mlsanityData to 14 Oct 2026

Sub-Sequential Physics-Informed Learning with State Space Model

arXiv 2502.00318 ↗First posted 1 Feb 2025cs.LG cs.NA math.NAcited by 10

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Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) are a kind of deep-learning-based numerical solvers for partial differential equations (PDEs). Existing PINNs often suffer from failure modes of being unable to propagate patterns of initial conditions. We discover that these failure modes are caused by the simplicity bias of neural networks and the mismatch between PDE's continuity and PINN's discrete sampling. We reveal that the State Space Model (SSM) can be a continuous-discrete articulation allowing initial condition propagation, and that simplicity bias can be eliminated by aligning a sequence of moderate granularity. Accordingly, we propose PINNMamba, a novel framework that introduces sub-sequence modeling with SSM. Experimental results show that PINNMamba can reduce errors by up to 86.3% compared with state-of-the-art architecture. Our code is available at https://github.com/miniHuiHui/PINNMamba.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 32 of its 47 references that are in the map. First posted on arXiv 1 Feb 2025.

Builds on

32 of 47 references.

References · 32

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,718
  4. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,465
  5. 2024Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Dualitycited by 1,336
  6. 2024Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Modelcited by 1,056
  7. 2024VMamba: Visual State Space Modelcited by 969
  8. 2022Simplified State Space Layers for Sequence Modelingcited by 788
  9. 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
  10. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  11. 2020HiPPO: Recurrent Memory with Optimal Polynomial Projectionscited by 605
  12. 2022Hungry Hungry Hippos: Towards Language Modeling with State Space Modelscited by 499
20 more
  1. 2023Hyena Hierarchy: Towards Larger Convolutional Language Modelscited by 393
  2. 2020The Pitfalls of Simplicity Bias in Neural Networkscited by 351
  3. 2020Gradient Starvation: A Learning Proclivity in Neural Networkscited by 267
  4. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 236
  5. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 222
  6. 2022Earthformer: Exploring Space-Time Transformers for Earth System Forecastingcited by 152
  7. 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 148
  8. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 118
  9. 2023PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEscited by 87
  10. 2021Evading the Simplicity Bias: Training a Diverse Set of Models Discovers Solutions with Superior OOD Generalizationcited by 83
  11. 2022Agree to Disagree: Diversity through Disagreement for Better Transferabilitycited by 70
  12. 2022Failure-informed adaptive sampling for PINNscited by 64
  13. 2023PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networkscited by 64
  14. 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 62
  15. 2022Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarioscited by 46
  16. 2021Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEscited by 43
  17. 2024Parameterized Physics-informed Neural Networks for Parameterized PDEscited by 38
  18. 2024State-space models are accurate and efficient neural operators for dynamical systemscited by 28
  19. 2024PARCv2: Physics-aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics Modelingcited by 10
  20. 2024Infinite-Dimensional Feature Interactioncited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 7.

10 papers.

  1. 2025FP64 is All You Need: Rethinking Failure Modes in Physics-Informed Neural Networkscited by 12
  2. 2025Revisiting Heat Flux Analysis of Tungsten Monoblock Divertor on EAST using Physics-Informed Neural Networkcited by 2
  3. 2025Physics-Informed Neural Networks with Fourier Features and Attention-Driven Decodingcited by 2
  4. 2026A Family of Adaptive Activation Functions for Mitigating Failure Modes in Physics-Informed Neural Networkscited by 0
  5. 2026PINNs Failure Modes are Overfittingcited by 0
  6. 2026Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solverscited by 0
  7. 2026Neither Precision Nor Architecture Alone: Controlled Tests of Failure Remedies for Physics-Informed Neural Networkscited by 0
  8. 2026PPIM: Pennes Physics-Informed Mamba for Heat-Source-Conditioned 3D Bioheat Simulationcited by 0
  9. 2026Constitutive State-Space Modeling of Path-Dependent Plasticity: A Resolution-Consistent and Parallelizable Computational Frameworkcited by 0
  10. 2026CI-PINN: Causal Integral Physics-Informed Neural Network for Solving Evolution Equationscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025KD-PINN: Knowledge-Distilled PINNs for ultra-low-latency real-time neural PDE solvers
  2. 2025Lang-PINN: From Language to Physics-Informed Neural Networks via a Multi-Agent Framework
  3. 2024Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts
  4. 2025Tensor-Compressed and Fully-Quantized Training of Neural PDE Solvers
  5. 2023LatentPINNs: Generative physics-informed neural networks via a latent representation learning
  6. 2024Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systems
  7. 2021Physics-Informed Neural Network Method for Solving One-Dimensional Advection Equation Using PyTorch
  8. 2025RL-PINNs: Reinforcement Learning-Driven Adaptive Sampling for Efficient Training of PINNs