PDE

TL;DR for operators For generated engineering code, successful execution should be treated as a feasibility check, not a correctness certificate. In the paper’s 7B ablation, reinforcement learning based only on program validity reaches pass@1 of 0.58 and pass@8 of 0.76. Adding continuous trajectory accuracy raises those figures to 0.71 and 0.84. The mechanism is straightforward. Generated solver code must first run, return the required output shape, and avoid non-finite values. Programs that clear those checks are then graded by how closely their numerical trajectories match hidden references and, where available, how consistent their outputs are with the governing PDE. ...