{"id":29115,"date":"2025-10-06T12:09:01","date_gmt":"2025-10-06T06:24:01","guid":{"rendered":"https:\/\/www.revoscience.com\/en\/?p=29115"},"modified":"2025-10-06T12:09:09","modified_gmt":"2025-10-06T06:24:09","slug":"new-ai-techniques-to-solve-complex-equations-in-physics","status":"publish","type":"post","link":"https:\/\/www.revoscience.com\/en\/new-ai-techniques-to-solve-complex-equations-in-physics\/","title":{"rendered":"New AI techniques to solve complex equations in physics"},"content":{"rendered":"\n
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Researchers from the Institute of Cosmos Sciences of the University of Barcelona (ICCUB) have developed a new framework based on machine learning that significantly improves the resolution of complex differential equations, especially in cases where traditional methods present difficulties.<\/p>\n\n\n\n

The study, led by experts Pedro Taranc\u00f3n-\u00c1lvarez and Pablo Tejerina-P\u00e9rez, has been published in the journal\u00a0Communications Physics<\/em><\/a>.<\/p>\n\n\n\n

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve very different scales or highly sensitive parameters), they become extremely difficult to solve. This is especially relevant in inverse problems, where scientists try to deduce unknown physical laws from observed data.<\/p>\n\n\n\n

To tackle this challenge, the researchers have enhanced the capabilities of Physics-Informed Neural Networks (PINNs), a type of artificial intelligence that incorporates physical laws into its learning process.<\/p>\n\n\n\n

Their approach combines two innovative techniques: Multi-Head (MH) training, which allows the neural network to learn a general space of solutions for a family of equations \u2014 rather than just one specific case \u2014, and Unimodular Regularization (UR), inspired by concepts from differential geometry and general relativity, which stabilizes the learning process and improves the network\u2019s ability to generalize to new, more difficult problems.<\/p>\n\n\n\n

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These methods were successfully applied to three increasingly complex systems: the flame equation, the Van der Pol oscillator, and the Einstein Field Equations in a holographic context. In the latter case, the researchers were able to recover unknown physical functions from synthetic data, a task previously considered nearly impossible.<\/p>\n\n\n\n

\u201cRecent advances in machine learning training efficiency have made PINNs increasingly popular in the past few years,\u201d says Pedro Taranc\u00f3n-\u00c1lvarez, doctoral student at ICCUB. \u201cThis framework offers several novel features compared to traditional numerical methods, most notably the ability to solve inverse problems.\u201d<\/p>\n\n\n\n

\u201cSolving these inverse problems is like trying to find the solution to a problem that is missing a piece; the correct piece will have a unique solution, incorrect ones may not have a solution, or multiple ones,\u201d adds Pablo Tejerina-P\u00e9rez, doctoral student at ICCUB. \u201cOne could try to invent the missing piece of the problem and then see if it can be solved properly \u2014 our PINNs do the same, but in a much smarter and efficient way than we could.\u201d<\/p>\n\n\n\n

The study was carried out in collaboration with Ra\u00fal Jim\u00e9nez (ICREA-ICCUB) and Pavlos Protopapas (Harvard University) and was funded by the Spanish Ministry of Science and Innovation and the Maria de Maeztu Excellence Programme.<\/p>\n","protected":false},"excerpt":{"rendered":"

Researchers from the Institute of Cosmos Sciences of the University of Barcelona (ICCUB) have developed a new framework based on machine learning that significantly improves the resolution of complex differential equations, especially in cases where traditional methods present difficulties.<\/p>\n","protected":false},"author":2,"featured_media":29116,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17],"tags":[],"class_list":["post-29115","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-research"],"featured_image_urls":{"full":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai.webp",640,448,false],"thumbnail":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai-200x200.webp",200,200,true],"medium":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai.webp",640,448,false],"medium_large":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai.webp",640,448,false],"large":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai.webp",640,448,false],"1536x1536":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai.webp",640,448,false],"2048x2048":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai.webp",640,448,false],"ultp_layout_landscape_large":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai.webp",640,448,false],"ultp_layout_landscape":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai.webp",640,448,false],"ultp_layout_portrait":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai-600x448.webp",600,448,true],"ultp_layout_square":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai-600x448.webp",600,448,true],"newspaper-x-single-post":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai.webp",640,448,false],"newspaper-x-recent-post-big":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai-550x360.webp",550,360,true],"newspaper-x-recent-post-list-image":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai-95x65.webp",95,65,true],"web-stories-poster-portrait":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai.webp",640,448,false],"web-stories-publisher-logo":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai-96x96.webp",96,96,true],"web-stories-thumbnail":["https:\/\/www.revoscience.com\/en\/wp-content\/uploads\/2025\/10\/communication-physics-ith-ai-150x105.webp",150,105,true]},"author_info":{"info":["RevoScience"]},"category_info":"Research<\/a>","tag_info":"Research","comment_count":"0","_links":{"self":[{"href":"https:\/\/www.revoscience.com\/en\/wp-json\/wp\/v2\/posts\/29115","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.revoscience.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.revoscience.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.revoscience.com\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.revoscience.com\/en\/wp-json\/wp\/v2\/comments?post=29115"}],"version-history":[{"count":1,"href":"https:\/\/www.revoscience.com\/en\/wp-json\/wp\/v2\/posts\/29115\/revisions"}],"predecessor-version":[{"id":29118,"href":"https:\/\/www.revoscience.com\/en\/wp-json\/wp\/v2\/posts\/29115\/revisions\/29118"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.revoscience.com\/en\/wp-json\/wp\/v2\/media\/29116"}],"wp:attachment":[{"href":"https:\/\/www.revoscience.com\/en\/wp-json\/wp\/v2\/media?parent=29115"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.revoscience.com\/en\/wp-json\/wp\/v2\/categories?post=29115"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.revoscience.com\/en\/wp-json\/wp\/v2\/tags?post=29115"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}