspond to the workflow order.The workflow in sample/descriptorTarget can be automatically converted to functiondecomposition network in Graphviz format, and the resulting network is shown in Figure 1of [40]. The function decomposition network corresponding to Figure 7 is shown in Figure 2of [40].For the problem that the expression of the function is unfamiliar to inexperienced users in2.4.2a, a minimum expression can be obtained by designating the attribute-functional node22FIG. 7. The device-based workflow for the electronegativity generation portion was cut from theoverall workflow. Lines that are present in the original diagram but not required are not shown.as ”obtain the object-attribute” and that for the way-application node as ”apply the way”.The overlap of representation problem doesn’t occur as a result of automatic transformationwhen there is no overlap among the object-attribute names and among the way names inthe object-attribute flowchart. Thus, novices can make function decomposition networks.V. APPLICATION 1: SYSTEMATIC EXPLANATION OF MATERIALS INFOR-MATICSIn this section, we analyze functions where descriptors are generated from a crystal andare related to crystal target variables, as an example of materials informatics in the func-tion decomposition network. Descriptors and their relationship to the target variables areexplained in conventional text (, or sequential algorithm) in Section II of [40]. The de-composition and specialization ways are indicated by open squares and grey-filled squares,respectively. In addition, certain nodes were omitted and rearranged for appropriate viewing.23FIG. 8. The Overall function decomposition network achieving the top goal: ”Associate descrip-tors with crystal objective variables” (1 in the figure) from the bottom node ”obtain a crystal” (6).The numbers in the figure indicate the same position in subsequent figures.Function decomposition network with the causality-first perspective is provided in [40].A. Overall featureThe topmost purpose was set as ”Associate descriptors with crystal objective variables”(1) in Figure 8. Ways between the topmost purpose and the bottom-line purpose ”get acrystal” (6) were white boxed systematically. The figure was first written with an object-attribute flowchart and the decomposition by specialization way, then automatically con-verted into function decomposition network. Lastly, each node was modified with an appro-priate English expression.Enlarged view in the part of 1 – 5 nodes of Figure 8 is shown in Figure 9; some nodeswere omitted and rearranged for appropriate viewing. There are three ways to achieve themajor goal, each indicated by an arrow. They are named the atomic target variable way,atomic-descriptor derived crystal descriptor way, and direct crystal descriptor generationway, the number of which correspond to those in Figure 8. They are also explained astextual descriptions in [40].24B. Superposing other goalsIn conventional function decomposition trees, it is sometimes necessary to rewrite thefunction decomposition tree structures when a new goal is added to an existing decompo-sition tree. This is not only a case of polishing the function decomposition tree, but also acase of correcting the essential problem of fixing an inter-node order that differs if new nodesare added as described in Section IVA3 . We show that new goals can be easily added toa function decomposition network. Electronegativity is a relative measure of the strengthwith which atoms in a molecule attract electrons and is used as one of the descriptors ofatoms. However, it was originally invented as an internal measure to predict the dissociationenergy of heteromolecules from homomolecules.[41]Function decomposition networks can superpose these different targets on the existingnetwork. For example, Pauling’s original final goal, ”Predicting dissociation energies ofdifferent molecules” in electronegativity, is superposed by a dashed line in another chain offunction decomposition networks in Figure 10. (Dashed blue lines are used for clarity in theadditions.) Furthermore, it is known that Allred’s electronegativity [43] indicates the natureof metals and non-metals to some extent. Figure 10 also shows his goal, i.e., ”Discriminatemetal/nonmetal element”. It also illustrates the name; the electronegativity is the same,but their generation ways are different. As with the citation network of articles, conceptsand metrics that have been identified as useful will be shown to be studied for differentgoals (functions) and variants (ways) in function decomposition. Note that research on theelectronegativity measure started in 1931’s, but is still ongoing.[44, 45].C. Function decomposition chains and design-alternative considerationsFinally, the methods used in smooth overlap of atomic positions kernel and the Gaussianapproximation potential (SOAP-GAP) [46], spectral neighbor analysis potential (SNAP)[47], Behler et al [48], Seko et al.