mlsanityData to 14 Oct 2026

Generalizing PDE Emulation with Equation-Aware Neural Operators

arXiv 2511.09729 ↗First posted 12 Nov 2025cs.LGcited by 2

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Abstract (arXiv)

Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for equation-aware emulation that generalizes to unseen PDEs, conditioning a neural model on a vector encoding representing the terms in a PDE and their coefficients. We present a baseline of four distinct modeling technqiues, trained on a family of 1D PDEs from the APEBench suite. Our approach achieves strong performance on parameter sets held out from the training distribution, with strong stability for rollout beyond the training window, and generalization to an entirely unseen PDE. This work was developed as part of a broader effort exploring AI systems that automate the creation of expert-level empirical software for scorable scientific tasks. The data and codebase are available at https://github.com/google-research/generalized-pde-emulator.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 15 of its 19 references that are in the map. First posted on arXiv 12 Nov 2025.

Builds on

15 of 19 references.

References · 15

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  4. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,333
  5. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  6. 2021Machine learning accelerated computational fluid dynamicscited by 471
  7. 2022Message Passing Neural PDE Solverscited by 386
  8. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 197
  9. 2023Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behaviorcited by 131
  10. 2024Latent Neural Operator for Solving Forward and Inverse PDE Problemscited by 80
  11. 2024APEBench: A Benchmark for Autoregressive Neural Emulators of PDEscited by 60
  12. 2025An AI system to help scientists write expert-level empirical softwarecited by 60
3 more
  1. 2023Learning Neural PDE Solvers with Parameter-Guided Channel Attentioncited by 38
  2. 2024Active Learning for Neural PDE Solverscited by 22
  3. 2023Physics Informed Token Transformer for Solving Partial Differential Equationscited by 21

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Neural-Schwarz Tiling for Geometry-Universal PDE Solving at Scalecited by 2
  2. 2026Fractional is Better: Learnable Derivative Orders in Neural Operator Learningcited by 0