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arXiv · 2609.37944

Identifiability Guarantees for Drivers and Dynamics of Delayed Physical Systems

Julien Boussard·Antoine Débouchage·Théo Saulus
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Abstract

A wide range of methods have been proposed, including physics-informed neural networks, which are powerful but do not guarantee identifiability of the dynamics, symbolic regression, which requires a set of precomputed operations, and causal discovery, which is more principled but usually relies on strong assumptions that physical systems may violate. In this work, we develop a theory-grounded method and prove that under a set of permissive assumptions, the structural drivers and drift of stochastic delayed differential equations are identifiable. Our method outperforms others on a benchmark for driver identifiability, and on a second benchmark to evaluate physical consistency of the learned dynamics.

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Julien Boussard, Antoine Débouchage, Théo Saulus. 2026-09-29. Identifiability Guarantees for Drivers and Dynamics of Delayed Physical Systems. https://arxiv.org/abs/2609.37944

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