Fit-DeepOKAN: Enhancing Neural Operator Learning of Soliton Dynamics via FitNets Distillation

Fit-DeepOKAN: Enhancing Neural Operator Learning of Soliton Dynamics via FitNets Distillation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Fit-DeepOKAN: Enhancing Neural Operator Learning of Soliton Dynamics via FitNets Distillation Lan Chen, Houhui Yi, Zhiyang Zhang, Muwei Liu, Wenjun Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7731789/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 26 Feb, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted 15 You are reading this latest preprint version Abstract The Nonlinear Schrödinger (NLS) equation plays a pivotal role in various physical domains, including optics, plasma physics, and quantum mechanics. Since solitons arise as fundamental localized solutions of the NLS equation, their efficient and accurate computation carries profound theoretical and engineering significance. In this work, we investigate the potential of neural operator frameworks for soliton modeling. As one of the most promising operator learning networks, DeepOKAN provides a powerful baseline for modeling nonlinear wave dynamics. Building upon this foundation, we propose a novel DeepOKAN architecture augmented with the FitNets distillation strategy, and conduct systematic evaluations on a range of NLS-type equations with diverse soliton families as benchmark problems.Furthermore, we explore the impact of different distillation schemes and the incorporation of activation functions on model performance. Quantitative results indicate that the FitNets-based distillation outperforms the logits-only scheme, reducing relative $l_2$ errors by over 16.4\%. In contrast, the incorporation of the tanh activation not only fails to enhance accuracy but, in the worst case, increases the error by an order of magnitude. Results from experiments show that even with limited network sizes, the suggested model has a great expressive potential. This highlights its capability in learning complex functional mappings and affirms the feasibility of embedding structured knowledge into operator learning models. The approach shows promising extensibility and potential for broader applications in scientific computing and engineering contexts. Mathematics Subject Classification (2020) 35Q55 · 37K40 · 68T07 Nonlinear Schr¨odinger equation Soliton solution DeepOKAN Knowledge distillation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 26 Feb, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 11 Nov, 2025 Reviews received at journal 11 Nov, 2025 Reviewers agreed at journal 11 Nov, 2025 Reviews received at journal 11 Nov, 2025 Reviewers agreed at journal 10 Nov, 2025 Reviewers agreed at journal 25 Oct, 2025 Reviewers agreed at journal 24 Oct, 2025 Reviewers agreed at journal 24 Oct, 2025 Reviewers agreed at journal 23 Oct, 2025 Reviewers agreed at journal 23 Oct, 2025 Reviewers agreed at journal 23 Oct, 2025 Reviewers invited by journal 23 Oct, 2025 Editor assigned by journal 30 Sep, 2025 Submission checks completed at journal 29 Sep, 2025 First submitted to journal 28 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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