◆ frontier32 mindraft

Gradients through physics

Make the solver itself differentiable and simulation becomes something you can optimise through - inverse problems, control, and learned dynamics all follow.

assumes you already have

Buying an order for free RK4, and where the magic numbers come from Why a worse method gives a better orbit

Planned outline

Forward versus reverse mode AD, and why reverse mode gives an n-dimensional gradient for the price of one evaluation.
Differentiating through an ODE solver: unrolling versus the adjoint method.
Neural ODEs and the memory argument for adjoints.
Physics-informed neural networks: making the PDE residual the loss.
Where PINNs genuinely win, and where a classical solver still beats them badly.
Learned solvers and structure-preserving networks - closing the loop with chapter 4.

Interactives planned

Each numbered point above gets at least one thing you can manipulate, not a figure. See AGENTS.md for the widget vocabulary and the rule that every lesson ships at least one graded interaction and one recall card.