mlsanityData to 7 Oct 2026

MultiPDENet: PDE-embedded Learning with Multi-time-stepping for Accelerated Flow Simulation

arXiv 2501.15987 ↗First posted 27 Jan 2025math.NA cs.AI cs.NAcited by 3

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Abstract (arXiv)

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but struggle with weak generalizability, interpretability, and data dependency, as well as suffer in long-term prediction. To this end, we propose a PDE-embedded network with multiscale time stepping (MultiPDENet), which fuses the scheme of numerical methods and machine learning, for accelerated simulation of flows. In particular, we design a convolutional filter based on the structure of finite difference stencils with a small number of parameters to optimize, which estimates the equivalent form of spatial derivative on a coarse grid to minimize the equation's residual. A Physics Block with a 4th-order Runge-Kutta integrator at the fine time scale is established that embeds the structure of PDEs to guide the prediction. To alleviate the curse of temporal error accumulation in long-term prediction, we introduce a multiscale time integration approach, where a neural network is used to correct the prediction error at a coarse time scale. Experiments across various PDE systems, including the Navier-Stokes equations, demonstrate that MultiPDENet can accurately predict long-term spatiotemporal dynamics, even given small and incomplete training data, e.g., spatiotemporally down-sampled datasets. MultiPDENet achieves the state-of-the-art performance compared with other neural baseline models, also with clear speedup compared to classical numerical methods.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 29 of its 48 references that are in the map. First posted on arXiv 27 Jan 2025.

Builds on

29 of 48 references.

References · 29

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17 more
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Cited by year

Citing papers per year: 2025: 3.

3 papers.

  1. 2025Hierarchical Implicit Neural Emulatorscited by 9
  2. 2025OmniFluids: Physics Pre-trained Modeling of Fluid Dynamicscited by 0
  3. 2025Stable spectral neural operator for learning stiff PDE systems from limited datacited by 0