Latent Mamba Operator for Partial Differential Equations

Neural operators have emerged as powerful datadriven frameworks for solving Partial Differential Equations (PDEs), offering significant speedups over numerical methods. However, existing neural operators struggle with scalability in highdimensional 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. Our code implementation is available at https://github.com/M3RG-IITD/LaMO . Continuum models describing physical systems are formulated as PDEs across various disciplines, including physics, chemistry, fluid mechanics, and robotics (Debnath & Debnath, 2005) . Traditionally, these PDEs are solved by classical numerical methods, such as finite element and spectral methods ( Ŝolín, 2005; Costa, 2004) . However, these