jax-pde
Advanced sub-skill for JAX focused on solving Partial Differential Equations (PDEs) and Differentiable Physics. Covers Finite Difference Methods (FDM), Neural Operators, and Physics-Informed Neural Networks (PINNs).
Best use case
jax-pde is best used when you need a repeatable AI agent workflow instead of a one-off prompt.
Advanced sub-skill for JAX focused on solving Partial Differential Equations (PDEs) and Differentiable Physics. Covers Finite Difference Methods (FDM), Neural Operators, and Physics-Informed Neural Networks (PINNs).
Teams using jax-pde should expect a more consistent output, faster repeated execution, less prompt rewriting.
When to use this skill
- You want a reusable workflow that can be run more than once with consistent structure.
When not to use this skill
- You only need a quick one-off answer and do not need a reusable workflow.
- You cannot install or maintain the underlying files, dependencies, or repository context.
Installation
Claude Code / Cursor / Codex
Manual Installation
- Download SKILL.md from GitHub
- Place it in
.claude/skills/jax-pde/SKILL.mdinside your project - Restart your AI agent — it will auto-discover the skill
How jax-pde Compares
| Feature / Agent | jax-pde | Standard Approach |
|---|---|---|
| Platform Support | Not specified | Limited / Varies |
| Context Awareness | High | Baseline |
| Installation Complexity | Unknown | N/A |
Frequently Asked Questions
What does this skill do?
Advanced sub-skill for JAX focused on solving Partial Differential Equations (PDEs) and Differentiable Physics. Covers Finite Difference Methods (FDM), Neural Operators, and Physics-Informed Neural Networks (PINNs).
Where can I find the source code?
You can find the source code on GitHub using the link provided at the top of the page.
SKILL.md Source
# JAX - Differentiable Physics & PDEs
JAX is uniquely suited for physics because it can differentiate through numerical solvers. This guide covers how to implement traditional PDE solvers that are "optimization-friendly" and how to build neural-hybrid physical models.
## When to Use
- Solving Navier-Stokes, Wave, or Heat equations on GPU.
- Implementing Physics-Informed Neural Networks (PINNs).
- Performing Inverse Design (finding material properties from observations).
- Creating differentiable simulations for robotics or climate modeling.
- Sensitivity analysis of physical systems.
## Core Principles
### 1. Differentiation through the Solver
In JAX, if you write an Euler or Runge-Kutta integrator using `jax.numpy`, you can automatically calculate ∂Result/∂InitialCondition or ∂Result/∂Viscosity.
### 2. Staggered Grids & Vmap
Physical fields (velocity, pressure) are often stored on grids. JAX's `vmap` allows you to parallelize solvers across different boundary conditions or parameter sets instantly.
### 3. The Adjoint Method
For very large systems, JAX's reverse-mode autodiff effectively implements the "Adjoint State Method" used in traditional CFD/Geophysics for gradient calculation.
## Implementation Patterns
### 1. PINNs (Physics-Informed Neural Networks)
```python
import jax.numpy as jnp
from jax import grad, vmap
# A simple MLP representing the solution u(x, t)
def model(params, x, t):
# standard neural net logic...
return result
# Residual of the PDE: u_t + u*u_x - nu*u_xx = 0 (Burgers Equation)
def pde_loss(params, x, t, nu):
u = lambda x, t: model(params, x, t)
# Automatic derivatives of the MODEL
u_t = grad(u, argnums=1)(x, t)
u_x = grad(u, argnums=0)(x, t)
u_xx = grad(grad(u, argnums=0), argnums=0)(x, t)
return jnp.mean((u_t + u * u_x - nu * u_xx)**2)
```
### 2. Differentiable Finite Difference Solver
```python
@jit
def update_step(u, dt, dx, nu):
"""One step of a diffusion solver."""
# Vectorized Laplacian using shifts (Zero-copy views)
u_left = jnp.roll(u, -1)
u_right = jnp.roll(u, 1)
laplacian = (u_left + u_right - 2*u) / (dx**2)
return u + dt * nu * laplacian
# We can now differentiate this solver!
def loss(initial_u, target_u):
final_u = integrate_pde(initial_u) # Loop of update_step
return jnp.sum((final_u - target_u)**2)
grad_initial_condition = grad(loss)(initial_u, target_u)
```
## Critical Rules
### ✅ DO
- **Use jax.lax.scan for time loops** - Standard Python for loops create massive XLA graphs. `scan` compiles the loop into a single efficient kernel.
- **Normalize your Grids** - Like ML, PINNs converge faster if x, t are scaled to [0,1] or [-1,1].
- **Combine Data and Physics** - Use PINNs where you have some sensor data + the physical law to "fill the gaps".
- **Use Double Precision for Physics** - Use `jax.config.update("jax_enable_x64", True)` for sensitive numerical solvers.
### ❌ DON'T
- **Don't use PINNs for everything** - Traditional solvers (FDM/FEM) are much faster for "forward" problems. PINNs excel at "inverse" problems.
- **Don't ignore Boundary Conditions (BCs)** - In PINNs, BCs must be added to the loss function: Loss = PDE_loss + BC_loss.
- **Don't forget the 'Ghost Cells'** - When implementing FDM, handle boundaries carefully to avoid artifacts.
## Practical Workflows: Inverse Problem
### Finding Viscosity from a Video of Fluid
```python
def objective(nu_guess):
# 1. Run simulation with nu_guess
final_state = run_simulation(initial_state, nu_guess)
# 2. Compare with experimental data
return jnp.mean((final_state - experimental_frame)**2)
# Gradient descent to find the real physical property
optimal_nu = optimize(grad(objective))
```
JAX PDE transforms physics from a static simulation into a dynamic, optimizable landscape. It allows researchers to ask "What physical parameters produced this result?" and find the answer through the power of gradients.Related Skills
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