WASSERSTEIN-GUIDED SYMBOLIC REGRESSION: MODEL DISCOVERY OF NETWORK DYNAMICS

Ramzi Dakhmouche, Ivan Lunati, Hossein Gorji

Keywords: Trajectory inference, Symbolic regression, Wasserstein metric, Network dynamics

TL;DR: We propose a probabilistic symbolic regression approach for trajectory inference from a limited number of screenshots accross time.

Abstract:

Real-world complex systems often miss high-fidelity physical descriptions and are typically subject to partial observability. Learning dynamics of such systems is a challenging and ubiquitous problem, encountered in diverse critical applications which require interpretability
and qualitative guarantees. Our paper addresses this problem in the case of probability distribution flows governed by ODEs. Specifically, we devise a ${\it white}$ ${\it box}$ approach -dubbed Symbolic Distribution Flow Learner ($\texttt{SDFL}$)- combining symbolic search with a Wasserstein-based loss function, resulting in robust model recovery scheme which naturally lends itself to cope with partial observability. Additionally, we furnish the proposed framework with theoretical guarantees on the number of required ${\it snapshots}$ to achieve a certain level of fidelity in the model-discovery. We illustrate the performance of the proposed scheme on the prototypical problem of Kuramoto networks and a standard benchmark of single-cell population trajectory data. The numerical experiments demonstrate the computational advantage of $\texttt{SDFL}$ in comparison to the state-of-the-art.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

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Submission Number: 7152