PACE: A Physics-Aware Mesh Coarsening Framework based on Error Equidistribution

Accurate mesh-based simulation relies on sufficient mesh resolution. However, increasing the global mesh resolution directly raises computational cost, making the balance between physical fidelity and efficiency a fundamental bottleneck in numerical simulation. While careful artificial mesh layout or adaptive mesh coarsening can mitigate this burden by eliminating redundant degrees of freedom, existing strategies often rely on costly iterative optimization. We introduce PACE, a physics-aware mesh coarsening framework based on error equidistribution. PACE designs a graph neural network for efficient edge-collapse selection that couples a coarse physical field with mesh geometric features to predict an edge-wise coarsening score map. PACE then realizes the predicted score map through topology-constrained parallel edge collapse to produce the final coarse mesh. Without assuming a uniquely defined target coarse mesh, PACE formulates error equidistribution as a self-supervised objective for learning how limited mesh resolution should be allocated according to local physical importance. We evaluate on multiple cases covering steady and transient regimes, and observe consistent gains in accuracy and efficiency compared to traditional mesh coarsening baselines.