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Latent Mamba Operator for Partial Differential Equations
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Latent Mamba Operator for Partial Differential Equations
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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.
Forward citations
Cited by 7 Pith papers
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SPAMoE reduces average MAE by 44.4% on OpenFWI datasets for full-waveform inversion via a spectral-preserving DINO encoder and dynamic frequency-band routing to specialized neural operators.
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SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion
SPAMoE reduces average MAE by 44.4% on ten OpenFWI sub-datasets via a spectral-preserving DINO encoder plus frequency-routed MoE of FNO, MNO and LNO experts.
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GraMO couples graph interactions and temporal state updates in one linear recurrence with input-dependent coefficients to simulate N-body, motion, and robotics systems with lower long-horizon error than prior GNN or S...
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