Regularised neural network-based nonlinear system identification with prior system knowledge

Abstract

Neural networks can learn the behaviour of nonlinear dynamical systems and achieve high prediction accuracy on test data that is drawn from the same distribution as the training data. However, these models fail to generalise during inference when excited with unseen input trajectories. We tackle this generalisation problem in the context of nonlinear system identification with a system-theoretical approach that ensures input–output stability. We enhance a linear approximation with a recurrent neural network (RNN) that models the residual behaviour to capture complex dynamics and to increase the model's generalisation capabilities. We impose constraints on the learnable parameters to ensure dissipativity, an intrinsic property of most physical systems. This leads to improved generalisation on previously unseen inputs. We evaluate our approach using in-distribution (ID) and out-of-distribution (OOD) data from three different use cases and compare it against non-regularised approaches.

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Identifiers

ORCID for Steffen Staab: orcid.org/0000-0002-0780-4154

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