{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-robust-numerical-solver-for-ode-via-self","title":"AttNS: Attention-Inspired Numerical Solving For Limited Data Scenarios","arxiv_id":"2302.10184","date":"2023-02-05","proceeding":null,"authors":["Zhongzhan Huang","Mingfu Liang","Shanshan Zhong","Liang Lin"],"abstract":"We propose the attention-inspired numerical solver (AttNS), a concise method that helps the generalization and robustness issues faced by the AI-Hybrid numerical solver in solving differential equations due to limited data. AttNS is inspired by the effectiveness of attention modules in Residual Neural Networks (ResNet) in enhancing model generalization and robustness for conventional deep learning tasks. Drawing from the dynamical system perspective of ResNet, we seamlessly incorporate attention mechanisms into the design of numerical methods tailored for the characteristics of solving differential equations. Our results on benchmarks, ranging from high-dimensional problems to chaotic systems, showcases AttNS consistently enhancing various numerical solvers without any intricate model crafting. Finally, we analyze AttNS experimentally and theoretically, demonstrating its ability to achieve strong generalization and robustness while ensuring the convergence of the solver. This includes requiring less data compared to other advanced methods to achieve comparable generalization errors and better prevention of numerical explosion issues when solving differential equations.","url_abs":"https://arxiv.org/abs/2302.10184v2","url_pdf":"https://arxiv.org/pdf/2302.10184v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"on-robust-numerical-solver-for-ode-via-self","repo_url":"https://github.com/dedekinds/neurvec","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2302.10184","atlas_url":"https://app.syntology.ai/?focus=2302.10184","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2302.10184"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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