NNPDEs

Numerical analysis of the convergence behavior of adjoint-optimized neural PDEs.

Many engineering and scientific fields have recently become interested in modeling terms in partial differential equations (PDEs) with neural networks. The resulting neural-network-PDE model, being a function of the neural network parameters, can be calibrated to available data by optimizing over the PDE using gradient descent, where the gradient is evaluated in a computationally efficient manner by solving an adjoint PDE. These neural-network PDE models have emerged as an important research area in scientific machine learning.

Version 1.0

Date 16.06.2025

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R e f e r e n c e s

Global Convergence of Adjoint-Optimized Neural PDEs

https://arxiv.org/abs/2103.15130

by

• Konstantin   R i e d l   (University of Oxford, Mathematical Institute),
• Justin Sirignano   S i r i g n a n o   (University of Oxford, Mathematical Institute),
• Konstantinos   S p i l i o p o u l o s   (Boston University, Department of Mathematics & Statistics)