Related papers: Learning Dynamical Systems by Leveraging Data from Similar Systems

Learning Dynamical Systems by Leveraging Data from Similar Systems

URL: http://arxiv.org/abs/2302.04344v2
Date: Fri, 24 May 2024 06:19:00 GMT
Title: Learning Dynamical Systems by Leveraging Data from Similar Systems
Authors: Lei Xin, Lintao Ye, George Chiu, Shreyas Sundaram,
Abstract summary: We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise.
Score: 1.3053088049015455
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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