Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems
The paper introduces Symplectic Neural Operators (SNOs) designed for modeling infinite-dimensional Hamiltonian systems. These operators aim to preserve the symplectic structure inherent in Hamiltonian partial differential equations (PDEs). The authors provide theoretical and numerical evidence supporting the effectiveness of SNOs in maintaining stability and improving energy behavior compared to traditional neural operators.
- ▪Symplectic Neural Operators are introduced to address challenges in modeling infinite-dimensional Hamiltonian systems.
- ▪The architecture is designed to preserve the symplectic structure intrinsic to Hamiltonian PDEs.
- ▪Theoretical results demonstrate long-term stability and improved energy behavior of SNOs over non-structure-preserving neural operators.
arXiv cs.AI files mainly under ai research. We currently carry 1,128 of its stories.
Story provenance
Source · retrieval · rights · ranking — open for full record
inspect →
Story provenance
Attribution is not the same as permission. This drawer separates discovery metadata, excerpts, WeSearch-generated summaries, reuse status, and whether the publisher receives the visit. Nothing here claims a legal grant the publisher has not made.
Record
| Original publisher | arXiv cs.AI |
| Canonical URL | https://arxiv.org/abs/2605.15881 |
| Publication time | Mon, 18 May 2026 00:00:00 -0400 |
| Retrieval time | 2026-05-18T04:04:54.418Z |
| Last seen | 2026-05-18T04:04:54.418Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | ZwTjSZIvPnhr |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
Rights status (four layers)
WeSearch handling by dimension
| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
Opening excerpt (first ~120 words) tap to expand
Mathematics > Dynamical Systems arXiv:2605.15881 (math) [Submitted on 15 May 2026] Title:Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems Authors:Yeang Makara, Yusuke Tanaka, Takashi Matsubara, Takaharu Yaguchi View a PDF of the paper titled Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems, by Yeang Makara and 3 other authors View PDF HTML (experimental) Abstract:The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational and structural challenges for standard data-driven architectures.
…
Excerpt limited to ~120 words for fair-use compliance. The full article is at arXiv cs.AI.
Discussion
0 commentsMore from arXiv cs.AI
