Title: Robust Latent Neural Operators through Augmented Sparse Observation Encoding
Primary area: learning on time series and dynamical systems
Keywords: neural operator, complex system, variational inference

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 multiple sparse observations in new domains. Therefore, we propose a robust latent neural operator based on the variational autoencoder framework. In this method, an encoder utilizing recurrent neural networks effectively captures sequential patterns and dynamical features from domain-specific sparse observations. Subsequently, a neural operator in latent space, followed by a decoder, enables the effective modeling of the original system. Additionally, for certain higher-dimensional complex systems, opting for a lower-dimensional latent space can reduce task complexity while still maintaining satisfactory modeling performance. We evaluate our approach on multiple representative systems, and experimental results demonstrate that it achieves superior modeling accuracy and enhanced robustness compared to state-of-the-art baseline methods.

TL;DR: We propose a robust latent neural operator based on a VAE framework with an RNN encoder, enhancing modeling accuracy and noise resilience in operator learning.