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This paper introduces RECAST, a machine-learning framework that enhances the accuracy of coarse-grid numerical solvers for time-dependent PDE simulations by integrating learned error correction and fine-grid state reconstruction within the numerical time-stepping loop. The framework was evaluated on six one-dimensional PDE systems, demonstrating a significant reduction in time-averaged relative error by 50-92% compared to uncorrected coarse-grid solvers, while maintaining alignment with fine-grid reference solutions. RECAST also shows robust generalization to unseen parameter values and outperforms existing coarse-correction architectures in long-horizon simulations, highlighting its potential for accelerating complex numerical simulations in various scientific fields.
RECAST achieves up to 92% error reduction in coarse-grid PDE simulations, proving that machine learning can drastically enhance numerical accuracy without increasing computational costs.
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.
