From 1D Benchmarks to Complex 3D Geometries: Can Agents Reliably Specify Problems for Automated PDE Simulation?

Abstract

Turning an engineering request into a simulation requires consistent geometry, physics, boundary conditions, and numerical settings. Recent agent-assisted systems automate simulation setup, but successful execution alone does not establish whether the specification preserves the intended problem or correctly handles missing information. We study whether agents can reliably construct complete executable JSON specifications for automated geometry creation, meshing, PDE solving, and result export. Our workflow combines model extraction with deterministic scientific and capability checks, explicit clarification, and validated local patches that preserve unrelated accepted fields. We evaluate specification correctness, execution completion, and numerical verification separately. On 120 template-related requests, the full workflow achieves 98.3% correct first-turn specification and decision outcomes, compared with 92.5% for schema-assisted single shot and 82.5% for model-only: gains of 5.8 and 15.8 percentage points, respectively. It makes no false-ready decisions among the 42 requests requiring clarification or rejection. Component ablations identify contributions from scientific checks and conditional repair. Separate downstream studies cover 1D, 2D, and 3D steady and unsteady, linear and nonlinear problems, including flow and elasticity with complex three-dimensional wing geometries. A 30-case gallery demonstrates automated execution from retained JSON specifications, while 9 of 12 selected live user-to-results tests achieve joint specification, execution, export, and numerical-reference success (75.0%). These results support traceable, engineer-reviewed simulation assistance within the tested scope, while fresh-response regressions identify consistency as a priority for further improvement.