Scalable Identification of Physics-Based and Neural Dynamics from Partial Measurements

Abstract:We present a scalable method for identifying nonlinear dynamics from partial measurements, supporting physics-based, neural-network, and gray-box models. We use the Prediction Error Method (PEM) coupled with state estimation performed by a Moving Horizon Estimation (MHE) scheme, which can account directly for general nonlinear dynamics. This results in a bi-level optimization problem that scales poorly with increasing model parameters. To improve computational efficiency, we derive a reformulation that avoids explicit parameter-wide sensitivity matrices and exploits the temporal structure of the underlying optimization problem. Numerical comparisons show up to a $215\times$ speedup in hypergradient evaluation. Racing-vehicle simulations demonstrate accurate prediction and physical-parameter recovery in tire-force identification. Real-world data show that the gray-box model improves prediction accuracy with a neural residual while retaining physical interpretability.

Systems and Control (eess.SY); Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2610.16559 [eess.SY]

(or arXiv:2610.16559v1 [eess.SY] for this version)

https://doi.org/10.48550/arXiv.2610.16559 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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