Symbolic Regression

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Overview

Symbolic regression aims to recover equations or other readable formulas from observations, helping researchers build models that can be inspected, tested, and extrapolated. Common approaches include evolutionary genetic programming, sparse identification methods such as SINDy, differentiable neural or tree-based models, and Bayesian searches that represent uncertainty over candidate expressions. Recent work also uses transformers and language-model agents to propose or guide searches, often combining these priors with numerical fitting and physical constraints; methods are tested on equation-recovery suites such as Feynman and SRBench as well as dynamical systems and PDE data. A central challenge is that good predictions do not guarantee recovery of the true law: noise, limited or uninformative measurements, and choices of search space can make distinct equations hard to distinguish, so robust evaluation and uncertainty estimates remain important.

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151 papers24 papers in the last four weeks, up 60% on the four weeks before. 0.2% of all new papers.

Oct 15, 2022

Symbolic Recovery of Differential Equations: The Identifiability Problem

Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to classical methods which assume the structure of the equation to be known and focus on the estimation of specific parameters, these algorithms aim to learn the structure and the parameters simultaneously. While the uniqueness and, therefore, the identifiability of parameters of governing equations are a well-addressed problem in the field of parameter estimation, it has not been investigated for symbolic recovery. However, this problem should be even more present in this field since the algorithms aim to cover larger spaces of governing equations. In this paper, we investigate under which conditions a solution of a differential equation does not uniquely determine the equation itself. For various classes of differential equations, we provide both necessary and sufficient conditions for a function to uniquely determine the corresponding differential equation. We then use our results to devise numerical algorithms aiming to determine whether a function solves a differential equation uniquely. Finally, we provide extensive numerical experiments showing that our algorithms can indeed guarantee the uniqueness of the learned governing differential equation, without assuming any knowledge about the analytic form of function, thereby ensuring the reliability of the learned equation.

Philipp Scholl, Aras Bacho, Holger Boche +1

Ludwig-Maximilians-Universität München Munich Germany · Technische Universität München Munich Center for Quantum Science and Technology (MCQST) Munich Quantum Valley (MQV) Munich Germany · Ludwig-Maximilians-Universität München University of Tromsø DLR-German Aerospace Center Munich Center for Machine Learning (MCML) Munich Germany

Parameter IdentifiabilityAutonomous Scientific DiscoverySymbolic Regression
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