LE-PDE++: Mamba for accelerating PDEs Simulations
On the map: State-space sequence models (S4, Mamba) → Time series forecasting with SSMs
Abstract (arXiv)
Partial Differential Equations are foundational in modeling science and natural systems such as fluid dynamics and weather forecasting. The Latent Evolution of PDEs method is designed to address the computational intensity of classical and deep learning-based PDE solvers by proposing a scalable and efficient alternative. To enhance the efficiency and accuracy of LE-PDE, we incorporate the Mamba model, an advanced machine learning model known for its predictive efficiency and robustness in handling complex dynamic systems with a progressive learning strategy. The LE-PDE was tested on several benchmark problems. The method demonstrated a marked reduction in computational time compared to traditional solvers and standalone deep learning models while maintaining high accuracy in predicting system behavior over time. Our method doubles the inference speed compared to the LE-PDE while retaining the same level of parameter efficiency, making it well-suited for scenarios requiring long-term predictions.
Key facts. No citing papers in the map yet (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 21 of its 34 references that are in the map. First posted on arXiv 4 Nov 2024.
Builds on
21 of 34 references.
References · 21
- 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,718
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2015Scheduled Sampling for Sequence Prediction with Recurrent Neural Networkscited by 803
- 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
- 2017DGM: A deep learning algorithm for solving partial differential equationscited by 678
- 2022Message Passing Neural PDE Solverscited by 386
- 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 349
- 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 235
- 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 221
- 2022Respecting causality is all you need for training physics-informed neural networkscited by 156
- 2022Clifford Neural Layers for PDE Modelingcited by 92
9 more
- 2022Learning to Accelerate Partial Differential Equations via Latent Global Evolutioncited by 39
- 2022Applications of physics informed neural operatorscited by 33
- 2023Koopman neural operator as a mesh-free solver of non-linear partial differential equationscited by 29
- 2023Physics informed WNOcited by 27
- 2024Scaling physics-informed hard constraints with mixture-of-expertscited by 24
- 2023Learning Controllable Adaptive Simulation for Multi-resolution Physicscited by 20
- 2024Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solvingcited by 17
- 2022Data-driven Science and Machine Learning Methods in Laser-Plasma Physicscited by 4
- 2018PDE Acceleration: A convergence rate analysis and applications to obstacle problemscited by 2
Built on by
Not cited yet.
Similar, not cited
Close in wording, no citation either way
- 2025Latent Mamba Operator for Partial Differential Equations
- 2026Adaptive Mamba Neural Operators
- 2025Towards a Foundation Model for Partial Differential Equations Across Physics Domains
- 2025GeoMaNO: Geometric Mamba Neural Operator for Partial Differential Equations
- 2024Text2PDE: Latent Diffusion Models for Accessible Physics Simulation
- 2024State-space models are accurate and efficient neural operators for dynamical systems
- 2024Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEs
- 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers