[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125999-en":3,"doc-seo-125999-105":31,"detail-sidebar-cat-0-en-105":93},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},125999,687207024643,"Oliver","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Uncertainty Quantification and Propagation in Atomistic Machine Learning","Machine learning in chemical and materials science often yields unreliable predictions when limited physics constraints and data scarcity lead to poor out-of-distribution behavior. Uncertainty quantification measures prediction confidence, while uncertainty propagation transfers that uncertainty to downstream chemical and materials simulations. This review organizes UQ and UP approaches for atomistic machine learning under a unified probabilistic modeling perspective, and evaluates methods via accuracy, precision, calibration, and efficiency metrics, including model recalibration strategies. It also surveys benchmarks on molecular and materials datasets and discusses challenges and future directions for UQ and UP.","arXiv :2405 .02461v3 [ cond-mat .mtrl-sci ] 20 Aug 2024  \nUncertainty Quantification and Propagation in Atomistic Machine Learning  \nJin Dai, Santosh Adhikari, and Mingjian Wen ∗  \nDepartment of Chemical and Biomolecular Engineering,  \nUniversity of Houston, Houston, TX, 77204, USA  \n(Dated: August 21, 2024)  \nMachine learning (ML) offers promising new approaches to tackle complex problems and has been increasingly adopted in chemical and materials sciences. Broadly speaking, ML models employ generic mathematical functions and attempt to learn essential physics and chemistry from a large amount of data. Consequently, because of the limited physical or chemical principles in the functional form, the reliability of the predictions is oftentimes not guaranteed, particularly for data far out of distribution. It is critical to quantify the uncertainty in model predictions and understand how the uncertainty propagates to downstream chemical and materials applications. Herein, we review existing uncertainty quantification (UQ) and uncertainty propagation (UP) methods for atomistic ML under a united framework of probabilistic modeling. We first categorize the UQ methods, with the aim to elucidate the similarities and differences between them. We also discuss performance metrics to evaluate the accuracy, precision, calibration, and efficiency of the UQ methods and techniques for model recalibration. With these metrics, we survey existing benchmark studies of the UQ methods using molecular and materials datasets. Furthermore, we discuss UP methods to propagate the uncertainty obtained from ML models in widely used materials and chemical simulation techniques, such as molecular dynamics and microkinetic modeling. We also provide remarks on the challenges and future opportunities of UQ and UP in atomistic ML.  \nKeywords: Uncertainty Quantification, Machine Learning, Model Calibration, Reliability, Molecular Simulation  \n1. INTRODUCTION  \nSince the breakthrough in image recognition using deep neural networks (NNs) back in 2012 (Krizhevsky et al. 2012), machine learning (ML) approaches have been increasingly leveraged to study complex chemical and materials systems. They have achieved remarkable successes, from designing catalysts (Back et al. 2019 , Zahrt et al. 2019), to discovering functional materials (Axelrod et al. 2022 , Rao et al. 2022) and studying protein folding (Baek et al. 2021 , Jumper et al. 2021), to name a few. The ML approaches applied in these tasks take advantage of a wide range of techniques, but they share a common core idea: modeling molecules, materials, and chemical reactions at the atomic scale and looking for patterns and trends in atomic data, which we refer to as atomistic machine learning.  \nOne of the most impactful developments in atomistic ML for chemical and materials science is creating interatomic potentials (i.e., force fields) to model the interactions between atoms. This goes from early endeavors that model individual molecular/material systems (e.g. , the feed-forward NN potential (Behler 2021 , Behler and Parrinello 2007) and Gaussian approximation potential (GAP) (Bart´ok et al. 2010 , Deringer et al. 2021)) to more recent efforts to build universal potentials for the entire periodic table (e.g., M3GNet (Chen and Ong 2022), CHGNet (Deng et al. 2023) and MACE-MP (Batatia et al. 2024)) . While interatomic potentials remain an active focus of atomistic ML, the field has moved beyond  \n∗ [mjwen@uh.edu](mjwen@uh.edu)  \nand expanded to encompass the prediction of arbitrarily complicated molecular, materials, and reaction properties (Ceriotti 2022 , Fedik et al. 2022) . These include molecular dipole moments (Gastegger et al. 2021 , Unke and Meuwly 2019), bond strength (St. John et al. 2020 , Wen et al. 2021), high-rank material tensors (Pakornchote et al. 2023 , Wen et al. 2024), neutron, x-ray, and vibrational spectroscopies (Chen et al. 2021 , Schienbein 2023), and reaction rates and yields (Heid and Gr","cbCaig4m580HT70J","https://ap.wps.com/l/cbCaig4m580HT70J","pdf",11304017,6,1,24,"English","en",105,"# Introduction\n## Background of atomistic machine learning in chemistry and materials\n## Reliability concerns and sources of uncertainty\n## Types of uncertainty: aleatoric and epistemic\n## Uncertainty quantification (UQ) and propagation (UP) workflow","[{\"question\":\"Why is uncertainty quantification necessary in atomistic machine learning?\",\"answer\":\"Because limited physical constraints and limited training data can make predictions unreliable, especially for out-of-distribution inputs. Quantifying uncertainty provides a measure of confidence and helps flag unreliable regions.\"},{\"question\":\"What are the two main types of uncertainty discussed?\",\"answer\":\"The document distinguishes aleatoric uncertainty (data uncertainty from irreducible noise) and epistemic uncertainty (model uncertainty from limitations in knowledge, model parameters, architecture, and hyperparameters).\"},{\"question\":\"How does uncertainty propagation relate to uncertainty quantification?\",\"answer\":\"Uncertainty quantification estimates uncertainty from atomistic ML models, and uncertainty propagation transmits that uncertainty to downstream chemical and materials simulation tasks such as molecular dynamics and microkinetic modeling.\"}]","Uncertainty Quantification and Propagation in Atomistic Machine Learning | PDF",1785902477,60,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":88,"head_meta":90,"extra_data":92,"updated_unix":29},"uncertainty-quantification-and-propagation-in-atomistic-machine-learning","",{"@graph":37,"@context":87},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/research-report/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/document/uncertainty-quantification-and-propagation-in-atomistic-machine-learning/125999/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-22","2026-08-05",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83],{"name":74,"@type":75,"acceptedAnswer":76},"Why is uncertainty quantification necessary in atomistic machine learning?","Question",{"text":77,"@type":78},"Because limited physical constraints and limited training data can make predictions unreliable, especially for out-of-distribution inputs. Quantifying uncertainty provides a measure of confidence and helps flag unreliable regions.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"What are the two main types of uncertainty discussed?",{"text":82,"@type":78},"The document distinguishes aleatoric uncertainty (data uncertainty from irreducible noise) and epistemic uncertainty (model uncertainty from limitations in knowledge, model parameters, architecture, and hyperparameters).",{"name":84,"@type":75,"acceptedAnswer":85},"How does uncertainty propagation relate to uncertainty quantification?",{"text":86,"@type":78},"Uncertainty quantification estimates uncertainty from atomistic ML models, and uncertainty propagation transmits that uncertainty to downstream chemical and materials simulation tasks such as molecular dynamics and microkinetic modeling.","https://schema.org",{"og:url":53,"og:type":89,"og:title":13,"og:site_name":60,"og:description":14},"article",{"robots":91,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":94},[95,99,103,107,111,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":96,"show_sort_weight":97,"slug":98},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":100,"show_sort_weight":101,"slug":102},"Literature",80,"literature",{"id":54,"doc_module":4,"doc_module_name":47,"category_name":104,"show_sort_weight":105,"slug":106},"Exam",70,"exam",{"id":108,"doc_module":4,"doc_module_name":47,"category_name":109,"show_sort_weight":30,"slug":110},5,"Comic","comic",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":112,"show_sort_weight":113,"slug":114},"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":47,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":47,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":47,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":47,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":47,"category_name":137,"show_sort_weight":108,"slug":138},19,"General","general"]