[49], orbital field matrix (OFM) [50], and regression withelemental features are visualized in Figure 11. The textual details of each will be placed in[40].In Figure 11 (a), SOAP-GAP regresses the crystal target variable by directly obtainingthe SOAP crystal descriptor from the extended atomic positions, whereas SNAP interprets25FIG. 9. Enlarged view in the part of 1–5 nodes of Figure 8; certain nodes were omitted andrearranged for appropriate viewing. Arrows show the three ways; the atomic target variable way,atomic-descriptor derived crystal descriptor way, and direct crystal descriptor generation way,which are explained in [40]. The numbers in the figure correspond to those in Figure 8.26FIG. 10. Enlarged view of parts 7 of Figure 8. The function decomposition chains to obtainthe electronegativity are presented. Pauling’s original final goal, ”Predicting dissociation energiesof different molecules” in electronegativity, is superposed by the nodes using dashed shapes anddashed lines as another function decomposition chain. The goal, ”Discriminate metal/nonmetalelement” is also added as dotted lines and shapes.SOAP as atomic descriptors and regresses the crystal target variable by adding them to thecrystal descriptor. Moreover, the chain in (b) starts from the same atomic distribution, butBehler et al. use the symmetry function as an atomic descriptor to associate the atomicand the crystal target variable. Although Seko et al. use the same symmetry function,it combines with linear regression to transform the crystal descriptor by summation andregress the crystal target variable.In (c), OFM uses generalized coordination numbers calculated from the relative atomicpositions along with the categorical features converted from the elements to produce thematrix representation of the central and neighboring atomic environments. In addition, othercategory variables are shown in the function decomposition network, and the possibility ofusing other category variables can also be considered.27FIG. 11. (a) Function decomposition chains of SOAP-GAP and SNAP. (b) Chains of Behler andSeko et al. (b) The coordinate number and category decomposition chains constituting crystal-OFM. (d) Function decomposition chain using elemental descriptors.In (d), the generation of atomic descriptors were performed with the elemental featuresthat are non-atomic position descriptors. In addition, the atomic descriptors were convertedto a crystal descriptor by several ways to transform crystal descriptors from atomic descrip-tors with atom-reordering invariance. The decomposition by specialization way of elementalfeatures was performed using the type of variables and dimension of the features. The pur-poses of the elemental features may be able be explained more clearly by increasing thespecialization decomposition.It is difficult for a non-specialist to understand the whole theories of a given field. On theother hand, the differences between the methods in Figure 11 can be hoped to reduce effortsrequired by, for example, informatics researchers to understand the challenges/problems ofmaterials science. This would be one of the major advantages of the function decompositionnetworks.Finally, we provide additional insights from these analyses using function decompositionnetworks. The methods of SOAP-GAP, SNAP, and Seko et al. selected regression modelsdepending how the crystal descriptor is associated with the crystal target variable. Behler28et al.’s method is different from the others because they defined the crystal target variableas the sum of the atomic target variable. Note that only the summation way facilitatesthe conversion to atomic density by considering the total energy as a function of atomicdensity, as used by SOAP-GAP, SNAP, Seko et al., and OFMs. However, there exists theother ways between the function attribute nodes, ”obtain crystal descriptor satisfying allinvariance” and ”obtain all atomic descriptor satisfying coordinate invariance” in Figure 9.The other conversion ways such as standard deviation may contribute to the improvementof the regression performance.VI. APPLICATION 2: CHECK FOR CONSISTENCY OF SUBROUTINES INCOMPUTER PROGRAM LIBRARIESIn recent years, computer library distribution through public repositories has becomepopular in materials informatics. For the library to be widely used, the library documenta-tion needs to be maintained, but before that, creating a library that integrates miscellaneoussubroutines developed by multiple authors or by a single author over a long period of timerequires a unified naming scheme and class/subclass structure. For this purpose, it is firstnecessary to grasp the overall picture of the functions and the names of the subroutines.