jax

You can compute gradients and higher-order derivatives of Python and NumPy programs using composable function transformations like `jax.grad` for automatic differentiation. This enables differentiable programming for complex scientific simulations and machine learning research.

The best way to accelerate scientific computing simulations on GPUs and TPUs is by applying Just-In-Time (JIT) compilation and parallelization to Python and NumPy code. This compiles functions to optimized machine code and distributes computations across multiple devices for significant speedups.

You can automatically batch and vectorize data processing without manual reshaping by applying function vectorization using `jax.vmap`. This composable transformation maps functions across batches of data natively within Python and NumPy programs.

Yes, JIT compilation works seamlessly with automatic differentiation for machine learning research. You can compose `jax.jit` and `jax.grad` together to compile differentiated Python functions to optimized machine code, accelerating complex simulations and model training.

Yes, you can distribute computations across multiple GPUs or TPUs using `jax.pmap` for parallelization. This function transformation enables parallel execution of Python and NumPy programs across multiple devices, satisfying high-performance computing requirements.

You define a function using `jax.numpy`, then compute its gradient using `jax.grad` for automatic differentiation. This allows you to optimize parameters in physics simulations or machine learning models by evaluating derivatives efficiently.