Symbolic regression via neural networks

Abstract

Mathematical models allow researchers to understand, analyze, and predict the behavior of systems of physical, biological, and technological interest, and are required for many techniques from dynamical systems and control theory to be used. Unfortunately, it is often impossible to derive mathematical models from first principles, and in such cases system identification is a powerful tool which can be used to deduce models from observed data. Many existing system identification techniques require pre-specification of a dictionary of possible terms in a mathematical model, limiting their ability to give models with the nonlinearities which can arise for biological and other complex systems. We present a methodology which overcomes this limitation by dynamically generating the terms in a model with the necessary complexity and nonlinearity to accurately describe a system’s dynamics. This uses a multilayered, operation-based symbolic regression approach, with the capacity to learn combinations and compositions of operations by training artificial neural networks. Our approach provides a powerful alternative to genetic programming strategies for symbolic regression, and can exploit many of the attractive features of artificial neural networks such as a straightforward learning strategy.

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