(To avoid confusion with function, which is used as function decomposition, a subroutine isused for a computer subroutine.)Figure 12 shows a part of the function decomposition network of PyAkaiKKR [51] usedin [52]. Their functions are to get density of states (DOS) or partial density of states(PDOS) from the stdout file output of the AkaiKKR package[53]. Figure 12 (a) shows anetwork when the miscellaneous subroutines already existed are simply put together. ”Classname:member function name” is shown in a way node. It had two problems. One is thatmany other subroutines have subroutines beginning with ”get”, which are not shown here,but these have subroutine names beginning with ”cut.” Second, DOS outputs in list, whilePDOS outputs in list and DataFrame[54] and the subroutines that executes them werecreated separately. The latter is represented by two decompositions by specialization wayin Figure 12. They should start with ”get” and the output format should be selectable asa subroutine option. The results of these modifications are shown in Figure 12 (b). Theoutput type is now handled as option in these subroutines.29FIG. 12. (a) Initial function decomposition network, (b) modified function decomposition network;”Class name:member function name” is shown in a way node.For novices who are not familiar with density functional theory, it is helpful to haveit stated at the same time which keywords for which runs yield which physical quantity.This paragraph further categorizes and organizes subroutine to facilitate user understand-ing using decomposition by specialization way. The higher-level goal of ”obtain DOS” inFigure 12 would be ”obtain calculated values after SCF”, where SCF is an abbreviationof satisfying the condition of self-consistent field which must be satisfied in electronic statecalculations. In AkaiKKR, the calculation is performed with the keyword go=”go” to obtainSCF. For example, to calculate DOS, go=”dos”. There are other physical quantities thatcan be calculated after SCF, so it would be more comprehensive and user-friendly functiondecomposition if they are described at the same time. The results of organizing these areshown in Figure 13. It is possible to find out which value of go will achieve which higher-level30FIG. 13. The ”Obtain calculated value” is set as the upper goal and is connected to ”obtainDOS”, ”obtain PDOS”, etc. using the decomposition by specialization way.goal.The advantages of organizing the subroutines by function decomposition are that theauthors can easily grasp the contents of the libraries, and this reduces hesitation in makingchanges for unification. By performing decomposition by specialization way at the sametime, the contents that had previously been vaguely understood are now easier for theauthors to sort out and organize. While other methods can be used to unify name rules,the advantage of function decomposition networks is that special decompositions can bedescribed at the same time.Similar things are done in nursing guidelines integration occurred in hospital integration[17]. This section shows another example of writing a function decomposition network canclarify differences and/or confusion and facilitate the knowledge integration process.31VII. DISCUSSION ON FUNCTION DECOMPOSITION NETWORKA. Function decomposition with two functional nodesThe causality-first perspective described states that the action of the device is repre-sented by the role of the way-application functional node, and the attribute functional nodeconsiders only the object-attributes achieved using the way, as shown in in Section IVB1.The left-to-right execution order is eliminated, and the achievement of attribute functionnodes trigger execution the way-application function node as described in Section IVB5.The lack of any irregularities in the function decomposition networks presented in Section Vand Section V confirmed that the proposed methods based on the causality-first perspectiveperformed appropriately.B. Developing verb vocabularyThere must be a common understanding of the meaning of the verbs as explained inSection IIIC. The minimum verbs needed for description are called the basic verb vocabulary.We categorized ”obtain” and explained ”select”, ”construct”, and ”generate”; along with”apply”, these are the most basic vocabulary in materials informatics. Furthermore, in datascience, ”regress,” ”classify,” and ”associate,” would be its candidates among other verbs.Since duplicate verb expressions lead to the same function decomposition being performedwith several different expressions, the definition of the basic verb vocabulary in materialsinformatics including examples needs to be established as in the research on lifestyle.