Multiple Physics Pretraining for Physical Surrogate Models
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Abstract (arXiv)
We introduce multiple physics pretraining (MPP), an autoregressive task-agnostic pretraining approach for physical surrogate modeling of spatiotemporal systems with transformers. In MPP, rather than training one model on a specific physical system, we train a backbone model to predict the dynamics of multiple heterogeneous physical systems simultaneously in order to learn features that are broadly useful across systems and facilitate transfer. In order to learn effectively in this setting, we introduce a shared embedding and normalization strategy that projects the fields of multiple systems into a shared embedding space. We validate the efficacy of our approach on both pretraining and downstream tasks over a broad fluid mechanics-oriented benchmark. We show that a single MPP-pretrained transformer is able to match or outperform task-specific baselines on all pretraining sub-tasks without the need for finetuning. For downstream tasks, we demonstrate that finetuning MPP-trained models results in more accurate predictions across multiple time-steps on systems with previously unseen physical components or higher dimensional systems compared to training from scratch or finetuning pretrained video foundation models. We open-source our code and model weights trained at multiple scales for reproducibility.
Key facts. Cited by 90 papers in the map (data through 7 Oct 2026). Builds on 72 of its 100 references that are in the map. First posted on arXiv 4 Oct 2023.
Builds on
72 of 100 references.
References · 72
- 2017Attention Is All You Needcited by 59,932
- 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
- 2020Language Models are Few-Shot Learnerscited by 32,199
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
- 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
- 2019Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformercited by 14,491
- 2021Swin Transformer: Hierarchical Vision Transformer using Shifted Windowscited by 12,082
- 2020A Simple Framework for Contrastive Learning of Visual Representationscited by 11,979
- 2021Masked Autoencoders Are Scalable Vision Learnerscited by 7,339
- 2020Scaling Laws for Neural Language Modelscited by 6,411
- 2021On the Opportunities and Risks of Foundation Modelscited by 3,961
- 2016Gaussian Error Linear Units (GELUs)cited by 3,431
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- 2022VideoMAE: Masked Autoencoders are Data-Efficient Learners for Self-Supervised Video Pre-Trainingcited by 1,305
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- 2016Instance Normalization: The Missing Ingredient for Fast Stylizationcited by 1,187
- 2017The "something something" video database for learning and evaluating visual common sensecited by 1,092
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- 2020On Layer Normalization in the Transformer Architecturecited by 906
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- 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
- 2018CCNet: Criss-Cross Attention for Semantic Segmentationcited by 717
- 2023Scaling Vision Transformers to 22 Billion Parameterscited by 690
- 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
- 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
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- 2021CSWin Transformer: A General Vision Transformer Backbone with Cross-Shaped Windowscited by 526
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- 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
- 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
- 2021Machine learning accelerated computational fluid dynamicscited by 461
- 2021Neural Operator: Learning Maps Between Function Spacescited by 413
- 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 396
- 2019Axial Attention in Multidimensional Transformerscited by 350
- 2020Universal Differential Equations for Scientific Machine Learningcited by 345
- 2021Choose a Transformer: Fourier or Galerkincited by 333
- 2020ChemBERTa: Large-Scale Self-Supervised Pretraining for Molecular Property Predictioncited by 332
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- 2021Scaling Laws for Transfercited by 265
- 2023A Cookbook of Self-Supervised Learningcited by 248
- 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 201
- 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
- 2022Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Modelscited by 172
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- 2026A survey detection channel overrides the pixels in an astronomical foundation model, and biases tomographic mean redshifts23 Aug 2026
- 2026TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learning4 Aug 2026
- 2026Small Models, Strong Priors: Architectural Inductive Bias for Parameter-Efficient Neural PDE Solvers25 May 2026
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- 2026LAtent Phase Inference from Short time sequences using SHallow REcurrent Decoders (LAPIS-SHRED)1 Apr 2026
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