Some Physics-Informed Machine Learning Tests

Equation solving with DeepXDE

• Effective one-body equations (Google Colab) -- An orbital mechanics integrator. Includes transfer learning solutions to increase integration time, hard boundary constraints through output transformations, and solutions with parametrized initial conditions as inputs.

• DGP Gravity (Google colab) -- Testing a solver for waves in DGP modified gravity.

• Inverse diffusion (Google colab) -- Testing a solver for the inverse diffusion problem (an ill-posed system of equations, so difficult to solve with traditional methods). Includes a basic grid search over some network hyperameters.

Modulus Tests

Files in this repository mostly contain scratch work for PDE solving using NVIDIA's Modulus. These include some assessments of how relevant physics-informed nets might be for studying cosmological systems, including self-gravitating matter and modifications to general relativity.