[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119332-en":3,"doc-seo-119332-105":30,"detail-sidebar-cat-0-en-105":91},{"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":4,"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},119332,1374391975076,"Riley","https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051",8,"Research & Report","Physics-Enhanced Machine Learning - a position paper for dynamical systems investigations","Physics-Enhanced Machine Learning (PEML), also called Scientific Machine Learning, is examined through strategies aimed at dynamical systems. The motivation to move beyond conventional machine learning includes limited informative data, the risk of accurate-but-wrong predictions, treatment of uncertainty, and requirements for explainable and interpretable inference. A general PEML definition is given via four physics/domain-knowledge biases, and three approach families—physics-guided, physics-encoded, and physics-informed—are organized and discussed. Engineering decision-making challenges with complex dynamical systems are analyzed.","arXiv :2405 .05987v3 [ cs .LG] 25 Dec 2024  \nPhysics-Enhanced Machine Learning: a position paper for dynamical systems investigations  \nAlice Cicirello  \nDepartment of Engineering, University of Cambridge, Trumpington Street, CB2 1PZ, Cambridge  \nE-mail: [ac685@cam.ac.uk](ac685@cam.ac.uk)  \nAbstract. This position paper takes a broad look at Physics-Enhanced Machine Learning (PEML) - also known as Scientific Machine Learning - with particular focus to those PEML strategies developed to tackle dynamical systems’ challenges. The need to go beyond Machine Learning (ML) strategies is driven by: (i) limited volume of informative data, (ii) avoiding accurate-but-wrong predictions; (iii) dealing with uncertainties; (iv) providing Explainable and Interpretable inferences. A general definition of PEML is provided by considering four physics and domain knowledge biases, and three broad groups of PEML approaches are discussed: physics-guided, physics-encoded and physics-informed. The advantages and challenges in developing PEML strategies for guiding high-consequence decision making in engineering applications involving complex dynamical systems, are presented.  \n1. Introduction  \nDynamical system models are used in engineering and applied science fields to identify, analyze, control and predict a wide range of behaviours of real-world systems which are typically composed by many components, which may interact with each other, and for which a linear time-invariant modelling assumption is often inadequate [1] . Systems are objects producing a signal (output), depending on other signals (inputs and disturbances) and depending on some initial conditions. Dynamical systems can be used to investigate problems in applied mechanics and structural dynamics that are usually multi-scale, multi-physics, high-dimensional, strongly nonlinear, and time-dependent [1, 2, 3] . Machine Learning (ML) approaches provide a very powerful set of tools for building the nonlinear dynamical systems model directly from observations. However, in many engineering applications, data is typically sparse, noisy, expensive to acquire, and ultimately quite limited. The resulting ML models based on dataonly cannot be fully deployed for guiding high-consequence decision making because they lack (i) generalisation to previously unseen conditions; (ii) interpretability; and (iii) robustness [4] .  \nScientific Machine Learning (SciML) was first mentioned in the report summarising the results of a workshop [4] . In general, SciML refers to the combination of computational science and ML approaches to leverage existing knowledge and physics models within learning schemes [5] . Much of the efforts in SciML have focused on accelerating solvers and on constraining ML-predictions by incorporating physics biases on data-driven architectures [3, 5, 6], consequently, PhysicsInformed Neural Networks (PINNs) architectures [3, 6, 7] are sometimes wrongly perceived asthe only SciML learning scheme. The term Physics-Enhanced Artificial Intelligence (PEAI) was introduced in [9] for “intelligently combining models from the domains of artificial intelligence  \nor machine learning with physical and expert models”. The distinction between Physics-Guided Neural Networks (NNs), Physics-Informed NNs and Physics-Encoded NNs was presented in [13] . Informed Machine Learning (IML) was introduced in [10] to describe prior knowledge integration into the learning process, and a taxonomy was developed to enable a structured categorization of different approaches. Since 2019, the term Physics-Enhanced Machine Learning (PEML) has been used in a broad sense to encompass strategies where “prior physics knowledge is embedded to the learner” [14], especially for dealing with dynamical systems in Engineering.  \nIt is worth noting that development of hybrid physics-data models to tackle real-world Engineering problems have been explored for more than two decades. For example, in Structural Health Monitoring (SHM","cbCaifPVHu71NHGA","https://ap.wps.com/l/cbCaifPVHu71NHGA","pdf",1794383,1,12,"English","en",105,"# Introduction\n## Background on dynamical systems and data limits\n## From SciML to PEML: terminology and taxonomy\n# Why go beyond data-driven for dynamical systems?\n## Drivers of ML adoption and data-driven framing\n## Limits in engineering for high-consequence decisions","[{\"question\":\"What problems in dynamical systems motivate PEML over standard ML?\",\"answer\":\"PEML is motivated by sparse and noisy data, the danger of accurate-but-wrong predictions, the need to handle uncertainty, and the requirement for explainable and interpretable inferences for high-consequence engineering decisions.\"},{\"question\":\"How does the paper define Physics-Enhanced Machine Learning (PEML)?\",\"answer\":\"It provides a general definition using four physics and domain-knowledge biases, enabling a framework that distinguishes three broad groups: physics-guided, physics-informed, and physics-encoded approaches.\"},{\"question\":\"What are the three broad families of PEML approaches discussed?\",\"answer\":\"The paper discusses three categories: physics-guided approaches, physics-encoded approaches, and physics-informed approaches, each incorporating physics or domain knowledge into the learning and modeling process differently.\"}]","Physics-Enhanced Machine Learning - 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