GeoMaNO: Geometric Mamba Neural Operator for Partial Differential Equations
On the map: State-space sequence models (S4, Mamba) → Time series forecasting with SSMs
Abstract (arXiv)
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 long-range dependencies in PDE dynamics. However, existing Transformer-based NOs suffer from quadratic complexity, lack geometric rigor, and thus suffer from sub-optimal performance on regular grids. As a remedy, we propose the Geometric Mamba Neural Operator (GeoMaNO) framework, which empowers NOs with Mamba's modeling capability, linear complexity, plus geometric rigor. We evaluate GeoMaNO's performance on multiple standard and popularly employed PDE benchmarks, spanning from Darcy flow problems to Navier-Stokes problems. GeoMaNO improves existing baselines in solution operator approximation by as much as 58.9%.
Key facts. Cited by 2 papers in the map (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 45 of its 57 references that are in the map. First posted on arXiv 17 May 2025.
Builds on
45 of 57 references.
Closest ancestors · 2
Same direction, newest first
- 2024Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEs3 Oct
- 2024State-space models are accurate and efficient neural operators for dynamical systems5 Sep
Other references · 43
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31 more
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