Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training
This addresses the problem of computational efficiency and stability in physics-informed generative models for PDE solving, representing an incremental improvement over existing consistency modeling approaches.
The paper tackles the stability challenge in physics-informed consistency models for solving PDEs, where PDE residuals can degrade the learned distribution, by introducing a structure-preserving two-stage training strategy that decouples distribution learning from physics enforcement. The result is a framework that achieves accuracy comparable to diffusion baselines with orders of magnitude reduction in computational cost.
We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference. We identify a key stability challenge in physics-constrained consistency training, where PDE residuals can drive the model toward trivial or degenerate solutions, degrading the learned data distribution. To address this, we introduce a structure-preserving two-stage training strategy that decouples distribution learning from physics enforcement by freezing the coefficient decoder during physics-informed fine-tuning. We further propose a two-step residual objective that enforces physical consistency on refined, structurally valid generative trajectories rather than noisy single-step predictions. The resulting framework enables stable, high-fidelity inference for both unconditional generation and forward problems. We demonstrate that forward solutions can be obtained via a projection-based zero-shot inpainting procedure, achieving consistent accuracy of diffusion baselines with orders of magnitude reduction in computational cost.