{"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/homotopy-based-training-of-neuralodes-for","title":"Homotopy-based training of NeuralODEs for accurate dynamics discovery","arxiv_id":"2210.01407","date":"2022-10-04","proceeding":"NeurIPS 2023 11","authors":["Joon-Hyuk Ko","Hankyul Koh","Nojun Park","Wonho Jhe"],"abstract":"Neural Ordinary Differential Equations (NeuralODEs) present an attractive way to extract dynamical laws from time series data, as they bridge neural networks with the differential equation-based modeling paradigm of the physical sciences. However, these models often display long training times and suboptimal results, especially for longer duration data. While a common strategy in the literature imposes strong constraints to the NeuralODE architecture to inherently promote stable model dynamics, such methods are ill-suited for dynamics discovery as the unknown governing equation is not guaranteed to satisfy the assumed constraints. In this paper, we develop a new training method for NeuralODEs, based on synchronization and homotopy optimization, that does not require changes to the model architecture. We show that synchronizing the model dynamics and the training data tames the originally irregular loss landscape, which homotopy optimization can then leverage to enhance training. Through benchmark experiments, we demonstrate our method achieves competitive or better training loss while often requiring less than half the number of training epochs compared to other model-agnostic techniques. Furthermore, models trained with our method display better extrapolation capabilities, highlighting the effectiveness of our method.","url_abs":"https://arxiv.org/abs/2210.01407v6","url_pdf":"https://arxiv.org/pdf/2210.01407v6.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":"homotopy-based-training-of-neuralodes-for","repo_url":"https://github.com/jhko725/neuralodehomotopy","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"time-series-1","task_name":"Time Series"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2210.01407","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2210.01407"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+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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