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Neural PDE Solvers for Irregular Domains
Neural network-based approaches for solving partial differential equations (PDEs) have recently received special attention.
NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs
We consider a mesh-based approach for training a neural network to produce field predictions of solutions to parametric partial differential equations (PDEs).
Differentiable Spline Approximations
Overall, we show that leveraging this redesigned Jacobian in the form of a differentiable "layer" in predictive models leads to improved performance in diverse applications such as image segmentation, 3D point cloud reconstruction, and finite element analysis.
Distributed Multigrid Neural Solvers on Megavoxel Domains
We specifically consider neural solvers for the generalized 3D Poisson equation over megavoxel domains.
Deep Generative Models that Solve PDEs: Distributed Computing for Training Large Data-Free Models
Here we report on a software framework for data parallel distributed deep learning that resolves the twin challenges of training these large SciML models - training in reasonable time as well as distributing the storage requirements.
