1994-Automated Model Selection for Simulation

From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. utomated Model Select’ for ulat io Yumi Iwasaki Alon Y. Levy Knowledge Systems Laboratory AT&T Bell Laboratories Stanford University AI Principles Research Department 701 Welch Road, Bldg. C 600 Mountain Ave., Room 2C-406 Palo Alto, California, 94304 Murray Hill, NJ 07974 [email protected] [email protected] .com Abstract define formally the concepts of adequacy and simplicity and show that the algorithm in fact generates an Constructing an appropriate model is crucial adequate and simplest model. in reasoning successfully about the behavior of a physical situation to answer a query. In The intuition underlying our algorithm is that the compositional modeling, a system is provided model construction problem can be viewed as a prob- with a library of composible pieces of knowl- lem of relevance reasoning [Subramanian and Gene- edge about the physical world called model sereth, 1987; Levy and Sagiv, 19931. Two types of rel- fragments. Its task is to select appropriate evance reasoning occur in this context. First, relevance model fragments to describe the situation, ei- reasoning is used to determine which phenomena can ther for static analysis of a single state, or affect the query. Intuitively, assuming that the goal of for the more complicated case simulation of modeling is to explain how the value of a term changes dynamic behavior over a sequence of states. over time, what is relevant to this goal is all the things In previous work we showed how the model that could causally influence the term. Consequently, construction problem in general can advanta- the high level mechanism driving the algorithm is back- geously be formulated as a problem of reason- ward chaining on the possible causal influences on the ing about relevance. This paper presents an goal term, determining the set of phenomena, terms actual algorithm, based on relevance reason- and objects that can affect the goal term directly or ing, for selecting model fragments efficiently indirectly. for the case of simulation. We show that the The second aspect of relevance reasoning is deciding algorithm produces an adequate model for a which level of detail is relevant to the goal. Often there given query and moreover, it is the simplest are multiple model-fragments describing the same phe- one given the constraints in the query. nomenon, (grouped into assumption classes [Falken- hainer and Forbus, 19911). Choosing between them de- pends on the underlying modeling assumptions being Introduction made, i.e., on the abstractions of the domain and the Constructing an appropriate model is crucial in reason- approximations being made. Deciding to make a cer- ing successfully about the behavior of a physical situa- tain abstraction can be viewed as stating that some de- tion to answer a query. In the compositional modeling tail is irrelevant to the goal and can hence be removed approach [Falkenhainer and Forbus, 19911, a system is from the representation of a phenomenon (see [Levy, provided with a library of composible pieces of knowl- 19941 for a more detailed account of the connection edge about the physical world called model fragments. between irrelevance and abstractions). We therefore The model construction problem involves selecting ap- use relevance reasoning to decide which modeling as- propriate model fragments to describe the situation. sumptions are appropriate for the goal. Furthermore, Model construction can be considered either for static explicit relevance claims can be used to express addi- analysis of a single state, or for simulation of dynamic tional domain knowledge that comes to bear in select- behavior over a sequence of states. The latter is signif- ing a model, thereby incorporating such knowledge in a icantly more difficult than the former since one must principled manner. Our algorithm alternates between select model fragments without knowing exactly what the two kinds of relevance reasoning. Given some mod- will happen in the future states. This paper presents eling assumptions it determines which additional phe- a general algorithm for model construction for simula- nomena are relevant to the goal, and given a set of tion. For such an algorithm to be useful, the gener- relevant phenomena it chooses the level of detail at ated model must be adequate for answering the given which to model them. The algorithm can be shown query and, at the same time, as simple as possible. We to run in time polynomial in the size of the resulting Modeling 1183 model under certain reasonable assumptions. taking place. The equations are used to determine the Compositional modeling is a very powerful approach next state of the situation. Each state has a simu- to automated modeling of physical devices. However, lation model along with a set of variable values and to enable efficient model construction, we must en- predicates that hold in the state. In order to perform force additional structure on the model fragment li- simulation effectively, we must be able to efficiently brary and the model-fragments (e.g., [Nayak, 1992b]). select the appropriate set of model fragments at ev- An important contribution of this paper is identifying ery state. The output of our algorithm is a small set additional structure that can be imposed on a model of model fragment instances, from which the system fragment library that is both natural and facilitates selects a simulation model at every step of the simula- efficient model construction. tion. Several pieces of work have addressed the model formulation problem for the compositional modeling ap- Problem definition proach [Falkenhainer and Forbus, 1991; Nayak, 1992a; This section defines the model formulation problem as Rickel and Porter, 19941. Our work is distinguished well as some key concepts in our approach. The follow- in that it derives its generality from general consider- ing problem definition is based on that by Falkenhainer ations of relevance reasoning. Specifically, it combines and Forbus ([Falkenhainer and Forbus, 19911, p. 98) model formulation for simulation with guarantees of with some modifications explained below: adequacy and simplicity, which are not found in other Given a scenario description, a domain theory, and a works. query about the scenario’s behavior, the model formulation problem is to produce the most useful, coherent Knowledge representation and behavior scenario model. We elaborate on each part of this def- prediction inition. Before describing the model formulation problem, we Scenario description: Our scenario description briefly describe the representation of physical knowl- specifies a set of facts about the initial state of the edge and the simulation method based on the com- situation to be modeled. This typically includes a set positional model approach. Compositional modeling of individuals (i.e., components of the system), their was first described by Forbus in his work on Qualita- properties and relations among them, representing the tive Process Theory (QPT) [Forbus, 19841, and is also physical structure in the initial state of the simulation. the basis of subsequent works on qualitative modeling Domain theory: The domain theory is represented by Falkenhainer and Forbus [Falkenhainer and Forbus, as a library of model fragments. As stated, each model 19911, Crawford and Farquhar [Crawford et al., 19901 fragment has a set of conditions which are further di- and Iwasaki and Low [Iwasaki and Low, 19931. In com- vided to operating conditions and modeling assump- positional modeling, a physical situation is modeled as tions. The operating conditions are conditions on val- a collection of model fragments. Each fragment rep- ues of variables in a current state that are required for resents some aspect of a physical object or a physi- the model fragment to be applicable. The modeling cal phenomenon. A model fragment consists of condi- assumptions are meta-level conditions describing the tions and consequences. The condition part specifies way we have decided to describe the domain, and are the conditions under which the phenomenon occurs, meant to accommodate different ways of modeling a including the individuals that must exist and the con- certain phenomenon. Examples include assumptions ditions they must satisfy for the phenomenon to oc- about the temporal granularity of the model, the sim- cur. The consequences specify the functional relations plifying assumptions or approximations it makes, or among the attributes of the objects that are entailed the accuracy level it provides. While operating condi- by the phenomenon. tions of a model fragment in the chosen scenario model If there exists individuals al, . , a, that satisfy the may be satisfied at a certain step of the simulation and conditions of a model fragment M at time t, we say cease to hold at a later point, modeling assumptions that an instance of A4 is active at that time. We are assumed to hold throughout the simulation. We will denote the instance as M(al, . , a,) and call make the following assumptions about the library of al,...,% its participants. The existence of an ac- model fragments. Their formal definitions are given in tive model fragment instance implies that the variables [Levy et al., 19941. mentioned in it are defined and that the consequences Coherence of the Library: The library coherence hold. assumption requires that if we have a set of model frag- The basic idea behind the prediction mechanism is ments that

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