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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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PGMNO: A physics-Guided mamba neural operator framework for partial differential equations.

Yanan Guo1, Junqiang Song2, Xiaoqun Cao3

  • 1College of Meteorology and Oceanography, National University of Defense Technology, No.109 Deya Road, Changsha, 410073, Hunan, China; College of Computer Science, National University of Defense Technology, No.109 Deya Road, Changsha, 410073, Hunan, China; Department of Atmospheric and Oceanic Sciences, School of Physics, Peking University, No.5 Yiheyuan Road, Beijing, 100871, Beijing, China.

Neural Networks : the Official Journal of the International Neural Network Society
|March 26, 2026
PubMed
Summary
This summary is machine-generated.

Physics-Guided Mamba Neural Operator (PGMNO) enhances operator learning for complex physical systems. This novel framework unifies numerical methods with state space models, improving accuracy and efficiency in modeling long-term spatiotemporal dynamics governed by partial differential equations.

Keywords:
Multistep methodOperator learningPDE LearningPhysics-Guided neural operatorScientific machine learningState space model

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Area of Science:

  • Scientific Computing
  • Machine Learning
  • Dynamical Systems Modeling

Background:

  • Operator learning faces challenges in modeling long-term evolution of complex physical systems governed by partial differential equations (PDEs).
  • Existing methods like Transformer-based operators have limitations in capturing long-range spatiotemporal dependencies and ensuring temporal stability.
  • Accurate and efficient modeling of these systems is crucial for scientific discovery and engineering applications.

Purpose of the Study:

  • Introduce the Physics-Guided Mamba Neural Operator (PGMNO) framework to address limitations in operator learning for PDEs.
  • Enhance the ability to capture long-range spatiotemporal dependencies and ensure temporal stability in modeling complex physical systems.
  • Develop a robust surrogate solver for PDE-governed dynamical systems.

Main Methods:

  • Unify linear multistep numerical methods with structured state space models (SSMs) to create the PGMNO.
  • Employ multistep temporal modeling in the forward pass for temporal stability.
  • Utilize an implicit backward differentiation formula (BDF)-based scheme during training and leverage SSMs' kernel integration for scalability.

Main Results:

  • PGMNO consistently outperforms state-of-the-art models in prediction accuracy, computational efficiency, and long-term stability across diverse PDE benchmarks.
  • The framework demonstrates strong resolution-invariant extrapolation capabilities.
  • PGMNO exhibits robust generalization across varying spatial discretizations.

Conclusions:

  • The PGMNO framework offers a significant advancement in operator learning for modeling complex physical systems governed by PDEs.
  • Unifying numerical integration techniques with state space modeling provides a powerful approach for building robust surrogate solvers.
  • This work highlights the potential for improved accuracy, efficiency, and stability in simulating long-term dynamical systems.