4.3 Article

Dimensionally consistent learning with Buckingham Pi

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Engineering, Industrial

Mechanistic artificial intelligence (mechanistic-AI) for modeling, design, and control of advanced manufacturing processes: Current state and perspectives

Mojtaba Mozaffar et al.

Summary: This study reviews recent advances in Mechanistic-AI in the field of manufacturing, introducing the benefits of this methodology and approaches to improve data requirements, generalizability, and explainability. It also identifies gaps in current research and directions for further development.

JOURNAL OF MATERIALS PROCESSING TECHNOLOGY (2022)

Article Engineering, Multidisciplinary

Hierarchical Deep Learning Neural Network (HiDeNN): An artificial intelligence (AI) framework for computational science and engineering

Sourav Saha et al.

Summary: The unified AI-framework HiDeNN is proposed for solving challenging computational science and engineering problems, with demonstrated accuracy, efficiency, and versatility in three example problems. The framework shows potential for advanced engineering problems that require state-of-the-art AI approaches.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2021)

Article Multidisciplinary Sciences

Learning dominant physical processes with data-driven balance models

Jared L. Callaham et al.

Summary: Traditional physics-based modeling relies on approximating observed dynamics as a balance between dominant processes within asymptotic regimes, but researchers have proposed a new approach using equation space to identify neglected terms in non-asymptotic regimes. Their data-driven balance models successfully delineate dominant physics in systems like turbulence, combustion, nonlinear optics, geophysical fluids, and neuroscience.

NATURE COMMUNICATIONS (2021)

Review Environmental Sciences

Bridging observations, theory and numerical simulation of the ocean using machine learning

Maike Sonnewald et al.

Summary: Progress in physical oceanography has been enhanced by the use of machine learning techniques, offering new possibilities for study and discovery. Challenges unique to ocean study, such as sparse spatial data and limited time series, can be addressed with ML. The use of ML in observations, theory, and numerical modeling shows promising opportunities for advancing oceanographic exploration.

ENVIRONMENTAL RESEARCH LETTERS (2021)

Review Physics, Applied

Physics-informed machine learning

George Em Karniadakis et al.

Summary: Physics-informed learning seamlessly integrates data and mathematical models through neural networks or kernel-based regression networks for accurate inference of realistic and high-dimensional multiphysics problems. Challenges remain in incorporating noisy data seamlessly, complex mesh generation, and addressing high-dimensional problems.

NATURE REVIEWS PHYSICS (2021)

Article Computer Science, Artificial Intelligence

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Lu Lu et al.

Summary: This study extends the capabilities of neural networks with the introduction of the deep operator network (DeepONet), which can be used to learn various operators, including explicit and implicit operators. Different formulations of the input function space were studied and their effect on generalization error for 16 diverse applications was examined.

NATURE MACHINE INTELLIGENCE (2021)

Review Mechanics

Machine Learning for Fluid Mechanics

Steven L. Brunton et al.

ANNUAL REVIEW OF FLUID MECHANICS, VOL 52 (2020)

Article Mechanics

Data-driven dimensional analysis of heat transfer in irradiated particle-laden turbulent flow

Lluis Jofre et al.

INTERNATIONAL JOURNAL OF MULTIPHASE FLOW (2020)

Article Multidisciplinary Sciences

Al Feynman: A physics-inspired method for symbolic regression

Silviu-Marian Udrescu et al.

SCIENCE ADVANCES (2020)

Review Mechanics

Turbulence Modeling in the Age of Data

Karthik Duraisamy et al.

ANNUAL REVIEW OF FLUID MECHANICS, VOL 51 (2019)

Article Computer Science, Interdisciplinary Applications

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

M. Raissi et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2019)

Article Astronomy & Astrophysics

Unsupervised Learning Reveals Geography of Global Ocean Dynamical Regions

Maike Sonnewald et al.

EARTH AND SPACE SCIENCE (2019)

Article Mathematics, Interdisciplinary Applications

Lurking Variable Detection via Dimensional Analysis

Zachary del Rosario et al.

SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION (2019)

Article Multidisciplinary Sciences

Data-driven discovery of coordinates and governing equations

Kathleen Champion et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2019)

Article Physics, Fluids & Plasmas

Perspective on machine learning for advancing fluid mechanics

M. P. Brenner et al.

PHYSICAL REVIEW FLUIDS (2019)

Article Mechanics

Constrained sparse Galerkin regression

Jean-Christophe Loiseau et al.

JOURNAL OF FLUID MECHANICS (2018)

Article Multidisciplinary Sciences

Turbulent superstructures in Rayleigh-Benard convection

Ambrish Pandey et al.

NATURE COMMUNICATIONS (2018)

Article Multidisciplinary Sciences

Reconstruction of normal forms by learning informed observation geometries from data

Or Yair et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2017)

Article Multidisciplinary Sciences

Data-driven discovery of partial differential equations

Samuel H. Rudy et al.

SCIENCE ADVANCES (2017)

Article Multidisciplinary Sciences

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

Steven L. Brunton et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2016)

Article Multidisciplinary Sciences

Osmotic spreading of Bacillus subtilis biofilms driven by an extracellular matrix

Agnese Seminara et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2012)

Article Multidisciplinary Sciences

Distilling Free-Form Natural Laws from Experimental Data

Michael Schmidt et al.

SCIENCE (2009)

Article Physics, Multidisciplinary

Geometry and physics of wrinkling

E Cerda et al.

PHYSICAL REVIEW LETTERS (2003)