Results
Benchmark results for every domain, with embedded plots, a best-solver ranking per category, and the task setup. Pick a domain below.
These are example results, produced automatically on GitHub Actions runners and refreshed on every release. Accuracy and gradient metrics are hardware-independent and reproducible; wall-clock numbers reflect commodity cloud hardware and are best read as relative scaling between solvers. For numbers that reflect your setup, run the benchmarks yourself on your target hardware.
Domains
Structural mechanics
Place a fixed budget of material in a clamped beam to make it as stiff as possible, differentiating through a finite-element solve. Covers deal.II, FEniCS, Firedrake, JAX-FEM, and TopOpt.jl on 2D cantilever compliance minimization with SIMP penalization.
Heat transfer
Invert for the conductivity field of a slab from its temperature, differentiating through a steady heat-conduction solve. Covers deal.II, FEniCS, Firedrake, JAX-FEM, and torch-fem on 2D steady-state heat conduction.
What each page reports
Every domain page scores its solvers on four axes:
- Forward — is the prediction right? Output vs. a trusted reference (and an analytic solution where one exists).
- Gradient — is the gradient right? AD/adjoint gradient vs. a finite-difference ground truth (magnitude and direction).
- Cost — what does it cost? Forward and VJP wall-clock scaling with problem size.
- Optimization — can you optimize through it? End-to-end convergence using each solver’s own gradients.
See the Overview for the full evaluation protocol.