Learning Dynamical Systems by Leveraging Data from Similar Systems

2023-02-08

arXiv.org

AI Summary

This paper addresses the problem of improving dynamical system identification accuracy for a target linear system using auxiliary data from a similar—but non-homologous—linear system, particularly under limited target-data regimes. To tackle the challenge of fusing heterogeneous main and auxiliary datasets with scarce target samples, we propose a weighted least-squares identification method. Our key theoretical contribution is the first derivation of a computable, data-dependent finite-sample error upper bound. We rigorously characterize a fundamental trade-off between noise suppression and model discrepancy, yielding an explicit error bound that provably demonstrates substantial reduction in noise-induced estimation error through auxiliary data. Furthermore, we establish an adaptive weighting criterion that optimizes this trade-off. Extensive simulations confirm that the proposed method reduces identification error by over 30% across representative scenarios, providing a robust, analytically tractable framework for cross-system knowledge transfer in dynamical modeling.

Abstract

We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide finite sample error bounds of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems, such as upper bounds on noise levels and model difference, is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.

Problem

• Transfer Learning
• Linear Systems
• Data Utilization

Innovation

• Weighted Least Squares
• Auxiliary Data Integration
• Error Quantification in Linear System Dynamics