Learning in latent spaces improves the predictive accuracy of deep neural operators

• URL: http://arxiv.org/abs/2304.07599v1
• Date: Sat, 15 Apr 2023 17:13:09 GMT
• Title: Learning in latent spaces improves the predictive accuracy of deep neural operators
• Authors: Katiana Kontolati, Somdatta Goswami, George Em Karniadakis, Michael D. Shields
• Abstract summary: L-DeepONet is an extension of standard DeepONet, which leverages latent representations of high-dimensional PDE input and output functions identified with suitable autoencoders. We show that L-DeepONet outperforms the standard approach in terms of both accuracy and computational efficiency across diverse time-dependent PDEs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate mappings between infinite-dimensional Banach spaces. As data-driven models, neural operators require the generation of labeled observations, which in cases of complex high-fidelity models result in high-dimensional datasets containing redundant and noisy features, which can hinder gradient-based optimization. Mapping these high-dimensional datasets to a low-dimensional latent space of salient features can make it easier to work with the data and also enhance learning. In this work, we investigate the latent deep operator network (L-DeepONet), an extension of standard DeepONet, which leverages latent representations of high-dimensional PDE input and output functions identified with suitable autoencoders. We illustrate that L-DeepONet outperforms the standard approach in terms of both accuracy and computational efficiency across diverse time-dependent PDEs, e.g., modeling the growth of fracture in brittle materials, convective fluid flows, and large-scale atmospheric flows exhibiting multiscale dynamical features.

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