Research Directions in Computational Mechanics (1991) / Chapter Skim
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4 Artificial Intelligence in Mathematical Modeling
4 Artificial Intelligence in Mathematical Modeling
Pages 39-57
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From page 39... ...
A variety of algorithms for heuristic search, planning, and geometric reasoning can provide effective and rigorous mechanisms for addressing problems such as shape description and transformation, and constraint-based model representation. Before discussing the applications of AI in mathematical modeling, we briefly review knowledge-based expert systems and problem-solving techniques.
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From page 40... ...
They have always incorporated expertise in the form of limitations, assumptions, and approximations, as discussed above, and their output has long ago been accepted as advice, not as "the answers to a problem. There is a need, therefore, to add an operational definition to distinguish the new wave of KBES from conventional algorithmic programs that incorporate substantial amounts of heuristics about a particular application area.
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From page 41... ...
to describe the operation and limitations of systems and to build specialized knowledge acquisition tools. Problem Solving Many problem-solving tasks can be formulated as a search in a state space.
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From page 42... ...
The mathematical modeling activities presented include model generation, interpretation of numerical results, and development and control of numerical algorithms. Note that these activities are not independent, and this organization is used primarily to assist in the exposition of ideas.
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From page 43... ...
Artificial Intelligence W~: Numeric Numeric Uodeilng 1 | Interpretation NL~ ~ | Solution l _ Physlcal | | Interpretation Physical ~ ~ Response (> FIGURE 4.1 Mathematical modeling process.
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From page 44... ...
With the availability of literally hundreds of computational mechanics codes, including a large number of generalpurpose finite element programs with a broad range of capabilities, model generation has become the primary activity of the analyst. However, in the current state of the art, the preparation of input data is a tedious, error-prone, and timeconsuming process.
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From page 45... ...
Customized preprocessors are knowledge-based programs that are integrated into the environment in which they operate. Customized preprocessors extract relevant features from a data base that describes the physical object to be modeled (often a simple geometric model)
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From page 46... ...
Assumptions encode a larger chunk of knowledge than rules and hence can provide a conceptual structure that is clearer and easier to manage than the typical knowledge-based or rule-based systems. Turkiyyah and Fenves provide an example of how assumptions can be represented in a modeling assistant for their Generation and Interpretation of Finite Element Models in a Knowledge Based Environments.
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From page 47... ...
MODEL INTERPRETATION This section describes the AI potential to assist in postanalysis operations. Postanalysis operations are generically referred to as interpretation, although they involve distinctly different types of processes, including model validation, response abstraction, response evaluation, and redesign suggestions.
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From page 48... ...
One interesting use of response abstractions assists the user in checking the "physical reasonableness" of numerical results by comparing the response abstractions between more refined models and simpler models. CONFORMANCE EVALUATION Conformance evaluation is the task of verifying that the computed results satisfy design specifications and functional criteria such as stress levels, ductility requirements, or deflection limitations.
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From page 49... ...
whose response satisfies the design specifications can be generated? Another problem that has to be addressed if computational methods are to be adequately incorporated in CAD is the general capability to provide analysis interpretations and design evaluations compatible with the progress of the design process from the initial conceptual sketch to a fully detailed description.
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From page 50... ...
SYMBOLIC PROCESSING One aspect of program development that is particularly time consuming and error prone is the transition from a continuum model involving operations of differentiation and integration to a computational model involving algebraic and matrix operations. A branch of AI deals with symbolic computations, culminating in symbolic computation programs such as MACSYMA and Mathematical Programs in this class operate on symbolic expressions, including operations of differentiation and integration, producing resulting expressions in symbolic form.
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From page 51... ...
Writing subroutines in this style requires the support of a programming language that provides higher-order procedures, streams, and other powerful abstraction mechanisms available in functional languages. The run-time efficiency does not necessarily suffer.
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From page 52... ...
It is possible to raise the level of abstraction present in large-scale scientific programs (i.e., allowing finite element programmers to deal directly with concepts such as elements and nodes) by identifying and separating levels of concern.
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From page 53... ...
The expert system would have to use both backward and forward chaining components -- the former to break down the goal into the program structure and the latter to select program components to "driver the low-level custom components. MONITORING NUMERICAL SOLUTIONS Combining numerical techniques with ideas from symbolic computation and with methods incorporating knowledge of the underlying physical phenomena can lead to a new category of intelligent computational tools for use in analysis.
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From page 54... ...
In a manner similar to the above, these taxonomies represent the capabilities, advantages, and limitations of analysis programs. The taxonomy must be rich enough so that the knowledge source invoking the programs can make recommendations on the appropriate programs to use based on the high-level abstractions generated by the other knowledge sources or, if a particular program is not available in the integrated system, to make recommendations on alternate modeling strategies so that the available programs)
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From page 55... ...
First principles can also be used to check the plausibility of conclusions reached by using specialized knowledge. A KBES developed using the present methodology is Idiosyncratic in the sense that its knowledge base represents the expertise of a single human domain expert or, at best, that of a small group of domain experts.
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From page 56... ...
Cyc is a large-scale knowledge base intended to encode knowledge spanning human consensus reality down to some reasonable level of depth -- knowledge that is assumed to be shared between people communicating in everyday situations. Cyc is a 1 0-year effort that started in 1984.
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From page 57... ...
ranging from very simple abstract data types such as lists to abstract notions such as synchronization and complex subsystems such as peripheral device drivers. The fundamental idea is that the knowledge base of cliches encode the knowledge that is believed to be shared by programmers.
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