Identifiability Guarantees for Drivers and Dynamics of Delayed Physical Systems
stat.ML, cs.LG, math.DS
Submitted: 2026-09-29
Updated: 2026-10-01
Comments: 46 pages, 2 figures
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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
Terminology
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.
Sources
- Beyond Predictions in Neural ODEs: Identification and Interventions
- Adam: A Method for Stochastic Optimization
- Gradients are Not All You Need
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