Scientific machine learning through physics-informed neural networks: where we are and what's next (Q2162315)

scientific article; zbMATH DE number 7568980

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English	Scientific machine learning through physics-informed neural networks: where we are and what's next	scientific article; zbMATH DE number 7568980

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instance of

scholarly article

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title

Scientific machine learning through physics-informed neural networks: where we are and what's next (English)

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author

Salvatore Cuomo

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Vincenzo Schiano Di Cola

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Journal of Scientific Computing

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publication date

5 August 2022

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full work available at URL

https://arxiv.org/abs/2201.05624

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zbMATH Keywords

physics-informed neural networks

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scientific machine learning

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deep neural networks

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nonlinear equations

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numerical methods

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partial differential equations

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uncertainty

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describes a project that uses

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Physics-informed neural network for modelling the thermochemical curing process of composite-tool systems during manufacture

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Active training of physics-informed neural networks to aggregate and interpolate parametric solutions to the Navier-Stokes equations

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On deep learning as a remedy for the curse of dimensionality in nonparametric regression

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

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Error estimates for deep learning methods in fluid dynamics

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DeepM\&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks

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Deep Learning Architectures

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Deep Neural Networks in a Mathematical Framework

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CAN-PINN: a fast physics-informed neural network based on coupled-automatic-numerical differentiation method

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Approximation by superpositions of a sigmoidal function

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On the approximation of functions by tanh neural networks

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Neural‐network‐based approximations for solving partial differential equations

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The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

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Deep Neural Network Approximation Theory

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PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain

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

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SciANN: a Keras/Tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks

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A nonlocal physics-informed deep learning framework using the peridynamic differential operator

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A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics

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Optimization with PDE Constraints

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Multilayer feedforward networks are universal approximators

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

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

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NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations

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\textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition

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

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Deep Learning in Computational Mechanics

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Conditional physics informed neural networks

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

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Neural algorithm for solving differential equations

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A physics-guided neural network framework for elastic plates: comparison of governing equations-based and energy-based approaches

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A seamless multiscale operator neural network for inferring bubble dynamics

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DeepXDE: A Deep Learning Library for Solving Differential Equations

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Physics-Informed Neural Networks with Hard Constraints for Inverse Design

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Physics-informed neural networks for high-speed flows

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DeepM\&Mnet for hypersonics: predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators

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Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network

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

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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

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Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm

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Bayesian Numerical Homogenization

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Kernel flows: from learning kernels from data into the abyss

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fPINNs: Fractional Physics-Informed Neural Networks

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Thermodynamically consistent physics-informed neural networks for hyperbolic systems

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Q4938227

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Numerical models for differential problems

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Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

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Hidden physics models: machine learning of nonlinear partial differential equations

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Inferring solutions of differential equations using noisy multi-fidelity data

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Machine learning of linear differential equations using Gaussian processes

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Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations

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

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

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SPINN: sparse, physics-based, and partially interpretable neural networks for PDEs

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Interpretable machine learning: fundamental principles and 10 grand challenges

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

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DGM: a deep learning algorithm for solving partial differential equations

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Large Sample Properties of Simulations Using Latin Hypercube Sampling

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

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Symplectic neural networks in Taylor series form for Hamiltonian systems

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Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning

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Theory-guided auto-encoder for surrogate construction and inverse modeling

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Deep learning of free boundary and Stefan problems

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Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

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When and why PINNs fail to train: a neural tangent kernel perspective

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

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Solving inverse problems in stochastic models using deep neural networks and adversarial training

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Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

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B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

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Adversarial uncertainty quantification in physics-informed neural networks

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Error bounds for approximations with deep ReLU networks

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A-PINN: auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations

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

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Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

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

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Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

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Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks

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

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Identifiers

Mathematics Subject Classification ID

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10.1007/S10915-022-01939-Z

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Sitelinks

Mathematics(1 entry)

mardi Publication:2162315