Neural Harmonic Measure Operator
NHMO learns a geometry-dependent boundary kernel so new boundary values can be solved without retraining.
The paper casts the harmonic measure as the reusable object for Dirichlet Laplace problems on variable-shape domains. It trains a transformer-based kernel from Walk-on-Spheres exit samples, then extends the method to Poisson problems with an auxiliary correction network. At inference, boundary values and source terms are integrated against the fitted components to produce PDE solutions. The authors report gains over four baselines on the MCB-B 3D variable-shape Poisson benchmark, and competitive results on a controlled 2D testbed. ArXiv · AI/CL/LG's note
The paper casts the harmonic measure as the reusable object for Dirichlet Laplace problems on variable-shape domains. It trains a transformer-based kernel from Walk-on-Spheres exit samples, then extends the method to Poisson problems with an auxiliary correction network. At inference, boundary values and source terms are integrated against the fitted components to produce PDE solutions. The authors report gains over four baselines on the MCB-B 3D variable-shape Poisson benchmark, and competitive results on a controlled 2D testbed. ArXiv · AI/CL/LG's note
score 4