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Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks
Adrian Celaya, Yimo Wang, David Fuentes +1
In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equati…
Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method
Adrian Celaya, David Fuentes, Beatrice Riviere
Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancem…
Solutions to Elliptic and Parabolic Problems via Finite Difference Based Unsupervised Small Linear Convolutional Neural Networks
Adrian Celaya, Keegan Kirk, David Fuentes +1
In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equa…