Physics-informed machine learning

No abstract is available for this paper.

• Publication year

  2021

• Venue

  Nature Reviews Physics

• Publication date

  2021-05-24

• Fields of study

  Not labeled

• Identifiers
  DOI 10.1038/s42254-021-00314-5
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• : a

  2022cited by this paper
• Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-informed Deep Generative Models

  2022cited by this paper
• : Fourier analysis sheds light on deep

  2022cited by this paper
• Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks

  2021cited by this paper
• Error estimates for DeepOnets: A deep learning framework in infinite dimensions

  2021cited by this paper
• Convergence rate of DeepONets for learning operators arising from advection-diffusion equations

  2021cited by this paper
• NVIDIA SimNet™: An AI-Accelerated Multi-Physics Simulation Framework

  2021cited by this paper
• Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains

  2020cited by this paper
• Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems

  2020cited by this paper
• Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs

  2020cited by this paper
• hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition

  2020cited by this paper
• DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks

  2020cited by this paper
• Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles

  2020cited by this paper
• SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems

  2020cited by this paper
• Large scale and linear scaling DFT with the CONQUEST code.

  2020cited by this paper
• When and why PINNs fail to train: A neural tangent kernel perspective

  2020influential reference
• Learning Unknown Physics of non-Newtonian Fluids

  2020cited by this paper
• Extraction of mechanical properties of materials through deep learning from instrumented indentation

  2020cited by this paper
• Learning with rare data: Using active importance sampling to optimize objectives dominated by rare events

  2020cited by this paper
• A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks

  2020cited by this paper
• Learning Constitutive Relations using Symmetric Positive Definite Neural Networks

  2020cited by this paper
• PFNN: A Penalty-Free Neural Network Method for Solving a Class of Second-Order Boundary-Value Problems on Complex Geometries

  2020cited by this paper
• NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework

  2020cited by this paper
• The Random Feature Model for Input-Output Maps between Banach Spaces

  2020cited by this paper
• SciANN: A Keras/TensorFlow wrapper for scientific computations and physics-informed deep learning using artificial neural networks

  2020cited by this paper
• The model reduction of the Vlasov-Poisson-Fokker-Planck system to the Poisson-Nernst-Planck system via the Deep Neural Network Approach

  2020cited by this paper
• Extended Physics-informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition based Deep Learning Framework for Nonlinear Partial Differential Equations

  2020cited by this paper
• Fourier Neural Operator for Parametric Partial Differential Equations

  2020cited by this paper
• Thermodynamically consistent physics-informed neural networks for hyperbolic systems

  2020cited by this paper
• ADCME: Learning Spatially-varying Physical Fields using Deep Neural Networks

  2020cited by this paper
• Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

  2020cited by this paper
• Systematic Construction of Neural Forms for Solving Partial Differential Equations Inside Rectangular Domains, Subject to Initial, Boundary and Interface Conditions

  2020cited by this paper
• Learning emergent PDEs in a learned emergent space

  2020cited by this paper
• Multipole Graph Neural Operator for Parametric Partial Differential Equations

  2020cited by this paper
• Understanding and mitigating gradient pathologies in physics-informed neural networks

  2020influential reference
• Bayesian differential programming for robust systems identification under uncertainty

  2020cited by this paper
• B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data

  2020cited by this paper
• An energy-based error bound of physics-informed neural network solutions in elasticity

  2020cited by this paper
• Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations

  2020cited by this paper
• Physics Constrained Learning for Data-driven Inverse Modeling from Sparse Observations

  2020cited by this paper
• Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

  2020cited by this paper
• Meta-Learning in Neural Networks: A Survey

  2020cited by this paper
• Do ideas have shape? Plato's theory of forms as the continuous limit of artificial neural networks

  2020cited by this paper
• Physics‐Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems

  2020cited by this paper
• Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

  2020cited by this paper
• Pushing the Limit of Molecular Dynamics with Ab Initio Accuracy to 100 Million Atoms with Machine Learning

  2020cited by this paper
• On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

  2020influential reference
• Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

  2020cited by this paper
• A general approach to seismic inversion with automatic differentiation

  2020cited by this paper
• Universal Differential Equations for Scientific Machine Learning

  2020cited by this paper
• Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory

  2020cited by this paper
• On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton-Jacobi partial differential equations

  2020cited by this paper
• Uncovering edge plasma dynamics via deep learning from partial observations

