4.6 Article

Scientific Machine Learning Through Physics-Informed Neural Networks: Where we are and What's Next

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Summary: This paper investigates the performance of PINNs for discovering the frequency dynamics of future power systems, aiming to address challenges such as stronger non-linearities of low-inertia systems, increased measurement noise, and limited availability of data.

2021 IEEE MADRID POWERTECH (2021)

Article Computer Science, Artificial Intelligence

Poisson CNN: Convolutional neural networks for the solution of the Poisson equation on a Cartesian mesh

Ali Girayhan Ozbay et al.

Summary: The study introduces a novel fully convolutional neural network architecture for solving the Poisson equation, providing flexibility in handling partial differential equations. The model is able to address boundary conditions using a unique approach and is trained with a novel loss function. Results show that the model performs well in solving the Poisson equation, aiding in improving computational efficiency.

DATA-CENTRIC ENGINEERING (2021)

Article Mathematics, Applied

PHYSICS-INFORMED NEURAL NETWORKS WITH HARD CONSTRAINTS FOR INVERSE DESIGN\ast

Lu Lu et al.

Summary: Inverse design, such as topology optimization, is widely used in engineering for achieving targeted properties by optimizing designed geometries. The proposed physics-informed neural networks with hard constraints (hPINNs) can effectively solve topology optimization problems without the need for a large dataset, demonstrating smoother design outcomes compared to conventional methods.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2021)

Article Computer Science, Information Systems

The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?

Stefano Markidis

Summary: The study explores the potential of Physics-Informed Neural Networks (PINN) as linear solvers for solving partial differential equations, particularly focusing on the Poisson equation. It is found that low-frequency components of the solution converge quickly, while accurate solutions for high frequencies require a significantly longer time. The integration of PINNs into traditional linear solvers leads to the development of new solvers with performance comparable to high-performance solvers such as PETSc conjugate gradient linear solvers.

FRONTIERS IN BIG DATA (2021)

Article Mathematics, Applied

UNDERSTANDING AND MITIGATING GRADIENT FLOW PATHOLOGIES IN PHYSICS-INFORMED NEURAL NETWORKS

Sifan Wang et al.

Summary: The study reviews recent advances in scientific machine learning, focusing specifically on the effectiveness of physics-informed neural networks in predicting outcomes of physical systems and discovering hidden physics from noisy data. It also proposes a learning rate annealing algorithm and a novel neural network architecture to address numerical stiffness issues in training constrained neural networks.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2021)

Article Computer Science, Interdisciplinary Applications

Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Ehsan Kharazmi et al.

Summary: This study employs physics-informed neural networks to analyze various epidemiological models, identifying time-dependent parameters and data-driven fractional differential operators, while inferring the spread of COVID-19 in different regions. The results show that identifying time-dependent parameters using neural networks is suitable for integer-order and time-delay models, while determining different time-dependent derivative orders using neural networks is suitable for fractional differential models.

NATURE COMPUTATIONAL SCIENCE (2021)

Article Computer Science, Hardware & Architecture

Recent advance in machine learning for partial differential equation

Ka Chun Cheung et al.

Summary: Machine learning methods have been successfully applied in various fields, including scientific computing, to solve complex problems such as partial differential equations. This data-driven approach has shown promising results in improving computational efficiency and model accuracy.

CCF TRANSACTIONS ON HIGH PERFORMANCE COMPUTING (2021)

Article Computer Science, Artificial Intelligence

Towards neural Earth system modelling by integrating artificial intelligence in Earth system science

Christopher Irrgang et al.

Summary: In recent years, artificial intelligence (AI) methods have been increasingly used to enhance Earth and climate modeling. This Perspective examines the opportunity to go further and build hybrid systems that integrate AI tools and models based on physical process knowledge to make more efficient use of daily observational data streams.

NATURE MACHINE INTELLIGENCE (2021)

Article Physics, Fluids & Plasmas

Reconstruction of nanoscale particles from single-shot wide-angle free-electron-laser diffraction patterns with physics-informed neural networks

Thomas Stielow et al.

Summary: Single-shot wide-angle diffraction imaging is a method widely used for investigating the structure of noncrystallizing objects, with no need for tomographic measurements to reconstruct the object's three-dimensional structure. Neural networks excel in image processing tasks and can be utilized for reconstructing object structures.

PHYSICAL REVIEW E (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)

Article Mathematics, Applied

DeepXDE: A Deep Learning Library for Solving Differential Equations

Lu Lu et al.

Summary: This article introduces an overview, implementation and applications of Physics-Informed Neural Networks (PINNs), along with a new residual-based adaptive refinement (RAR) method. By comparing with finite element methods, the advantages of PINNs and the versatile applications of the Python library DeepXDE are demonstrated. Overall, DeepXDE contributes to the more rapid development of the emerging scientific machine learning field.

