Live PDE surrogates

Each page solves a parametric PDE as you move the controls, through a fast surrogate of the full solver. Press "compare with the full solver" on any page to see the reference solution, both times and the error.

Flow past an object

Steady Navier–Stokes in a channel. Drag the object through the flow and reshape it in the editor; set the viscosity (Reynolds numbers up to 200 based on the object). Above about 50 the real flow would be unsteady: what you see is the steady branch.

Diffusion with a draggable object

Drag an inclusion through a heterogeneous medium and reshape its boundary with control points; the solution and the flux follow. Contrast 0.01 to 100. One model for every shape and position.

Diffusion with a KL-type coefficient

Set the first ten coefficients and the decay exponent s of a 200-term expansion, or draw everything at random; rough and smooth coefficients from one surrogate.

3D diffusion, 64³

A three-dimensional parametric coefficient; scrub through the volume with slice sliders. Tens of milliseconds against about a second for the full solve.

Jakob Zech, Heidelberg, 2026. Surrogate details to appear.