Title: CaNDiCE: Causal Discovery of Nonlinear Dynamics Through Counterfactual Explanations
Primary area: learning on time series and dynamical systems
Keywords: governing equations, nonlinear dynamics, causality, counterfactuals

Abstract: The problem of discovering governing equations from noisy observational data has broad applications in scientific discovery, control, and prediction of complex systems. However, existing approaches that infer dynamics directly from data—whether symbolic regression (e.g., tree-based methods) or sparse identification with pre-defined basis functions—often suffer from poor generalizability, sensitivity to noise, and the inclusion of spurious terms. In this work, we present a causality-preserving counterfactual explanations framework for discovering governing equations in dynamical systems. Counterfactuals in this setting are hypothetical governing equations obtained by minimally perturbing basis function coefficients to induce out-of-distribution trajectories. By penalizing counterfactuals that deviate from the observed topological causality, a measure of directed effective influence between state variables, the resulting trajectories remain consistent with the causal structure of the true dynamics inferred from observed data. As such, resulting counterfactuals are obtained only by perturbing causal terms in the governing equation, while spurious terms are naturally suppressed since their perturbations violate causal consistency.  We evaluate our approach across a range of dynamical system benchmarks and show that it outperforms state-of-the-art methods, including symbolic regression, library-based sparse regression, and deep learning models, in identifying robust and parsimonious governing equations.