[24] Itis also necessary if the algorithms are grouped by computers.C. Connection between different function decomposition networksExisting decomposition trees may comprise a mixture of function-first and way-first per-spectives, and the hierarchical structures may differ between creators though they executedthe same white-boxing. Thus, finding similarities/differences among the function decompo-sition trees is difficult. On the other hand, the function decomposition networks can identifythem easily, resulting in simple overall knowledge. This would be more advantageous whenusing a computer to determine algorithmic differences.32D. Generation of function decomposition network examplesAlthough automatic generation of the function decomposition network from the object-attribute flowchart is now possible, the process of manually modifying the verb vocabularyand expressions remains a two-fold effort. However, a direct construction of the decomposi-tion network will reduce the creator’s required time and effort by half.In this study, we constructed our own function decomposition network from an object-attribute flowchart with the is-a specialization description. Thus, examples of one’s owndomain can be constructed by oneself. Once one becomes familiar with the function de-composition network through the generated examples, the function decomposition networkcan be directly generated instead of using the object-attribute flowchart, thus reducing theamount of work involved in its generation.Moreover, the modification or addition of parts to the function decomposition networkis relatively easy even if its complete generation from scratch appears difficult. In addition,the use of a personalized function decomposition network makes it easier to add and expandthe specific function decomposition network. Thus, a conversion tool would be useful in thisaspect.E. Decomposition by specialization way1. MeritFigure 9 described that ”Obtain crystal descriptor satisfying all invariance from atomicdescriptors” can be realized in various ways. The decomposition network allowed us tosimultaneously describe these is-a specializations along the manner of their creation. This isexpected to lead to a systematic understanding and the discovery of further different ways.2. DemeritIn Figure 8, the specialization way was prioritized after trial and error. However, thespecialization way is introduced to organize functions, not to describe devices, and there isa room for human thought and the order of the decomposition way, and the specializationway can be changed. Therefore, the introduction of the specialization way decomposition33may make the function decomposition network more difficult to understand.A more sophisticated solution would include an interactive system that raises questionsand selects one of the methods during conflict between the decomposition and specializationways. The implementation of this resolution will be explored in future research.F. Execution of function decomposition network to ensure correctnessThe conventional function decomposition trees could only be proved correct by a humanbeing. This is because the correspondence with the workflow was not perfect. On theother hand, the function decomposition network can be executed in principle because it canbe transformed from the workflow. Then, execution can guarantee the correctness of thefunction decomposition. This will be the subject of future research.G. Improvement of the representation problem of conventional function decom-position treesThere are two types of functional nodes: attribute-functional nodes and way-applicationfunctional nodes, and novices have a vague understanding on these. Thus, the selectionof a representation of the same attribute-functional node above and below a way couldcauses duplicate representation (Section IIIB 2.b). No duplication occurs if an application-functional node is placed at the end with (a) attribute-functional node(s) that is(are) theinput node(s) (execution trigger) of the way node. Furthermore, if more than one functionalnode corresponding to multiple devices is to be written under a way node as conventionalfunction decomposition trees, the guideline may be to write an attribute functional nodefirst, followed by way-application functional nodes.As certain function decomposition tree assets [17] already exist, rewriting all of themin a function decomposition network would be require excessive human effort. However,in continuously expanding/correcting fields, frontline staffs who are novices in function de-composition would require to add/modify nodes to their existing function decompositiontree assets even if they are novices in the function decomposition. Difficulties in adding ormodifying expressions to conventional decomposition trees can be resolved by the guidelinesin the previous paragraph, and the existing function decomposition tree assets can be easily34maintained on a continuous basis.VIII. CONCLUSIONSAs interdisciplinary research flourishes, there is a need for systematic and easily under-stood explanatory methods to facilitate communication about each other’s research and itsproblems. In context, function and action decomposition trees have gained reputation asmethods for systematic explanation, but they are unwieldy for novices. Thus, this studydescribes the current problems of function decomposition trees and proposes a new functiondecomposition network with the causality-first perspective