76 citations · 164 across the 14 of their papers we have counts for
4 papers · 1 filter
Learning, Solving and Optimizing PDEs with TensorGalerkin: an efficient high-performance Galerkin assembly algorithm
Shizheng Wen, Mingyuan Chi, Tianwei Yu +5
We present a unified algorithmic framework for the numerical solution, constrained optimization, and physics-informed learning of PDEs with a variational structure. Our framework i…
Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domains
Levi Lingsch, Mike Y. Michelis, Emmanuel de Bezenac +3
The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations.…
Physics-constrained Unsupervised Learning of Partial Differential Equations using Meshes
Mike Y. Michelis, Robert K. Katzschmann
Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural ne…
On Linear Interpolation in the Latent Space of Deep Generative Models
Mike Yan Michelis, Quentin Becker
The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilitie…