arXiv:2605.22222v1 Announce Type: new Abstract: Partial differential equation (PDE) foundation models are pretrained networks that forecast how physical fields like velocity and pressure evolve from a single reusable solver. On unfamiliar flows their predictions drift step by step, errors concentrate in a few regions, yet retraining destabilizes the network and uniform post-hoc correction overlooks this spatial concentration. To address this, we propose a frozen-solver post-hoc correction framework, Adaptive Risk-Calibrated Spatial Triage for Auditable Refinement (ARC-STAR). ARC-STAR organizes
The increasing reliance on PDE Foundation Models in scientific computing necessitates robust error correction mechanisms as these models are deployed in diverse and unfamiliar scenarios.
Improving the accuracy and reliability of PDE Foundation Models broadens their applicability across various scientific and engineering disciplines currently constrained by predictive drift.
PDE Foundation Models can now be more effectively corrected post-hoc without destabilizing the network, making them more adaptable and trustworthy for critical applications.
- · Scientific computing teams
- · Engineering research institutions
- · AI model developers
- · Industries relying on physical simulations
- · Traditional, computationally intensive PDE solvers for specific tasks
- · Models prone to significant predictive drift without robust correction
PDE Foundation Models gain increased utility and adoption across new domains due to enhanced reliability.
Accelerated research and development cycles in fields like materials science, climate modeling, and aerospace design become possible.
The development of highly specialized, domain-specific PDE models may slow as generalist foundation models become more reliable and adaptable with correction frameworks.
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