Nonlinear System Identification Using Coevolution of Models and Tests

Abstract

We present a coevolutionary algorithm for inferring the topology and parameters of a wide range of hidden nonlinear systems with a minimum of experimentation on the target system. The algorithm synthesizes an explicit model directly from the observed data produced by intelligently generated tests. The algorithm is composed of two coevolving populations. One population evolves candidate models that estimate the structure of the hidden system. The second population evolves informative tests that either extract new information from the hidden system or elicit desirable behavior from it. The fitness of candidate models is their ability to explain behavior of the target system observed in response to all tests carried out so far; the fitness of candidate tests is their ability to make the models disagree in their predictions. We demonstrate the generality of this estimation-exploration algorithm by applying it to four different problems-grammar induction, gene network inference, evolutionary robotics, and robot damage recovery-and discuss how it overcomes several of the pathologies commonly found in other coevolutionary algorithms. We show that the algorithm is able to successfully infer and/or manipulate highly nonlinear hidden systems using very few tests, and that the benefit of this approach increases as the hidden systems possess more degrees of freedom, or become more biased or unobservable. The algorithm provides a systematic method for posing synthesis or analysis tasks to a coevolutionary system.

Automated reverse engineering of nonlinear dynamical systems

“…Here we introduce a scalable approach for automated symbolic regression, made possible by three advances introduced here: partitioning, in which equations describing each variable of the system can be synthesized separately, thereby significantly reducing the search space; automated probing, which automates experimentation in addition to modeling, leading to an automated ''scientific process'' (17)(18)(19)(20); and snipping, an ''Occam's Razor'' process that automatically simplifies and restructures models as they are synthesized to increase their accuracy, to accelerate their evaluation, and to render them more parsimonious and human-comprehensible. We describe these three components and validate their performance on a number of simulated and real dynamical systems.…”

Incrementally Discovering Testable Specifications from Program Executions

“…To apply to realistic traces, it will necessitate the investigation of more powerful data constraint / function identification techniques -techniques that can identify more relevant complex data transformations, that perhaps incorporate nonlinear variable relationships (c.f. work by Bongard and Lipson on identifying non-linear functions from data [26]). …”

A Comparison of Sampling Strategies for Parameter Estimation of a Robot Simulator

“…The approaches taken in Back-to-Reality (BTR) [20,21], estimationexploration (EE) [22,23], and using sequential surrogate optimization (SSO) [24] are largely similar to each other: Two coupled optimization algorithms are run in an interleaved fashion, one to search for solutions to a primary task such as simulated robot locomotion and another to improve the accuracy of the simulator. The product of each run of the primary search (a controller for a simulated robot) is evaluated in reality and then used in subsequent simulator optimizations; and the product of each simulator optimization is used in the following primary search.…”