Recently, members of the TAMU Scientific Machine Learning community have been collaborating on a software package named TensorDiffEq, designed to implement collocation-based neuralPDE solvers, data assimilation solvers, as well as parameter inference and PDE discovery.
Additionally, TensorDiffEq implements Self-Adaptive Solvers, which have experimentally demonstrated the ability to solve semi-stiff PDEs such as the Allen-Cahn equation using collocation-based solvers far more effectively than the baseline NeuralPDE solvers. This self-adaptive framework opens the possibility to solving more problems using the NeuralPDE methodology.
Advantages to the NeuralPDE framework are that it is embarrassingly parallelizable, which TensorDiffEq takes advantage of in its Multi-GPU solving capabilities. This could allow for faster solutions in large or complex domains in which traditional iterative solvers are slow or demonstrate convergence issues.