DOLFINx-ADJOINT

Automatic differentiation for DOLFINx using the adjoint method. Efficient sensitivity analysis and gradient-based optimization for finite element simulations.

Documentation

Full documentation is available at unistuttgart-cmcs.github.io/dolfinx-adjoint.

Installation

git clone https://github.com/unistuttgart-cmcs/dolfinx-adjoint.git
cd dolfinx-adjoint
pip install -e .

Requires Python >= 3.12 and DOLFINx >= 0.10.0. For demos and tests, use pip install -e ".[all]".

Quick Example

Compute dJ/df for a Poisson problem:

from dolfinx_adjoint import Graph, fem

graph_ = Graph()

# Set up your DOLFINx problem, passing graph= to track operations
f  = fem.Function(W, name="f", graph=graph_)
uh = fem.Function(V, name="u", graph=graph_)

problem = fem.petsc.LinearProblem(a, L, u=uh, bcs=bcs, graph=graph_)
problem.solve(graph=graph_)

J = fem.assemble_scalar(fem.form(J_form, graph=graph_), graph=graph_)

# Compute the gradient
dJdf = graph_.backprop(id(J), id(f))

Demos

The demos/ directory contains comprehensive Jupyter notebook examples demonstrating various PDE problems:

• poisson.ipynb - Poisson equation with gradient computation w.r.t. source term, diffusion coefficient, and boundary conditions
• heat_equation.ipynb - Time-dependent heat equation with sensitivity analysis
• linear_elasticity.ipynb - Linear elasticity problem with parameter sensitivities
• stokes.ipynb - Stokes flow with obstacle, computing gradients w.r.t. viscosity and boundary conditions

Acknowledgments

This library builds upon the excellent work of the FEniCS Project and uses DOLFINx as its foundation.