Robust Latent Neural Operators for a Family of Systems with Sparse Observations

Xin Li, Chengli Zhao, Xue Zhang, Xiaojun Duan

Keywords: Neural operator, complex system, variational autoencoder, recurrent neural network

TL;DR: We propose a robust latent neural operator using a variational autoencoder framework, which enhances both modeling accuracy and robustness for systems with sparse observations, significantly outperforming SOTA baseline methods.

Abstract:

Neural operator methods have achieved significant success in the efficient simulation and inverse problems of complex systems by learning a mapping between two infinite-dimensional Banach spaces. However, existing methods still exhibit room for optimization in terms of robustness and modeling accuracy. Specifically, existing methods are characterized by sensitivity to noise and a tendency to overlook the importance of sparse observations. Therefore, we propose a robust latent neural operator based on the variational autoencoder framework. In this method, an encoder based on recurrent neural networks effectively extracts sequential information and dynamical characteristics embedded in sparse observations. Subsequently, a neural operator in latent space and a decoder facilitate the modelling of the original system. Additionally, for certain higher-dimensional systems, opting for a lower-dimensional latent space can reduce task complexity while still maintaining satisfactory modeling performance. We conduct experiments across several representative systems, and the results validate that our method achieves superior modeling accuracy and enhanced robustness compared to the state of the art baseline approaches.

Primary Area: learning on time series and dynamical systems

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Submission Number: 103