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PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks

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arxiv 2307.11833 v3 pith:YSSSPEOH submitted 2023-07-21 cs.CE cs.LG

Zhiyuan Zhao , Xueying Ding , B. Aditya Prakash This is my paper
classification cs.CEcs.LG
keywords pinnsformerpinnsframeworknetworksneuralsolutionsaccuratelycapture
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Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons (MLP), neglect the crucial temporal dependencies inherent in practical physics systems and thus fail to propagate the initial condition constraints globally and accurately capture the true solutions under various scenarios. In this paper, we introduce a novel Transformer-based framework, termed PINNsFormer, designed to address this limitation. PINNsFormer can accurately approximate PDE solutions by utilizing multi-head attention mechanisms to capture temporal dependencies. PINNsFormer transforms point-wise inputs into pseudo sequences and replaces point-wise PINNs loss with a sequential loss. Additionally, it incorporates a novel activation function, Wavelet, which anticipates Fourier decomposition through deep neural networks. Empirical results demonstrate that PINNsFormer achieves superior generalization ability and accuracy across various scenarios, including PINNs failure modes and high-dimensional PDEs. Moreover, PINNsFormer offers flexibility in integrating existing learning schemes for PINNs, further enhancing its performance.

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Cited by 11 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cosmo-SPINN: Fuzzy Dark Matter Simulations with Physics-Informed Generative Networks

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    Physics-informed generative U-Nets evolve and super-resolve fuzzy dark matter fields under Schrödinger–Poisson constraints with far less supervised data than pure data-driven baselines.

  2. Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology

    physics.flu-dyn 2026-07 conditional novelty 6.0 of 10

    A four-term tensor-basis neural network trained only on oscillatory shear data, embedded in a finite-volume CFD solver, qualitatively reproduces viscoelastic contraction and cross-slot flows, including the onset of el...

  3. SPINN: Advancing Cosmological Simulations of Fuzzy Dark Matter with Physics Informed Neural Networks

    astro-ph.CO 2025-06 conditional novelty 6.0 of 10

    A physics-informed neural network (SPINN) solves the Schrödinger-Poisson equations for fuzzy dark matter collapse in 1D and 3D, matching a spectral solver on a sinusoidal test case.

  4. Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems

    cs.AI 2025-05 conditional novelty 6.0 of 10

    HEAP, a hierarchical autoencoder with a predictor that advances multiple scale layers in sync, achieves several-fold lower long-term rollout error than flat ResNet baselines on Hasegawa-Wakatani turbulence.

  5. LLT: Local Linear Transformer for PDE Operator Learning

    cs.LG 2026-07 conditional novelty 5.0 of 10

    Local Linear Transformer learns PDE operators by combining linear global attention with local spatial mixing, achieving competitive accuracy and lower training-step cost than prior transformers.

  6. Integrating Fourier Neural Operator with Diffusion Model for Autoregressive Predictions of Three-dimensional Turbulence

    physics.flu-dyn 2025-12 conditional novelty 5.0 of 10

    DiAFNO, an implicit adaptive Fourier neural operator used as the denoiser inside an EDM diffusion model, gives more accurate autoregressive predictions of 3D turbulence than EDM or dynamic Smagorinsky LES.

  7. Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation

    math.NA 2025-11 reject novelty 5.0 of 10

    NeuralMD solves the oscillatory NKGE by training one network on the slow NLSW envelope and another on the remainder, but its model-selection step requires the exact solution as ground truth.

  8. Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs

    physics.flu-dyn 2026-07 conditional novelty 4.0 of 10

    Split complex-valued PINNs achieve lower benchmark errors than real-valued PINNs, but the comparison is confounded by doubled parameters and unresolved internal error inconsistencies.

  9. A new strategy for physics-informed neural networks based on hierarchical collocation point refinement

    math.NA 2026-07 conditional novelty 4.0 of 10

    Training a single PINN on progressively finer collocation point sets, carrying over network parameters, cuts training time by an order of magnitude on tested Poisson, convection-diffusion-reaction, and Helmholtz bench...

  10. Learning Mappings in Mesh-based Simulations

    cs.LG 2025-06 conditional novelty 3.0 of 10

    A bilinear scatter encoding plus a masked UNet yields competitive surrogate accuracy and data efficiency on several mesh-based simulation benchmarks, though the encoding is a standard technique.

  11. Towards Digital Twins for Optimal Radioembolization

    eess.IV 2025-08 unverdicted novelty 2.0 of 10

    A review proposing a liver radioembolization digital twin that combines CFD with physics-informed neural networks to plan microsphere delivery.

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