ISLA: A Coordinate-Free, Measure-Weighted Transformer for Boundary-Driven PDEs
ISLA reports velocity and pressure errors at least 3.1 and 3.3 times lower than any baseline on AeroZoo.
The benchmark covers 2,816 flows varying in shape, size, speed and boundary conditions. ISLA uses distances and relative angles instead of feeding coordinates into learned operations, and weights boundary sums by the measure of each cell. With every boundary cell included and an exact boundary read, the model preserves its behavior under rotations, reflections and changes of units, while remaining consistent as the mesh is refined. On AirfRANS, its errors rank behind GLOBE’s but are at least 1.6 times lower than those of Transolver and GeoTransolver.
ArXiv · AI/CL/LG's note
The benchmark covers 2,816 flows varying in shape, size, speed and boundary conditions. ISLA uses distances and relative angles instead of feeding coordinates into learned operations, and weights boundary sums by the measure of each cell. With every boundary cell included and an exact boundary read, the model preserves its behavior under rotations, reflections and changes of units, while remaining consistent as the mesh is refined. On AirfRANS, its errors rank behind GLOBE’s but are at least 1.6 times lower than those of Transolver and GeoTransolver.
ArXiv · AI/CL/LG's note
score 5