mlsanityData to 14 Oct 2026

Latent Mamba Operator for Partial Differential Equations

arXiv 2505.19105 ↗First posted 25 May 2025cs.LGcited by 10

On the map: State-space sequence models (S4, Mamba) → Time series forecasting with SSMs

Abstract (arXiv)

Neural operators have emerged as powerful data-driven frameworks for solving Partial Differential Equations (PDEs), offering significant speedups over numerical methods. However, existing neural operators struggle with scalability in high-dimensional spaces, incur high computational costs, and face challenges in capturing continuous and long-range dependencies in PDE dynamics. To address these limitations, we introduce the Latent Mamba Operator (LaMO), which integrates the efficiency of state-space models (SSMs) in latent space with the expressive power of kernel integral formulations in neural operators. We also establish a theoretical connection between state-space models (SSMs) and the kernel integral of neural operators. Extensive experiments across diverse PDE benchmarks on regular grids, structured meshes, and point clouds covering solid and fluid physics datasets, LaMOs achieve consistent state-of-the-art (SOTA) performance, with a 32.3% improvement over existing baselines in solution operator approximation, highlighting its efficacy in modeling complex PDE solutions.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba). Builds on 46 of its 61 references that are in the map. First posted on arXiv 25 May 2025.

Builds on

46 of 61 references.

Closest ancestors · 2

Same direction, newest first

  1. 2024Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEs3 Oct
  2. 2024State-space models are accurate and efficient neural operators for dynamical systems5 Sep

Other references · 44

  1. 2017Attention Is All You Needcited by 60,361
  2. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  3. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 30,186
  4. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  5. 2021Swin Transformer: Hierarchical Vision Transformer using Shifted Windowscited by 12,139
  6. 2016Layer Normalizationcited by 5,669
  7. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,718
  8. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  9. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,465
  10. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  11. 2017Decoupled Weight Decay Regularizationcited by 1,831
  12. 2024Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Dualitycited by 1,336
32 more
  1. 2021Perceiver: General Perception with Iterative Attentioncited by 1,104
  2. 2024Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Modelcited by 1,056
  3. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 950
  4. 2021Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layerscited by 608
  5. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 427
  6. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  7. 2021Choose a Transformer: Fourier or Galerkincited by 343
  8. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 336
  9. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 326
  10. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 297
  11. 2022Transformer for Partial Differential Equations' Operator Learningcited by 283
  12. 2021Factorized Fourier Neural Operatorscited by 249
  13. 2021Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformerscited by 248
  14. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 234
  15. 2022U-NO: U-shaped Neural Operatorscited by 230
  16. 2022FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operatorscited by 188
  17. 2022Fast Sampling of Diffusion Models via Operator Learningcited by 175
  18. 2024DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Trainingcited by 151
  19. 2022Anti-Oversmoothing in Deep Vision Transformers via the Fourier Domain Analysis: From Theory to Practicecited by 136
  20. 2023Scalable Transformer for PDE Surrogate Modelingcited by 128
  21. 2023Solving High-Dimensional PDEs with Latent Spectral Modelscited by 89
  22. 2023Improved Operator Learning by Orthogonal Attentioncited by 61
  23. 2023GateLoop: Fully Data-Controlled Linear Recurrence for Sequence Modelingcited by 46
  24. 2021Koopman Operator Dynamical Models: Learning, Analysis and Controlcited by 42
  25. 2024A Survey of Mambacited by 39
  26. 2024Audio Mamba: Bidirectional State Space Model for Audio Representation Learningcited by 37
  27. 2024On the Benefits of Memory for Modeling Time-Dependent PDEscited by 31
  28. 2024State Space Models as Foundation Models: A Control Theoretic Overviewcited by 19
  29. 2021Fourier Neural Operator Networks: A Fast and General Solver for the Photoacoustic Wave Equationcited by 10
  30. 2023Centered Self-Attention Layerscited by 7
  31. 2024CoNO: Complex Neural Operator for Continous Dynamical Physical Systemscited by 3
  32. 2025CoNOAir: A Neural Operator for Forecasting Carbon Monoxide Evolution in Citiescited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 10.

10 papers.

  1. 2026Structure-Preserving Learning Improves Geometry Generalization in Neural PDEscited by 8
  2. 2026Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagatorscited by 1
  3. 2026Agentic Neural Architecture Searchcited by 1
  4. 2026Adaptive Mamba Neural Operatorscited by 1
  5. 2026SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversioncited by 0
  6. 2026Graph Mamba Operator: A Latent Simulator for Interacting Particle Systemscited by 0
  7. 2026Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEscited by 0
  8. 2026Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEscited by 0
  9. 2026Advectra: Asymmetric Latent Transport for Non-Stationary Physicscited by 0
  10. 2026METRO: Metric-Enhanced Token Routing Operatorcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025GeoMaNO: Geometric Mamba Neural Operator for Partial Differential Equations
  2. 2024LE-PDE++: Mamba for accelerating PDEs Simulations
  3. 2025Merging Memory and Space: A State Space Neural Operator
  4. 2026Stability and Discretization Error of State Space Model Neural Operators
  5. 2026Learning Physical Operators using Neural Operators
  6. 2026Autoregression-Free Neural Operators for Time-Dependent PDEs
  7. 2025CFO: Learning Continuous-Time PDE Dynamics via Flow-Matched Neural Operators
  8. 2025Towards a Foundation Model for Partial Differential Equations Across Physics Domains