{"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/learning-equations-from-biological-data-with","title":"Learning Equations from Biological Data with Limited Time Samples","arxiv_id":"2005.09622","date":"2020-05-19","proceeding":null,"authors":[],"abstract":"Equation learning methods present a promising tool to aid scientists in the\nmodeling process for biological data. Previous equation learning studies have\ndemonstrated that these methods can infer models from rich datasets, however,\nthe performance of these methods in the presence of common challenges from\nbiological data has not been thoroughly explored. We present an equation\nlearning methodology comprised of data denoising, equation learning, model\nselection and post-processing steps that infers a dynamical systems model from\nnoisy spatiotemporal data. The performance of this methodology is thoroughly\ninvestigated in the face of several common challenges presented by biological\ndata, namely, sparse data sampling, large noise levels, and heterogeneity\nbetween datasets. We find that this methodology can accurately infer the\ncorrect underlying equation and predict unobserved system dynamics from a small\nnumber of time samples when the data is sampled over a time interval exhibiting\nboth linear and nonlinear dynamics. Our findings suggest that equation learning\nmethods can be used for model discovery and selection in many areas of biology\nwhen an informative dataset is used. We focus on glioblastoma multiforme\nmodeling as a case study in this work to highlight how these results are\ninformative for data-driven modeling-based tumor invasion predictions.","url_abs":"http://arxiv.org/abs/2005.09622v1","url_pdf":"http://arxiv.org/pdf/2005.09622v1.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":"learning-equations-from-biological-data-with","repo_url":"https://github.com/biomathlab/PDE-Learning-few-time-samples","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"model-discovery","task_name":"Model Discovery"},{"task_slug":"model-selection","task_name":"Model Selection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}