mlsanityData to 14 Oct 2026

INC: An Indirect Neural Corrector for Auto-Regressive Hybrid PDE Solvers

arXiv 2511.12764 ↗First posted 16 Nov 2025cs.LGcited by 3

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Abstract (arXiv)

When simulating partial differential equations, hybrid solvers combine coarse numerical solvers with learned correctors. They promise accelerated simulations while adhering to physical constraints. However, as shown in our theoretical framework, directly applying learned corrections to solver outputs leads to significant autoregressive errors, which originate from amplified perturbations that accumulate during long-term rollouts, especially in chaotic regimes. To overcome this, we propose the Indirect Neural Corrector (INC), which integrates learned corrections into the governing equations rather than applying direct state updates. Our key insight is that INC reduces the error amplification on the order of Delta t-1 + L, where Delta t is the timestep and L the Lipschitz constant. At the same time, our framework poses no architectural requirements and integrates seamlessly with arbitrary neural networks and solvers. We test INC in extensive benchmarks, covering numerous differentiable solvers, neural backbones, and test cases ranging from a 1D chaotic system to 3D turbulence. INC improves the long-term trajectory performance (R2) by up to 158.7%, stabilizes blowups under aggressive coarsening, and for complex 3D turbulence cases yields speed-ups of several orders of magnitude. INC thus enables stable, efficient PDE emulation with formal error reduction, paving the way for faster scientific and engineering simulations with reliable physics guarantees. Our source code is available at https://github.com/tum-pbs/INC

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 28 of its 62 references that are in the map. First posted on arXiv 16 Nov 2025.

Builds on

28 of 62 references.

References · 28

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16 more
  1. 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 205
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  16. 2023Gradient-free online learning of subgrid-scale dynamics with neural emulatorscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Error-Conditioned Neural Solverscited by 1
  2. 2026Learning Heat-based Equations in Self-similar variablescited by 0
  3. 2026ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Modelscited by 0