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Symbolic regression is a powerful system identification technique inindustrial scenarios where no prior knowledge on model structure is available.Such scenarios often require specific model properties such asinterpretability, robustness, trustworthiness and plausibility, that are noteasily achievable using standard approaches like genetic programming forsymbolic regression. In this chapter we introduce a deterministic symbolicregression algorithm specifically designed to address these issues. Thealgorithm uses a context-free grammar to produce models that are parameterizedby a non-linear least squares local optimization procedure. A finiteenumeration of all possible models is guaranteed by structural restrictions aswell as a caching mechanism for detecting semantically equivalent solutions.Enumeration order is established via heuristics designed to improve searchefficiency. Empirical tests on a comprehensive benchmark suite show that ourapproach is competitive with genetic programming in many noiseless problemswhile maintaining desirable properties such as simple, reliable models andreproducibility.

Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication