Manifold meta-learning for reduced-complexity neural system identification
This work addresses computational efficiency in neural system identification for researchers and practitioners dealing with nonlinear dynamical systems, representing an incremental improvement over existing meta-learning methods.
The paper tackled the challenge of deep learning models requiring large datasets and high computational resources for system identification by proposing a meta-learning framework that discovers a low-dimensional manifold in neural network parameters, enabling efficient training and accurate modeling in small-data scenarios, as validated on Bouc-Wen oscillators.
System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep learning models often require large datasets and significant computational resources at training and inference due to their high-dimensional parameterizations. To address this challenge, we propose a meta-learning framework that discovers a low-dimensional manifold within the parameter space of an over-parameterized neural network architecture. This manifold is learned from a meta-dataset of input-output sequences generated by a class of related dynamical systems, enabling efficient model training while preserving the network's expressive power for the considered system class. Unlike bilevel meta-learning approaches, our method employs an auxiliary neural network to map datasets directly onto the learned manifold, eliminating the need for costly second-order gradient computations during meta-training and reducing the number of first-order updates required in inference, which could be expensive for large models. We validate our approach on a family of Bouc-Wen oscillators, which is a well-studied nonlinear system identification benchmark. We demonstrate that we are able to learn accurate models even in small-data scenarios.