A neural network compresses high-dimensional PDE coordinates into a low-dimensional latent space, where a PDE-constrained Gaussian process achieves accurate solutions and uncertainty estimates on test problems up to 50 dimensions.
Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics
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PDE-DKL: PDE-constrained deep kernel learning in high dimensionality
A neural network compresses high-dimensional PDE coordinates into a low-dimensional latent space, where a PDE-constrained Gaussian process achieves accurate solutions and uncertainty estimates on test problems up to 50 dimensions.