GRADSOLVE: fast exact gradients for ODE ensembles on GPUs

What the math gives to ML

The paper's transferable asset is a practical separation between adaptive mesh selection and differentiable execution: record accepted step sizes once, then replay a fixed chain of one-step maps for subsequent reverse-mode gradients. This removes adaptive branching and variable-length control flow from GPU autodiff while preserving the exact discrete derivative of the recorded numerical computation. The strongest neural-network target is a neural ODE or probability-flow diffusion model whose vector field and parameters are reused across many optimization steps, trajectories, or noise-condition ensembles. A padded fixed-mesh replay kernel can provide predictable GPU execution and cheaper gradients than checkpointed adaptive differentiation, provided the mesh is refreshed when parameter drift makes the replay inaccurate.