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warpSPHIntegratorsMethods, examples and practical guidance

Differentiable ODE integrators for PyTorch — 142 schemes across 11 families, from explicit RK through coupled fully-implicit collocation to exponential integrators.

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142 schemes, 11 families

Start with decay and a damped oscillator, then compare accuracy, stability and measured work. Friendly method names appear alongside their exact enum values and coefficient references.

Solving stiff problems

Implicit methods solve stage equations. Jacobian-free Newton–Krylov (JFNK) uses Jacobian actions rather than a stored matrix; diagnostics report nonlinear convergence, RHS work and Krylov iterations.

Gradients and custom systems

Begin with a tensor ODE or use the state protocol for coupled fields and stage-dependent quantities. Each family documents its gradient, operator and history assumptions, with runnable examples.