{"slug": "universal-learning-of-nonlinear-dynamics", "title": "Universal Learning of Nonlinear Dynamics", "summary": "Researchers have developed a new algorithm for learning marginally stable nonlinear dynamical systems, based on spectral filtering and online convex optimization, that achieves vanishing prediction error. The method generalizes prior spectral filtering algorithms to handle asymmetric dynamics and noise correction, with implications for control theory and machine learning.", "body_md": "# Computer Science > Machine Learning\n\n[Submitted on 16 Aug 2025]\n\n# Title:Universal Learning of Nonlinear Dynamics\n\n[View PDF](/pdf/2508.11990)\n\n[HTML (experimental)](https://arxiv.org/html/2508.11990v1)\n\nAbstract:We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to the next based on a spectral representation of the system. Using techniques from online convex optimization, we prove vanishing prediction error for any nonlinear dynamical system that has finitely many marginally stable modes, with rates governed by a novel quantitative control-theoretic notion of learnability. The main technical component of our method is a new spectral filtering algorithm for linear dynamical systems, which incorporates past observations and applies to general noisy and marginally stable systems. This significantly generalizes the original spectral filtering algorithm to both asymmetric dynamics as well as incorporating noise correction, and is of independent interest.\n\n## Submission history\n\nFrom: Anand Brahmbhatt [[view email](/show-email/2cda8732/2508.11990)]\n\n**[v1]** Sat, 16 Aug 2025 09:14:47 UTC (4,365 KB)\n\n### Current browse context:\n\ncs.LG\n\n### References & Citations\n\nLoading...\n\n# Bibliographic and Citation Tools\n\nBibliographic Explorer\n\n*(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))\nConnected Papers\n\n*(*[What is Connected Papers?](https://www.connectedpapers.com/about))\nLitmaps\n\n*(*[What is Litmaps?](https://www.litmaps.co/))\nscite Smart Citations\n\n*(*[What are Smart Citations?](https://www.scite.ai/))# Code, Data and Media Associated with this Article\n\nalphaXiv\n\n*(*[What is alphaXiv?](https://alphaxiv.org/))\nCatalyzeX Code Finder for Papers\n\n*(*[What is CatalyzeX?](https://www.catalyzex.com))\nDagsHub\n\n*(*[What is DagsHub?](https://dagshub.com/))\nGotit.pub\n\n*(*[What is GotitPub?](http://gotit.pub/faq))\nHugging Face\n\n*(*[What is Huggingface?](https://huggingface.co/huggingface))\nScienceCast\n\n*(*[What is ScienceCast?](https://sciencecast.org/welcome))# Demos\n\n# Recommenders and Search Tools\n\nInfluence Flower\n\n*(*[What are Influence Flowers?](https://influencemap.cmlab.dev/))\nCORE Recommender\n\n*(*[What is CORE?](https://core.ac.uk/services/recommender))\nIArxiv Recommender\n\n*(*[What is IArxiv?](https://iarxiv.org/about))# arXivLabs: experimental projects with community collaborators\n\narXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.\n\nBoth individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.\n\nHave an idea for a project that will add value for arXiv's community? [ Learn more about arXivLabs](https://info.arxiv.org/labs/index.html).", "url": "https://wpnews.pro/news/universal-learning-of-nonlinear-dynamics", "canonical_source": "https://arxiv.org/abs/2508.11990", "published_at": "2026-07-13 00:06:27+00:00", "updated_at": "2026-07-13 00:35:17.865420+00:00", "lang": "en", "topics": ["machine-learning", "artificial-intelligence"], "entities": ["Anand Brahmbhatt"], "alternates": {"html": "https://wpnews.pro/news/universal-learning-of-nonlinear-dynamics", "markdown": "https://wpnews.pro/news/universal-learning-of-nonlinear-dynamics.md", "text": "https://wpnews.pro/news/universal-learning-of-nonlinear-dynamics.txt", "jsonld": "https://wpnews.pro/news/universal-learning-of-nonlinear-dynamics.jsonld"}}