Reference: Nayak, P. Automated Modeling of Physical Systems. Ph.D dissertation, Knowledge Systems Laboratory, 1992.
Abstract: Effective reasoning about complex physical systems requires the use of models that are adequate for the task. Constructing such adequate models is often difficult. In this dissertation, we address this difficulty by developing efficient techniques for automatically selecting adequate models of physical systems. We focus on the important task of generating parsimonious causal explanations for phenomena of interest. Formally, we propose answers to the following: (a) what is a model and what is the space of possible models; (b) what is an adequate model; and (c) how do we find adequate models. We define a model as a set of model fragments, where a model fragment is a set of independent equations that partially describes some physical phenomenon. The space of possible models is defined implicitly by the set of applicable model fragments: different subsets of this set correspond to different models. An adequate model is defined as a simplest model that explain the phenomenon if interest, and that satisfies any domain-independent and domain-dependent constraints on the structure and behavior of the physical system. We show that, in general, finding an adequate model is intractable (NP-hard). We address this intractability, by introducing a set of restrictions, and use these restrictions to develop an efficient algorithm for finding adequate models. The most significant restriction is that the approximation relations between model fragments are required to be causal approximations. In practice this is not a serious restriction because most commonly used approximations are causal approximations. We also develop a novel order of magnitude reasoning technique, which strikes a balance between purely qualitative and purely quantitative methods. The order of magnitude of a parameter is defined on a logarithmic scale, and a set of rules propagate orders of magnitudes through equations. A novel feature of these rules is that they effectively handle non-linear simultaneous equations, using linear programming in conjunction with backtracking. The techniques described in the dissertation have been implemented and have been tested on a variety of electromechanical devices. These tests provide empirical evidence for the theoretical claims of the dissertation.