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- Title
Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems.
- Authors
Kontolati, Katiana; Goswami, Somdatta; Em Karniadakis, George; Shields, Michael D.
- Abstract
Predicting complex dynamics in physical applications governed by partial differential equations in real-time is nearly impossible with traditional numerical simulations due to high computational cost. Neural operators offer a solution by approximating mappings between infinite-dimensional Banach spaces, yet their performance degrades with system size and complexity. We propose an approach for learning neural operators in latent spaces, facilitating real-time predictions for highly nonlinear and multiscale systems on high-dimensional domains. Our method utilizes the deep operator network architecture on a low-dimensional latent space to efficiently approximate underlying operators. Demonstrations on material fracture, fluid flow prediction, and climate modeling highlight superior prediction accuracy and computational efficiency compared to existing methods. Notably, our approach enables approximating large-scale atmospheric flows with millions of degrees, enhancing weather and climate forecasts. Here we show that the proposed approach enables real-time predictions that can facilitate decision-making for a wide range of applications in science and engineering. Real-time prediction of dynamics for complex physical systems governed by partial differential equations is challenging and computationally expensive. The authors propose a framework for learning neural operators in latent spaces that allows real-time predictions of high-dimensional nonlinear systems.
- Subjects
LATENT variables; NONLINEAR operators; PARTIAL differential equations; SYSTEM dynamics; FRACTURE mechanics; BANACH spaces; FLUID flow
- Publication
Nature Communications, 2024, Vol 15, Issue 1, p1
- ISSN
2041-1723
- Publication type
Article
- DOI
10.1038/s41467-024-49411-w