Tutorials

In this section, we provide a series of tutorials on the modeling, simulation, and inference capabilities of diff-soup. We demonstrate these features on a unique physical system for each tutorial, to showcase a diverse range of models diff-soup can simulate. For more advanced inference workflows, we also provide the worked examples section providing code demos of the examples in the diff-soup paper.

• Basic PDE example: the Allen-Cahn equation for a moving phase boundary. A model declared with the Recipe API, solved with pdesolve and checked against its exact solution.
• Stiff reaction-diffusion at scale: two reacting chemicals whose spots divide until they fill a square. The solver, the tolerances, the linear backend and the precision of a large stiff solve.
• Phase separation with electrostatics: a charged species phase-separating under the Cahn-Hilliard equation, coupled to the Poisson equation for its potential. A DAE with an algebraic field, consistent initialization, and an event that stops the solve.
• Cooling a bowl of soup: when soup in a ceramic bowl cools to 60 °C. Triangle meshes with two materials and heat leaving through their edges.
• Gradients through a shock: a wave steepening into a shock under the viscous Burgers equation. Forward- and reverse-mode derivatives through the solve, and their cost as the number of inputs grows.
• Fitting a nerve pulse: a pulse on a nerve fibre recorded by four noisy electrodes. FitzHugh-Nagumo parameters fitted to data, their uncertainty and their identifiability.
• Learning a soil's diffusivity with a neural network: water soaking into dry garden soil. A neural network inside the model, trained through the simulation on several experiments.