Scalable method finds physical and neural dynamics from limited data
Scalable Identification of Physics-Based and Neural Dynamics from Partial Measurements
Machine Learning
Summary
Understanding how things move or behave often requires measuring all parts, which can be hard or impossible. The authors present a way to figure out the rules behind a system's movement even when only partial measurements are available. They combine traditional physics-based models with neural networks and solve a complex math problem more efficiently than before. Tests show their method is much faster and can accurately predict system behavior like tire forces in racing cars while keeping some physical meaning.
What this means in practice
- •For automotive engineering teams: Identify complex vehicle dynamics like tire forces from limited sensor data to improve performance and safety.
- •For industrial control engineers: Enhance model-based controllers by efficiently estimating physical and neural network parameters from partial system measurements.
Authors
Yibo Zhou, Johannes Köhler
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.