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Multi evolutional deep neural networks (Multi-EDNN)
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PRE
AI
DOI：10.1016/j.jcp.2025.113910.png)
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摘要
En 中文
Evolutional deep neural networks (EDNN) solve partial differential equations (PDEs) by marching the network representation of the solution fields, using the governing equations. Use of a single network to solve coupled PDEs on large domains requires a large number of network parameters and incurs a significant computational cost. We introduce coupled EDNN (C-EDNN) to solve systems of PDEs by using independent networks for each state variable, which are only coupled through the governing equations. We also introduce distributed EDNN (D-EDNN) by spatially partitioning the global domain into several elements and assigning individual EDNNs to each element to solve the local evolution of the PDE. The networks then exchange the solution and fluxes at their interfaces and ensure that the PDE dynamics are accurately preserved between neighboring elements. While D-EDNN has similarities with flux-reconstruction methods, technical differences in the function basis, the evaluation of derivatives, and representation of the fluxes require novel methodology and the appropriate choice of correction functions. Together C-EDNN and D-EDNN form the general class of Multi-EDNN methods. We demonstrate these methods with aid of canonical problems including linear advection, the heat equation, and the compressible Navier-Stokes equations in Couette and Taylor-Green flows.
Keyword:
Scientific computing
Partial differential equations
Machine learning
Deep neural networks
