Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone. However, positing a universal physical law from data is challenging without simultaneously proposing an accompanying discrepancy model to account for the inevitable mismatch between theory and measurements. By revisiting the classic problem of modeling falling objects of different size and mass, we highlight a number of nuanced issues that must be addressed by modern data-driven methods for automated physics discovery. Specifically, we show that measurement noise and complex secondary physical mechanisms, like unsteady fluid drag forces, can obscure the underlying law of gravitation, leading to an erroneous model. We use the sparse identification of nonlinear dynamics (SINDy) method to identify governing equations for real-world measurement data and simulated trajectories. Incorporating into SINDy the assumption that each falling object is governed by a similar physical law is shown to improve the robustness of the learned models, but discrepancies between the predictions and observations persist due to subtleties in drag dynamics. This work highlights the fact that the naive application of ML/AI will generally be insufficient to infer universal physical laws without further modification.
Automated discovery of symbolic laws governing skill acquisition from naturally occurring data
National Engineering Research Center of Educational Big Data, Central China Normal University（华中师范大学教育大数据国家工程研究中心）；Faculty of Artificial Intelligence in Education, Central China Normal University（华中师范大学人工智能教育学部）；National Engineering Research Center for E-learning, Central China Normal University（华中师范大学国家数字化学习工程技术研究中心）
AI-Newton: A Concept-Driven Physical Law Discovery System without Prior Physical Knowledge
School of Physics, Peking University, Beijing 100871, China（物理系，北京大学，北京100871，中国）；Center for High Energy Physics, Peking University, Beijing 100871, China（高能物理中心，北京大学，北京100871，中国）
Can LLMs Discover Scientific Laws in Real and Parallel Worlds?
University of California San Diego（加州大学圣地亚哥分校）；University of California, Irvine（加州大学欧文分校）；Cushing Academy（卡欣学院）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials
Sibley School of Mechanical and Aerospace Engineering, Cornell University（科林斯大学机械与航空航天工程学院）；Department of Materials Science and Engineering, Technion - Israel Institute of Technology（技术学院-以色列理工学院材料科学与工程系）；Sandia National Laboratories（桑地亚国家实验室）；Center for Applied Mathematics, Ithaca, NY 14850（应用数学中心）；Pasteur Labs, Brooklyn, NY 11205（帕斯特实验室）
Symbolic Graph Networks for Robust PDE Discovery from Noisy Sparse Data
School of Software Engineering, Chengdu University of Information Technology（成都信息科技学院软件工程学院）；School of Statistics, Chengdu University of Information Technology（成都信息科技学院统计学院）；College of Applied Mathematics, Chengdu University of Information Technology（成都信息科技学院应用数学学院）；Key Laboratory of Mathematical Meteorology, Chengdu University of Information Technology（成都信息科技学院数学气象重点实验室）
Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations
Carnegie Mellon University（卡内基梅隆大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；Ningbo Institute of Digital Twin, Eastern Institute of Technology（东方理工大学宁波数字孪生研究院）；Hefei University of Technology（合肥工业大学）；RealAI（瑞莱智慧）；Tsinghua University（清华大学）
Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization
Zhejiang Key Laboratory of Industrial Intelligence and Digital Twin, Eastern Institute of Technology（浙江工业智能与数字孪生重点实验室，东方理工高等研究院）；Department of Electrical Engineering, Tsinghua University（清华大学电机工程系）；Ningbo Institute of Digital Twin, Eastern Institute of Technology（东方理工高等研究院宁波数字孪生研究院）
LLM4ED: Large Language Models for Automatic Equation Discovery
College of Engineering（工学院）；Peking University（北京大学）；Ningbo Institute of Digital Twin（宁波数字孪生研究院）；Eastern Institute of Technology（东方理工学院）；School of Environmental Science and Engineering（环境科学与工程学院）；Southern University of Science and Technology（南方科技大学）；National Center for Applied Mathematics Shenzhen (NCAMS)（深圳国家应用数学中心）
GPT-Micro: A large language paradigm for accelerated, inexpensive, and thermodynamics-consistent discovery of constitutive models in manufacturing
Department of Mechanical and Aerospace Engineering, Rutgers University（罗格斯大学机械与航空航天工程系）；Department of Mechanical, Aerospace & Manufacturing Engineering, University of Connecticut（康涅狄格大学机械、航空航天与制造工程系）；Edison Welding Institute（埃迪森焊接研究所）；Manufacturing Science Division, Oak Ridge National Laboratory（橡树岭国家实验室制造科学分会）；Department of Aerospace and Mechanical Engineering, University of Texas at El Paso（德克萨斯州埃尔帕索大学航空航天与机械工程系）
CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data
Department of BioMechanical Engineering, Faculty of Mechanical Engineering, Delft University of Technology（生物机械工程系，机械工程学院，代尔夫特理工大学）；Department of Material Science Engineering, Faculty of Mechanical Engineering, Delft University of Technology（材料科学与工程系，机械工程学院，代尔夫特理工大学）
Data-driven discovery of governing differential equations across physical systems
School of Computer Science, Shanghai Jiao Tong University（上海交通大学计算机科学与工程学院）；Ningbo Key Laboratory of Advanced Manufacturing Simulation, Eastern Institute of Technology（东部理工学院宁波先进制造仿真重点实验室）；The State Key Lab of Brain-Machine Intelligence, Zhejiang University（浙江大学脑机智能全国重点实验室）；Department of Statistics and Data Science, Yale University（耶鲁大学统计与数据科学系）；Department of Chemical and Environmental Engineering, Yale University（耶鲁大学化学与环境工程系）；Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学高瓴人工智能学院）；School of Engineering Sciences, University of Chinese Academy of Sciences（中国科学院大学工程科学学院）；DP Technology
When Literature Data Mislead Artificial Intelligence in Materials Discovery
Advanced Institute for Materials Research (WPI-AIMR), Tohoku University（东北大学材料研究高等研究院（WPI-AIMR））；The University of Tokyo（东京大学）；Institute for Materials Research, Tohoku University（东北大学材料研究所）
Machine Discovery of Partial Differential Equations from Spatiotemporal Data
Huazhong University of Science and Technology（华中科技大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Georgia Institute of Technology（佐治亚理工学院）；Wuhan University（武汉大学）；University of Cambridge（剑桥大学）；University of Luxembourg（卢森堡大学）；Weill Cornell Medical College（威尔康奈尔医学院）
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；The University of Hong Kong（香港大学）；University of Electronic Science and Technology of China（电子科技大学）；Tsinghua University（清华大学）；Peking University（北京大学）
Discovering Causal Relations and Equations from Data
Universitat de València（瓦伦西亚大学）；German Aerospace Center（德国航空航天中心）；Technische Universität Berlin（柏林工业大学）；University of Tübingen（图宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Bournemouth University（伯恩茅斯大学）；Heidelberg University（海德堡大学）；KTH Royal Institute of Technology（KTH皇家理工学院）；New York University（纽约大学）
Uncovering Neural Scaling Laws in Molecular Representation Learning
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of California, Los Angeles（加州大学洛杉矶分校）；University of Washington（华盛顿大学）；Cornell University（康奈尔大学）；The Chinese University of Hong Kong（香港中文大学）
Discovering physical laws with parallel symbolic enumeration
Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学人工智能学院）；School of Engineering Science, University of Chinese Academy of Sciences（中国科学院大学工程科学学院）；State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所非线性力学重点实验室）；Department of Computer Science and Engineering, HKUST（香港科技大学计算机科学与工程系）