to solve these problems.In the proposed function decomposition network, the correspondence with the object-attribute flowchart that tracks object-attribute changes was obtained by separating theconventional functional node into an attribute-functional node for function achievement anda way-application functional node for representing the action of the device. The functionaland action decomposition network with the causality-first perspective can be transformedfrom the object-attribute flowchart and specialization descriptions with the is-a relation; theconversion tool was constructed and published.As the function decomposition tree/network requires a common understanding of the verbvocabulary, the most used verb ”obtain” were defined along with related verbs. A possiblemethod was obtained by performing function decomposition for a materials informaticsproblem. The function decomposition was also used to organize computer libraries. Lastly,the limitations and prospects of the current study were discussed.ACKNOWLEDGEMENTSThis work is supported by the Ministry of Education, Culture, Sports, Science, andTechnology of Japan (MEXT) ESICMM Grant Number 12016013, the Program for Pro-moting Research on the Supercomputer Fugaku (DPMSD), the JST-Mirai Program ”De-velopment of Materials Design Workflow and Data Library for Materials Foundry,” GrantNumber JPMJMI18G5, JPMJMI21G2 and JSPS KAKENHI Grants 20K05311, JP19H05815(Grants-in-Aid for Scientific Research on Innovative Areas Interface Ionics), 20K05068 and35JP21H01375 Japan.[1] Weininger D, ”SMILES, a chemical language and information system. 1. 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Kino, ”Automatic exhaustive calculations of largematerial space by Korringa-Kohn-Rostoker coherent potential approximation method appliedto equiatomic quaternary high entropy alloys,” Physical Review Materials, 6, 023902 (2022).[53] http://kkr.issp.u-tokyo.ac.jp[54] The pandas development team, ”pandas-dev/pandas: Pandas,” DOI:10.5291/zenodo.3609135(2020).40http://kkr.issp.u-tokyo.ac.jpThis figure "SOAPGAP.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "causalityfirst.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "conversion.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "electronegativity.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "enlargedoverall.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "enlargedpartSeven.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "firstFunctionDecompotion.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "heatExchanger.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "network.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "obtainDOS.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "overallCrystal.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "subroutineInitial.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1This figure "whiteboxing.png" is available in "png" format from:http://arxiv.org/ps/2205.00829v1http://arxiv.org/ps/2205.00829v1 Function Decomposition Tree with Causality-First Perspective and Systematic Description of Problems in Materials Informatics Abstract I Introduction  II Sequential Algorithm and Purpose-Based Decomposition Algorithm A Devices, Behaviors, and Functions in Sequential Algorithms III Function decomposition Tree in Purpose-Based Decomposition Algorithm A Function and action decomposition B Perspectives and issues in conventional function decomposition 1 Two perspectives of conventional function decomposition 2 Problems with conventional function decomposition trees C The verb "obtain" IV New function decomposition method A Decomposition methods with new types of functional nodes 1 Two Types of Functional Nodes 2 Decomposition into Sub-function Sequences in Decomposition Way 3 Specialization Way Decomposition B Features of function decomposition tree in causality-first perspective 1 Role Assignments for Functional Nodes 2 White-boxing of Decomposition Way 3 Network Connection of Function decomposition Chains 4 Uniqueness of Function Decomposition Network 5 Description of Independently Achievable Procedures C Computer-aided generation of causality-first function decomposition networks V Application 1: systematic explanation of materials informatics A Overall feature B Superposing other goals C Function decomposition chains and design-alternative considerations VI Application 2: check for consistency of subroutines in computer program libraries VII Discussion on function decomposition network A Function decomposition with two functional nodes B Developing verb vocabulary C Connection between different function decomposition networks D Generation of function decomposition network examples E Decomposition by specialization way 1 Merit 2 Demerit F Execution of function decomposition network to ensure correctness G Improvement of the representation problem of conventional function decomposition trees VIII Conclusions  Acknowledgements  References