Performs a systematic review of the ML-for-PDE solving literature. Finds that 79% (60/76) of articles compare to weak baselines. Concludes that ML-for-PDE solving research is systemically overoptimistic.
An algorithm for constraining ML-PDE solvers to satisfy conservation laws and other physical invariances, without restricting the network architecture or losing accuracy.
A meta-learning approach for solving PDEs with neural networks. Amortizes the cost across varying boundary conditions, parameters, and geometries.
Improves a standard algorithm for converting the Biot-Savart law from second-order to fourth-order accuracy. Useful for fast, accurate magnetic field computation.
Describes FOCUSADD, a stellarator coil-design code that optimizes finite-build coils via gradient-based methods. Introduced autodiff to the stellarator optimization community.
A stochastic gradient approximation framework that reduces the memory cost of reverse-mode AD by sparsifying the computational graph. Trades exactness for memory savings in ReLU networks.