mlsanityData to 7 Oct 2026

Adaptive Mamba Neural Operators

arXiv 2607.18043 ↗First posted 20 Jul 2026cs.LG cs.NA math.APcited by 0

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

Abstract (arXiv)

Accurately solving partial differential equations (PDEs) on arbitrary geometries and a variety of meshes is an important task in science and engineering applications. In this paper, we propose Adaptive Mamba Neural Operators (AMO), which integrates reproducing kernels for state-space models (SSMs) rather than the kernel integral formulation of SSMs. This is achieved by constructing Takenaka-Malmquist systems for the PDEs. AMO offers new representations that align well with the adaptive Fourier decomposition (AFD) theory and can approximate the solution manifold of PDEs on a wide range of geometries and meshes. In several challenging benchmark PDE problems in the fields of fluid physics, solid physics, and finance on point clouds, structured meshes, regular grids, and irregular domains, AMO consistently outperforms state-of-the-art solvers in terms of relative L2 error. Overall, this work presents a new paradigm for designing explainable neural operator frameworks.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba). Builds on 24 of its 37 references that are in the map. First posted on arXiv 20 Jul 2026.

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24 of 37 references.

Closest ancestors · 3

Same direction, newest first

  1. 2025Latent Mamba Operator for Partial Differential Equations25 May
  2. 2024Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEs3 Oct
  3. 2024State-space models are accurate and efficient neural operators for dynamical systems5 Sep

Other references · 21

  1. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,616
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,424
  4. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
  5. 2021Choose a Transformer: Fourier or Galerkincited by 333
  6. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
  7. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 292
  8. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  9. 2021Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformerscited by 237
  10. 2021Factorized Fourier Neural Operatorscited by 237
  11. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 229
  12. 2022U-NO: U-shaped Neural Operatorscited by 219
9 more
  1. 2025Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometriescited by 89
  2. 2023Solving High-Dimensional PDEs with Latent Spectral Modelscited by 84
  3. 2024Latent Neural Operator for Solving Forward and Inverse PDE Problemscited by 76
  4. 2022Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modelingcited by 65
  5. 2023Improved Operator Learning by Orthogonal Attentioncited by 58
  6. 2023Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domainscited by 20
  7. 2024State-Free Inference of State-Space Models: The Transfer Function Approachcited by 18
  8. 2024Nonlocal Attention Operator: Materializing Hidden Knowledge Towards Interpretable Physics Discoverycited by 18
  9. 2023Coupled Multiwavelet Neural Operator Learning for Coupled Partial Differential Equationscited by 10

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