Latent Mamba Operator for Partial Differential Equations
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.
Code (0)
등록된 구현이 없습니다.
Tasks
MambaState Space ModelsMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
GeoMaNO: Geometric Mamba Neural Operator for Partial Differential Equations
The neural operator (NO) framework has emerged as a powerful tool for solving partial differential equations (PDEs). Recent NOs are dominated by the Transformer architecture, which offers NOs the capability to capture lo…
MambaHyena Neural Operator for Partial Differential Equations
Numerically solving partial differential equations typically requires fine discretization to resolve necessary spatiotemporal scales, which can be computationally expensive. Recent advances in deep learning have provided…
An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator
This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) …
DecoderGeometric Neural Operators via Lie Group-Constrained Latent Dynamics
Neural operators offer an effective framework for learning solutions of partial differential equations for many physical systems in a resolution-invariant and data-driven manner. Existing neural operators, however, often…
Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical…
Gaussian Processes