PINNs & Deep Fourier Residal Benchmark (Keras Core) - JAX & TensorFlow.

PINNs & Deep Fourier Residual Benchmark (Keras Core) - JAX & TensorFlow. Benchmarking for efficient PDE solving with NN.

Welcome to the "PINNs and Deep Fourier Residual Method Benchmark" repository, a collaborative effort by the MATHMODE group (https://www.mathmode.science/). Our goal is to provide a comprehensive benchmarking platform for different basic implementations of Physics-Informed Neural Networks (PINNs) and the Deep Fourier Residual Method (DFR), all based on the versatile Keras Core framework.

https://www.sciencedirect.com/science/article/abs/pii/S0045782522008064

The repository includes:

1. PINNs_TF: PINNs basic code using TensorFlow backend. The implementation solves the Poisson problem using a NN architecture with a collocation method for the loss function.

2. PINNs_jax: PINNs basic code using the JAX backend.

3. PINNs_pytorch: PINNs basic code using the TORCH backend.

   • TODO: The results of this code are not as good as expected and different from the other implementations.

4. DFR method in 1D using TensorFlow backend. The implementation solves the Poisson problem using a NN architecture with a loss function based on the dual norm ($H^{-1}$) of the weak residual.

5. DFR method in 1D using Jax backend.

6. DFR Method with hybrid optimizer based on Least-squares solver.

   • TODO: The vectorial derivatives need to be improved here and we are still missing the Jax version of it.