Demos & tutorials

End-to-end demos, case studies with real engineering tools, and smaller tutorials that teach the mechanics.

Realistic use cases

Differentiable Fortran (Enzyme)

Solve inverse heat-transfer problems through a Fortran solver differentiated by Enzyme.

Inverse heat transfer with automatic differentiation
Multi-physics optimization

Differentiate through the equilibrium of coupled thermal and structural Tesseracts.

Multi-physics pipeline with end-to-end gradient optimization
Learned closure (PyTorch)

Train a PyTorch closure model through a Burgers’ solver running in its own process.

Learned closure: Training a neural viscosity model through a PDE solver (PyTorch)
FEM shape optimization

Combine finite-difference geometry gradients with a jax-fem solver to minimize compliance.

Parametric shape optimization with differentiable FEM simulation

Case studies

Rocket grid fin optimization

Ansys SpaceClaim, a mesher, and PyMAPDL in one gradient, with three differentiation strategies.

Optimizing rocket fins across CAD, mesher, and FEA with end-to-end gradients
Tesseract Hackathon 2026

Winning entries, from NOAA’s Fortran hydrology models to Sentaurus TCAD.

Tesseract Hackathon winners push the boundaries of differentiable scientific pipelines
Ansys integration gallery

SpaceClaim served without a container, and MAPDL with an analytic adjoint.

Example gallery: Integrating with Ansys products

Learn the mechanics

These components are small enough to rewrite in JAX or PyTorch, so read them as walkthroughs of the mechanics, not as examples of when to use Tesseract (see When to use Tesseract).

4D-Var data assimilation

Build a differentiable Lorenz-96 Tesseract and run 4D-Var through it.

4D-variational data assimilation for a chaotic dynamical system
Bayesian Inference

Recover a posterior with gradient-based MCMC in NumPyro, using the same Lorenz-96 Tesseract.

Simulator-in-the-loop Bayesian inference with Tesseract
CFD flow optimization

Optimize a 2D Navier-Stokes initial condition through JAX-CFD, which is no longer maintained upstream.

Gradient-based optimization of fluid flows

More walkthroughs: