[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122905-en":3,"doc-seo-122905-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},122905,137441390410,"Hazel","https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984",8,"Research & Report","STEP - extraction of underlying physics with robust machine learning","Inverse problems in modern physics require extracting physical quantities from experimental measurements, yet end-to-end machine learning often loses physical information encoded in existing models, demanding overly complex estimators and reducing accuracy, especially in low-data and high-noise regimes. STEP (surrogate training embedded in physics) constructs a neural surrogate by making the physical model auto-differentiable and embedding ML only for unknown components, training via loss on total model output backpropagated through known physics. STEP generalizes well and remains robust against overfitting and significant noise, enabling dynamic kernel deconvolution for resonant inelastic X-ray scattering spectra with surprisingly simple architectures.","Cite this article: Alaa El-Din KK, Forte A, Kasim  \nMF, Miniati F, Vinko SM. 2024 STEP: extraction of underlying physics with robust machine learning.  \nR. Soc. Open Sci. 11: 231374.  \n[https://doi.org/10.1098/rsos.231374](https://doi.org/10.1098/rsos.231374)  \n[Received: 19 September 2023](Received: 19 September 2023)  \n[Accepted: 20 March 2024](Accepted: 20 March 2024)  \nSubject Category:  \nPhysics and biophysics  \nSubject Areas:  \nspectroscopy, artificial intelligence, plasma physics  \nKeywords:  \nphysics, machine learning, artificial intelligence, differentiable modelling, resonant inelastic X-ray scattering, spectroscopy  \nAuthor for correspondence:  \nKarim K. Alaa El-Din  \ne-mails: [karim.alaael-din@physics.ox.ac.uk](karim.alaael-din@physics.ox.ac.uk); [karim@aedin.dev](karim@aedin.dev)  \nElectronic supplementary material is available online at [https://doi.org/10.6084/](https://doi.org/10.6084/)[ ](https://doi.org/10.6084/)[m9.figshare.c.7247039.](m9.figshare.c.7247039.)  \nSTEP: extraction of underlying physics with robust machine learning  \nKarim K. Alaa El-Din1, Alessandro Forte1, Muhammad Firmansyah Kasim1,2, Francesco Miniati1 and Sam M. Vinko1,3  \n1Department of Physics, University of Oxford, Oxford, UK 2Machine Discovery, Oxford OX4 4GP, UK  \n3Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot, OX11 0QX, UK  KKAE-D, 0000-0001-9140-4489  \nA prevalent class of challenges in modern physics are inverse problems, where physical quantities must be extracted from experimental measurements. End-to-end machine learning approaches to inverse problems typically require constructing sophisticated estimators to achieve the desired accuracy, largely because they need to learn the complex underlying physical model. Here, we discuss an alternative paradigm: by making the physical model auto-differentiable we can construct a neural surrogate to represent the unknown physical quantity sought, while avoiding having to relearn the known physics entirely. We dub this process surrogate training embedded in physics (STEP) and illustrate that it generalizes well and is robust against overfitting and significant noise in the data. We demonstrate how STEP can be applied to perform dynamic kernel deconvolution to analyse resonant inelastic X-ray scattering spectra and show that surprisingly simple estimator architectures suffice to extract the relevant physical information.  \n1. Introduction  \nIn modern science, complex integrated experiments are a key tool for discovery [1–3] . They allow researchers to probe phenomena that would otherwise be inaccessible but provide only indirect or integrated measurement data. Therefore, the extraction of quantities of interest from these data constitutes a significant and important challenge in its own right. Explicitly inverting complex models for integrated experiments is often computationally prohibitive or ineffective, particularly in a low-data, highnoise regime. While machine learning (ML) tends to perform very  \n© 2024 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License [http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, provided the original author and source are credited.  \nwell for such inverse problems [4–6], it frequently struggles with accuracy when simply used as an end-toend replacement for the inverse model. A key problem with such end-to-end approaches is the loss of physical information encoded in existing models. This information has tobe captured directly by the ML estimator, leading to massively increased estimator complexity to account for lost inductive bias.  \nTo address this challenge, we describe an approach that combines existing physical models with ML in a process we dub surrogate training embedded in physics (STEP) . In STEP, we explicitly choose a separation of the components of the physical model into those assumed to be known a prio","cbCailR0L2buWjfp","https://ap.wps.com/l/cbCailR0L2buWjfp","pdf",1260771,1,12,"English","en",105,"# Introduction\n## Surrogate training embedded in physics (STEP)\n## Robustness to noise and overfitting\n## Application to kernel deconvolution and RIXS spectra","[{\"question\":\"What problem does STEP address in physics inverse problems?\",\"answer\":\"STEP targets inverse problems where physical quantities must be extracted from indirect experimental measurements. It addresses the accuracy and complexity issues of end-to-end machine learning by preserving known physics during training.\"},{\"question\":\"How does STEP differ from end-to-end machine learning estimators?\",\"answer\":\"STEP separates the physical model into known components and unknown components, keeps the known physics, and trains an ML surrogate only for the unknown part. Gradients are propagated through the known physics using the auto-differentiable model.\"},{\"question\":\"Why is STEP robust against overfitting and noisy data?\",\"answer\":\"The ML estimator is constrained to represent only the unknown subset of the model, while the known physics provides strong inductive bias. This reduced complexity yields robustness under data paucity and low signal-to-noise ratio.\"}]","STEP - extraction of underlying physics with robust machine learning | PDF",1785813589,30,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"step-extraction-of-underlying-physics-with-robust-machine-learning","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/step-extraction-of-underlying-physics-with-robust-machine-learning/122905/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-04",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does STEP address in physics inverse problems?","Question",{"text":76,"@type":77},"STEP targets inverse problems where physical quantities must be extracted from indirect experimental measurements. It addresses the accuracy and complexity issues of end-to-end machine learning by preserving known physics during training.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does STEP differ from end-to-end machine learning estimators?",{"text":81,"@type":77},"STEP separates the physical model into known components and unknown components, keeps the known physics, and trains an ML surrogate only for the unknown part. Gradients are propagated through the known physics using the auto-differentiable model.",{"name":83,"@type":74,"acceptedAnswer":84},"Why is STEP robust against overfitting and noisy data?",{"text":85,"@type":77},"The ML estimator is constrained to represent only the unknown subset of the model, while the known physics provides strong inductive bias. 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