Demos & Tutorials¶
End-to-end examples that show Tesseracts in action — from optimization workflows to data assimilation.
Tip
For more community-contributed examples, check out the Tesseract Showcase on the forum.
Data assimilation demo¶
A complete 4D-Variational data assimilation scheme for a chaotic dynamical system, built with differentiable Tesseracts.
Full walkthrough of a 4D-Var scheme using a differentiable Lorenz-96 Tesseract — from building the Tesseract to running the optimization loop.
Detailed implementation of the JAX-based Lorenz-96 solver Tesseract used in the 4D-Var demo.
Use the same Lorenz-96 Tesseract as the forward model inside a NumPyro probabilistic workflow — recover the posterior over an unknown forcing parameter with gradient-based MCMC.
Simulation & design optimization demos¶
End-to-end differentiable optimization through physics simulators, composing Tesseracts with JAX or PyTorch code via Tesseract-JAX and Tesseract-Torch.
Optimize the initial velocity field of a 2D Navier-Stokes simulation so its vorticity evolves into a target image — gradient-based optimization through a JAX-CFD Tesseract.
Compose a geometry Tesseract (PyVista, finite-difference gradients) with a FEM Tesseract (jax-fem) to optimize structural bar configurations for minimum compliance.
Couple two independently built thermal and structural Tesseracts with two-way thermoelastic feedback, and differentiate through the resulting equilibrium to solve an inverse-design problem — with constant-memory gradients via implicit differentiation.
Solve two inverse heat-transfer problems by differentiating a Fortran solver end-to-end: Enzyme generates exact derivatives at the LLVM IR level, and jax.value_and_grad drives the optimization through Tesseract-JAX.
Train a native PyTorch neural viscosity closure end-to-end through a containerized Burgers’ equation solver Tesseract used as a differentiable layer. Gradients flow from the loss through the solver’s VJP, over HTTP, into the network using Tesseract-Torch.
Optimization tutorials¶
These tutorials walk through complete optimization workflows using Tesseracts with different autodiff frameworks:
End-to-end function minimization using JAX autodiff with Tesseract-JAX.
End-to-end function minimization using PyTorch autodiff.
Gaussian radial basis function fitting with JAX automatic differentiation.