SIAM REVIEW (2021)

Proceedings Paper Computer Science, Hardware & Architecture

Distributed Multigrid Neural Solvers on Megavoxel Domains

Aditya Balu et al.

Summary: The study focuses on the distributed training of large scale neural networks as PDE solvers, introducing a scalable framework that integrates multigrid technique and distributed deep learning framework to significantly reduce solve time and predict output solutions at high resolutions.

SC21: INTERNATIONAL CONFERENCE FOR HIGH PERFORMANCE COMPUTING, NETWORKING, STORAGE AND ANALYSIS (2021)

Proceedings Paper Acoustics

Modeling of the Forward Wave Propagation Using Physics-Informed Neural Networks

Shaikhah Alkhadhr et al.

Summary: The article discusses the importance of simulating the wave equation in medical ultrasound applications, highlights the potential of deep neural networks for solving PDEs, and presents the use of PINNs to simulate the numerical solution of the wave equation.

INTERNATIONAL ULTRASONICS SYMPOSIUM (IEEE IUS 2021) (2021)

Review Computer Science, Interdisciplinary Applications

A Survey of Deep Learning and Its Applications: A New Paradigm to Machine Learning

Shaveta Dargan et al.

ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING (2020)

Article Engineering, Multidisciplinary

Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data

Luning Sun et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2020)

Article Computer Science, Interdisciplinary Applications

Adaptive activation functions accelerate convergence in deep and physics-informed neural networks

Ameya D. Jagtap et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2020)

Article Computer Science, Interdisciplinary Applications

Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks

Nicholas Geneva et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2020)

Article Computer Science, Artificial Intelligence

Deep learning approaches for anomaly-based intrusion detection systems: A survey, taxonomy, and open issues

Arwa Aldweesh et al.

KNOWLEDGE-BASED SYSTEMS (2020)

Article Engineering, Multidisciplinary

Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks

Georgios Kissas et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2020)

Article Engineering, Multidisciplinary

Physics-informed neural networks for high-speed flows

Zhiping Mao et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2020)

Article Computer Science, Interdisciplinary Applications

Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations

Heng Xiao et al.

COMPUTERS & FLUIDS (2020)

Review Computer Science, Artificial Intelligence

A review of deep learning with special emphasis on architectures, applications and recent trends

Saptarshi Sengupta et al.

KNOWLEDGE-BASED SYSTEMS (2020)

Article Multidisciplinary Sciences

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

Maziar Raissi et al.

SCIENCE (2020)

Article Mathematics, Applied

PHYSICS-INFORMED GENERATIVE ADVERSARIAL NETWORKS FOR STOCHASTIC DIFFERENTIAL EQUATIONS

Liu Yang et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2020)

Article Physics, Multidisciplinary

Physics-Informed Neural Networks for Cardiac Activation Mapping

Francisco Sahli Costabal et al.

FRONTIERS IN PHYSICS (2020)

Article Multidisciplinary Sciences

Extraction of mechanical properties of materials through deep learning from instrumented indentation

Lu Lu et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2020)

Article Engineering, Mechanical

Transfer learning enhanced physics informed neural network for phase-field modeling of fracture

Somdatta Goswami et al.

THEORETICAL AND APPLIED FRACTURE MECHANICS (2020)

Article Materials Science, Multidisciplinary

Theory-training deep neural networks for an alloy solidification benchmark problem

M. Torabi Rad et al.

COMPUTATIONAL MATERIALS SCIENCE (2020)

Article Engineering, Multidisciplinary

Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems

Ameya D. Jagtap et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2020)

Article Automation & Control Systems

A Survey of Optimization Methods From a Machine Learning Perspective

Shiliang Sun et al.

IEEE TRANSACTIONS ON CYBERNETICS (2020)

Article Engineering, Multidisciplinary

A surrogate model for computational homogenization of elastostatics at finite strain using high-dimensional model representation-based neural network

Vien Minh Nguyen-Thanh et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2020)

Article Engineering, Multidisciplinary

PPINN: Parareal physics-informed neural network for time-dependent PDEs

Xuhui Meng et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2020)

Article Engineering, Multidisciplinary

Physics-informed multi-LSTM networks for metamodeling of nonlinear structures

Ruiyang Zhang et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2020)

Article Physics, Mathematical

Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

Zhi-Qin John Xu et al.

COMMUNICATIONS IN COMPUTATIONAL PHYSICS (2020)

Article Physics, Mathematical

On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

Yeonjong Shin et al.

COMMUNICATIONS IN COMPUTATIONAL PHYSICS (2020)

Article Automation & Control Systems

A tutorial on solving ordinary differential equations using Python and hybrid physics-informed neural network

Renato G. Nascimento et al.

ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE (2020)

Article Mathematics, Applied

LEARNING IN MODAL SPACE: SOLVING TIME-DEPENDENT STOCHASTIC PDEs USING PHYSICS-INFORMED NEURAL NETWORKS

Dongkun Zhang et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2020)

Article Computer Science, Information Systems

A Physics-Informed Neural Network Framework for PDEs on 3D Surfaces: Time Independent Problems

Zhiwei Fang et al.

IEEE ACCESS (2020)

Article Computer Science, Information Systems

Deep Physical Informed Neural Networks for Metamaterial Design

Zhiwei Fang et al.

IEEE ACCESS (2020)

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 Computer Science, Interdisciplinary Applications

Kernel Flows: From learning kernels from data into the abyss

Houman Owhadi et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2019)

Review Computer Science, Information Systems

A State-of-the-Art Survey on Deep Learning Theory and Architectures

Md Zahangir Alom et al.

ELECTRONICS (2019)

Article Computer Science, Interdisciplinary Applications

Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

Yinhao Zhu et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2019)

Article Computer Science, Interdisciplinary Applications

Adversarial uncertainty quantification in physics-informed neural networks

Yibo Yang et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2019)

Article Computer Science, Interdisciplinary Applications

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

Dongkun Zhang et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2019)

Article Multidisciplinary Sciences

Reconciling modern machine-learning practice and the classical bias-variance trade-off

Mikhail Belkin et al.

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

Article Statistics & Probability

ON DEEP LEARNING AS A REMEDY FOR THE CURSE OF DIMENSIONALITY IN NONPARAMETRIC REGRESSION

Benedikt Bauer et al.

ANNALS OF STATISTICS (2019)

Review Behavioral Sciences

Reconciling deep learning with symbolic artificial intelligence: representing objects and relations

Marta Garnelo et al.

CURRENT OPINION IN BEHAVIORAL SCIENCES (2019)

Article Mathematics, Applied

DISCOVERING A UNIVERSAL VARIABLE-ORDER FRACTIONAL MODEL FOR TURBULENT COUETTE FLOW USING A PHYSICS-INFORMED NEURAL NETWORK

Pavan Pranjivan Mehta et al.

FRACTIONAL CALCULUS AND APPLIED ANALYSIS (2019)

Article Mathematics, Applied

fPINNs: FRACTIONAL PHYSICS-INFORMED NEURAL NETWORKS

Guofei Pang et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2019)

Review Computer Science, Information Systems

A Survey of Deep Learning Methods for Cyber Security

Daniel S. Berman et al.

INFORMATION (2019)

Review Computer Science, Information Systems

Review of Deep Learning Algorithms and Architectures

Ajay Shrestha et al.

IEEE ACCESS (2019)

Review Pharmacology & Pharmacy

The rise of deep learning in drug discovery

Hongming Chen et al.

DRUG DISCOVERY TODAY (2018)

Article Computer Science, Interdisciplinary Applications

Hidden physics models: Machine learning of nonlinear partial differential equations

Maziar Raissi et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2018)

Article Mathematics, Applied

NUMERICAL GAUSSIAN PROCESSES FOR TIME-DEPENDENT AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

Maziar Raissi et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2018)

Article Computer Science, Interdisciplinary Applications

DGM: A deep learning algorithm for solving partial differential equations

Justin Sirignano et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2018)

Article Computer Science, Artificial Intelligence

A unified deep artificial neural network approach to partial differential equations in complex geometries

Jens Berg et al.

NEUROCOMPUTING (2018)

Article Mathematics

The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems

E. Weinan et al.

COMMUNICATIONS IN MATHEMATICS AND STATISTICS (2018)

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Deep Reinforcement Learning A brief survey

Kai Arulkumaran et al.

IEEE SIGNAL PROCESSING MAGAZINE (2017)

Article Computer Science, Interdisciplinary Applications

Machine learning of linear differential equations using Gaussian processes

Maziar Raissi et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2017)

Article Computer Science, Interdisciplinary Applications

Inferring solutions of differential equations using noisy multi-fidelity data

Maziar Raissi et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2017)

Article Computer Science, Artificial Intelligence

Error bounds for approximations with deep ReLU networks

Dmitry Yarotsky

NEURAL NETWORKS (2017)

Review Multidisciplinary Sciences

Understanding deep convolutional networks

Stephane Mallat

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2016)

Article Mathematics, Interdisciplinary Applications

BAYESIAN NUMERICAL HOMOGENIZATION

Houman Owhadi

MULTISCALE MODELING & SIMULATION (2015)

Review Multidisciplinary Sciences

Deep learning

Yann LeCun et al.

NATURE (2015)

Article Mathematics, Applied

Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: A survey

Manoj Kumar et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2011)

Article Computer Science, Artificial Intelligence

Extreme learning machines: a survey

Guang-Bin Huang et al.

INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS (2011)

Article Computer Science, Artificial Intelligence

Neural-network methods for boundary value problems with irregular boundaries

IE Lagaris et al.

IEEE TRANSACTIONS ON NEURAL NETWORKS (2000)