Physics-Informed Deep Neural Operator Networks

Goswami, Somdatta; Bora, Aniruddha; Yu, Yue; Karniadakis, George Em

doi:10.1007/978-3-031-36644-4_6

Cited by 23 publications

(3 citation statements)

References 43 publications

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“…One unique feature, as a result of learning in Fourier space, is that FNO is not restricted to a particular discretization and is considered as a type of neural operator that learns mappings between function spaces (Goswami et al., 2022). Equation shows that FNO is resolution‐independent because it mainly learns the interactions at the truncated Fourier space through learnable parameters R ϕ , and therefore, FNO can be evaluated in a space that is discretized in an arbitrary way.…”

Section: Methodsmentioning

confidence: 99%

Efficient Super‐Resolution of Near‐Surface Climate Modeling Using the Fourier Neural Operator

Jiang

Yang

Wang

et al. 2023

J Adv Model Earth Syst

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Section: Methodsmentioning

confidence: 99%

Efficient Super‐Resolution of Near‐Surface Climate Modeling Using the Fourier Neural Operator

Jiang

Yang

Wang

et al. 2023

J Adv Model Earth Syst

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“…Recently, physics‐informed NOs, for example, both the physics‐informed Deep Operator Network proposed by Goswami et al. (2022) and physics‐informed Fourier NO proposed by Li et al. (2021) employ both data and physics losses on operator learning to overcome the shortcomings of purely PINN or data‐driven learning.…”

Section: Introductionmentioning

confidence: 99%

Accelerating Atmospheric Gravity Wave Simulations Using Machine Learning: Kelvin‐Helmholtz Instability and Mountain Wave Sources Driving Gravity Wave Breaking and Secondary Gravity Wave Generation

Dong

Fritts

Liu

et al. 2023

Geophysical Research Letters

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Gravity waves (GWs) and their associated multi‐scale dynamics are known to play fundamental roles in energy and momentum transport and deposition processes throughout the atmosphere. We describe an initial machine learning model—the Compressible Atmosphere Model Network (CAM‐Net). CAM‐Net is trained on high‐resolution simulations by the state‐of‐the‐art model Complex Geometry Compressible Atmosphere Model (CGCAM). Two initial applications to a Kelvin‐Helmholtz instability source and mountain wave generation, propagation, breaking, and Secondary GW (SGW) generation in two wind environments are described here. Results show that CAM‐Net can capture the key 2‐D dynamics modeled by CGCAM with high precision. Spectral characteristics of primary and SGWs estimated by CAM‐Net agree well with those from CGCAM. Our results show that CAM‐Net can achieve a several order‐of‐magnitude acceleration relative to CGCAM without sacrificing accuracy and suggests a potential for machine learning to enable efficient and accurate descriptions of primary and secondary GWs in global atmospheric models.

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“…Since its first appearance, standard DeepONet has been employed to tackle challenging problems involving complex high-dimensional dynamical systems [13][14][15][16][17] . In addition, extensions of DeepONet have been recently proposed in the context of multi-fidelity learning [18][19][20] , integration of multiple-input continuous operators 21,22 , hybrid transferable numerical solvers 23 , transfer learning 24 , and physics-informed learning to satisfy the underlying PDE 25,26 .…”

mentioning

confidence: 99%

Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems

Kontolati,

Goswami,

Em Karniadakis

et al. 2024

Nat Commun

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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.

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Physics-Informed Deep Neural Operator Networks

Cited by 23 publications

References 43 publications

Efficient Super‐Resolution of Near‐Surface Climate Modeling Using the Fourier Neural Operator

Efficient Super‐Resolution of Near‐Surface Climate Modeling Using the Fourier Neural Operator

Accelerating Atmospheric Gravity Wave Simulations Using Machine Learning: Kelvin‐Helmholtz Instability and Mountain Wave Sources Driving Gravity Wave Breaking and Secondary Gravity Wave Generation

Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems

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