RECAST: A Machine-Learning Framework for Correction and Super-Resolution of Coarse-Grid PDE Solvers

arXiv cs.LG Papers
machine-learning pde-solvers super-resolution error-correction coarse-grid scientific-computing

Summary

RECAST is a machine-learning framework that combines learned correction and super-resolution to restore accuracy in coarse-grid PDE solvers, reducing error by 50-92% across six 1D PDE systems and enabling coarser simulations without losing fidelity.

arXiv:2608.11572v1 Announce Type: new Abstract: Coarse-grid numerical solvers can substantially reduce the computational cost of time-dependent PDE simulation, but under-resolution often degrades both the trajectory and the spatial fidelity of the solution. We introduce RECAST (Recurrent Error Correction And Super-resolution of coarse-grid Trajectories), a machine-learning framework designed to restore this lost accuracy while retaining coarse-grid evolution. RECAST combines learned correction within the numerical time-stepping loop with reconstruction of the corresponding fine-grid state from the corrected coarse history. We evaluate the framework on six one-dimensional PDE systems spanning transport, diffusion, dispersion, reaction, and wave dynamics, using spatial grids coarsened by factors of 8-16 and 1000-step closed-loop rollouts from unseen initial conditions. Across the test cases, RECAST remains closely aligned with the fine-grid reference solutions and reduces time-averaged relative error by approximately 50-92% compared with the corresponding uncorrected coarse-grid solvers. Additional tests show generalization to unseen PDE parameter values, while comparison with a contemporary coarse-correction architecture shows that RECAST achieves lower error and better long-horizon agreement with the fine-grid reference over 5000-step rollouts. These results demonstrate that the learned correction and reconstruction capabilities of RECAST can enable substantially coarser PDE evolution without the corresponding loss of solution fidelity, providing a proof-of-concept route toward machine-learning acceleration of higher-dimensional numerical simulations across science and engineering.
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# RECAST: A Machine-Learning Framework for Correction and Super-Resolution of Coarse-Grid PDE Solvers
Source: [https://arxiv.org/abs/2608.11572](https://arxiv.org/abs/2608.11572)
[View PDF](https://arxiv.org/pdf/2608.11572)

> Abstract:Coarse\-grid numerical solvers can substantially reduce the computational cost of time\-dependent PDE simulation, but under\-resolution often degrades both the trajectory and the spatial fidelity of the solution\. We introduce RECAST \(Recurrent Error Correction And Super\-resolution of coarse\-grid Trajectories\), a machine\-learning framework designed to restore this lost accuracy while retaining coarse\-grid evolution\. RECAST combines learned correction within the numerical time\-stepping loop with reconstruction of the corresponding fine\-grid state from the corrected coarse history\. We evaluate the framework on six one\-dimensional PDE systems spanning transport, diffusion, dispersion, reaction, and wave dynamics, using spatial grids coarsened by factors of 8\-16 and 1000\-step closed\-loop rollouts from unseen initial conditions\. Across the test cases, RECAST remains closely aligned with the fine\-grid reference solutions and reduces time\-averaged relative error by approximately 50\-92% compared with the corresponding uncorrected coarse\-grid solvers\. Additional tests show generalization to unseen PDE parameter values, while comparison with a contemporary coarse\-correction architecture shows that RECAST achieves lower error and better long\-horizon agreement with the fine\-grid reference over 5000\-step rollouts\. These results demonstrate that the learned correction and reconstruction capabilities of RECAST can enable substantially coarser PDE evolution without the corresponding loss of solution fidelity, providing a proof\-of\-concept route toward machine\-learning acceleration of higher\-dimensional numerical simulations across science and engineering\.

## Submission history

From: Maryam Reza \[[view email](https://arxiv.org/show-email/9a68f109/2608.11572)\] **\[v1\]**Wed, 12 Aug 2026 02:30:49 UTC \(5,194 KB\)

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