The overall theme of my research is reasoning with and refining imprecise models of physical processes. Because we cannot know the world precisely, imprecision is implicit in any modeling task. However, it is often the case that imprecision is simply ignored since it has no place in many existing modeling and simulation methodologies. Sometimes, this is of no consequence, but in other cases, the mismatch between prediction and true behavior may lead to erroneous conclusions. In fields where imprecision is addressed (for example, in robust control), the methods are often resticted in terms of the types of imprecision allowed or are not guaranteed to produce all the predictions inherent in the model or produce predictions that are too weak to provide useful guidance. What is needed is a general method for representing and reasoning with imprecison that can capture the typical types of imprecision inherent in modeling tasks and can produce predictions that maintain precision consistent with the model imprecision. In the next section, I describe SQSim, a representation and simulation method that meets these goals.
While imprecision is inherent in any modeling task, it is also true that a model's precision can be improved with experience with the underlying physical process. Learning a model from a combination of prior knowledge and empirical data is the task of system identification. Typically, identification methods work under the assumption that a parametric model of the process exists and searches the model space for the precise model that best matches the empirical data. Confidence bounds on the parameters (and hence the prediction) can also be determined to represent the uncertainty inherent in using a finite amount of data. This method can be quite efficient in cases where the search space has good properties (such as an easily computable gradient). For cases where this does not hold, however, (for example, if we allow functional as well as parametric uncertainty), finding an optimal model may be very difficult. In addition, identification methods require that empirical data be informative enough to provide complete experience with the system over the desired operating range. If such conditions cannot be met, the resulting model may differ greatly from the true model. In the third section, I describe SQUID, a method for refining an existing model by using possibly uninformative data.
SQSim and SQUID provide two key technologies for automating the model-building task. By combining them with a method for postulating initial qualitative models from data, one could construct a system that can automatically construct models using a combination of empirical and prior knowledge.