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× 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.
Related
- Identification and Recovery of Linear Dynamics from Partial Trajectories
- Scalable partial information decomposition for symptom networks via supervised embeddings
- AKAPINN: Adaptive Kolmogorov-Arnold Physics-Informed Neural Networks for approximating solutions to quasilinear partial differential equations
- PE-MHL: Physics-Encoded Modular Hybrid Layers for Scalable Learning of Complex Systems
- Identification through Heteroskedasticity in One Lemma: Partial Identification, an Eigenvalue Construction, and a Caution on Rank Tests
BibTeX
@misc{zhou2026scalable,
title = {{Scalable Identification of Physics-Based and Neural Dynamics from Partial Measurements}},
author = {Yibo Zhou and Johannes Köhler},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16559},
eprint = {2610.16559},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16559},
}
RIS
TY - UNPB
TI - Scalable Identification of Physics-Based and Neural Dynamics from Partial Measurements
AU - Yibo Zhou
AU - Johannes Köhler
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16559
UR - https://arxiv.org/abs/2610.16559
AB - 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× 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.
ER -