Watch a neural network learn a differential equation.
A Neural ODE replaces a hand-written dy/dx = f(x,y) with a small neural network trained to
be that function. Below, train one two ways: reconstruct a known system's vector field purely from
sampled points, or watch a continuous flow warp two tangled point clouds apart until they're separable —
the classic demo from the original Neural ODE paper. All training happens locally, in your browser.
Training
No eval, ever
Sampled training systems are still typed as expressions and still run through the same whitelisted parser as every other profpi tool — the network itself is just plain arithmetic, never generated code.
Bounded by design
Hidden layer width, epoch count, sample count, and integration steps all have hard caps, and training runs in small chunks per animation frame — nothing you configure can freeze the tab.
Gradient-checked
The hand-written backpropagation — including through the unrolled flow used in "Classify with a flow" — is verified against numerical finite-difference gradients before it ever reaches this page.