Merging Memory and Space: A State Space Neural Operator
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914372449730560 |
|---|---|
| author | Koren, Nodens Lanthaler, Samuel |
| author_facet | Koren, Nodens Lanthaler, Samuel |
| contents | We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint spatiotemporal modeling, introducing two key mechanisms: *adaptive damping*, which stabilizes learning by localizing receptive fields, and *learnable frequency modulation*, which enables data-driven spectral selection. These components provide a unified framework for capturing long-range dependencies with parameter efficiency. Theoretically, we establish connections between SSMs and neural operators, proving a universality theorem for convolutional architectures with full field-of-view. Empirically, SS-NO achieves state-of-the-art performance across diverse PDE benchmarks-including 1D Burgers' and Kuramoto-Sivashinsky equations, and 2D Navier-Stokes and compressible Euler flows-while using significantly fewer parameters than competing approaches. A factorized variant of SS-NO further demonstrates scalable performance on challenging 2D problems. Our results highlight the effectiveness of damping and frequency learning in operator modeling, while showing that lightweight factorization provides a complementary path toward efficient large-scale PDE learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Merging Memory and Space: A State Space Neural Operator Koren, Nodens Lanthaler, Samuel Machine Learning We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint spatiotemporal modeling, introducing two key mechanisms: *adaptive damping*, which stabilizes learning by localizing receptive fields, and *learnable frequency modulation*, which enables data-driven spectral selection. These components provide a unified framework for capturing long-range dependencies with parameter efficiency. Theoretically, we establish connections between SSMs and neural operators, proving a universality theorem for convolutional architectures with full field-of-view. Empirically, SS-NO achieves state-of-the-art performance across diverse PDE benchmarks-including 1D Burgers' and Kuramoto-Sivashinsky equations, and 2D Navier-Stokes and compressible Euler flows-while using significantly fewer parameters than competing approaches. A factorized variant of SS-NO further demonstrates scalable performance on challenging 2D problems. Our results highlight the effectiveness of damping and frequency learning in operator modeling, while showing that lightweight factorization provides a complementary path toward efficient large-scale PDE learning. |
| title | Merging Memory and Space: A State Space Neural Operator |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2507.23428 |