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.
We investigate whether a pretrained generative image-editing model can provide a common interface for numerical simulation. Physical inputs and solutions are rendered as images, while scalar quantities such as material properties, diffusivity, and loading parameters enter through lightweight adapters. Using established numerical and analytic solvers for supervision, we apply the same architecture and training protocol to heterogeneous elliptic equations, forced heat and Burgers evolution, complex Ginzburg-Landau dynamics, two-dimensional Navier-Stokes prediction, potential flow, elasticity, eikonal travel time, phase-field fracture, and entropic optimal transport. The results show that a pretrained image model can represent diverse static and time-dependent physical mappings, including unstable and shock-like behavior, when each task is expressed through a suitable visual encoding. This work is a capability study rather than an attempt to surpass specialized solvers. It also identifies fundamental constraints: image and latent representations complicate numerical range selection and direct enforcement of governing equations or invariants, while a failed Kuramoto-Sivashinsky experiment indicates that representation errors prevent meaningful long-horizon simulation of chaotic systems.