jax-pde

What problem does it solve?

This Skill enables the solution of complex Partial Differential Equations (PDEs) and the development of differentiable physics models using the JAX library, bridging traditional numerical methods with modern machine learning techniques.

Core Features & Use Cases

• Differentiable Solvers: Leverage JAX's automatic differentiation to compute gradients through PDE solvers, enabling inverse problems and sensitivity analysis.
• Physics-Informed Neural Networks (PINNs): Implement neural networks that incorporate physical laws as constraints for solving PDEs, especially useful for inverse design and data-driven modeling.
• Finite Difference Methods (FDM): Apply and differentiate traditional numerical methods like FDM for solving PDEs on grids.
• Use Case: Optimize material properties (e.g., viscosity) of a fluid by comparing simulation results with experimental data, using JAX to efficiently compute the gradients of the objective function with respect to these properties.

Quick Start

Use the jax-pde skill to implement a PINN for solving the Burgers' equation.