  2020cited by this paper
• ContactNets: Learning of Discontinuous Contact Dynamics with Smooth, Implicit Representations

  2020cited by this paper
• Transformers for Modeling Physical Systems

  2020cited by this paper
• A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries

  2020cited by this paper
• Multi-scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains

  2020cited by this paper
• Error estimates of residual minimization using neural networks for linear PDEs

  2020cited by this paper
• On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

  2020cited by this paper
• Inverse Modeling of Viscoelasticity Materials using Physics Constrained Learning

  2020cited by this paper
• Distributed Machine Learning for Computational Engineering using MPI

  2020cited by this paper
• DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators

  2020cited by this paper
• Learning dynamical systems from data: a simple cross-validation perspective

  2020cited by this paper
• Deep learning of free boundary and Stefan problems

  2020cited by this paper
• Physics-Informed Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks

  2020cited by this paper
• NeuroDiffEq: A Python package for solving differential equations with neural networks

  2020cited by this paper
• The Convergence Rate of Neural Networks for Learned Functions of Different Frequencies

  2019cited by this paper
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks

  2019cited by this paper
• Coupled Time‐Lapse Full‐Waveform Inversion for Subsurface Flow Problems Using Intrusive Automatic Differentiation

  2019cited by this paper
• Adversarial Numerical Analysis for Inverse Problems

  2019cited by this paper
• Deep Neural Network Approach to Forward-Inverse Problems

  2019cited by this paper
• Transformer Dissection: An Unified Understanding for Transformer’s Attention via the Lens of Kernel

  2019cited by this paper
• Neural Tangents: Fast and Easy Infinite Neural Networks in Python

  2019cited by this paper
• The Neural Network Approach to Inverse Problems in Differential Equations

  2019cited by this paper
• Statistical Numerical Approximation

  2019cited by this paper
• Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks

  2019cited by this paper
• A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

  2019cited by this paper
• Machine learning in cardiovascular flows modeling: Predicting pulse wave propagation from non-invasive clinical measurements using physics-informed deep learning

  2019cited by this paper
• Encoding Invariances in Deep Generative Models

  2019cited by this paper
• DPM: A deep learning PDE augmentation method (with application to large-eddy simulation)

  2019cited by this paper
• DeepXDE: A Deep Learning Library for Solving Differential Equations

  2019cited by this paper
• AutoML: A Survey of the State-of-the-Art

  2019cited by this paper
• Physical Symmetries Embedded in Neural Networks

  2019cited by this paper
• Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

  2019cited by this paper
• PyDEns: a Python Framework for Solving Differential Equations with Neural Networks

  2019cited by this paper
• Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

  2019cited by this paper
• Neural Jump Stochastic Differential Equations

  2019cited by this paper
• Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction

  2019cited by this paper
• Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks

  2019cited by this paper
• PyTorch: An Imperative Style, High-Performance Deep Learning Library

  2019cited by this paper
• Deep learning and process understanding for data-driven Earth system science

  2019cited by this paper
• Transfer learning enhanced physics informed neural network for phase-field modeling of fracture

  2019cited by this paper
• ConvPDE-UQ: Convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains

  2019cited by this paper
• Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization

  2019cited by this paper
• Gauge Equivariant Convolutional Networks and the Icosahedral CNN

  2019cited by this paper
• Towards Understanding the Spectral Bias of Deep Learning

  2019cited by this paper
• Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems

  2019cited by this paper
• Equivariant Transformer Networks

  2019cited by this paper
• Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

  2019cited by this paper
• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data

  2019cited by this paper

• Numerical differentiation by integrated series expansion (NDBISE) for data driven ordinary differential equation estimation problems

  2026cites this paper
• I-FENN with DeepONets: Accelerating simulations in coupled multiphysics problems

  2026cites this paper
• Physics-informed reinforcement learning for air-to-air F16 target aiming

  2026cites this paper
• A comparative study of deep learning models for two-dimensional MXene ferroelectric data

  2026cites this paper
• Optimal control of chaos in a novel SITR epidemic model with generalized incidence and adaptive treatment dynamics: A deep neural network analysis

  2026cites this paper
• A label-free physics informed neural network with hard constraints and Fourier features spectrally-enhanced for multi-frequency seismic structural dynamic response

  2026cites this paper
• Diff-FlowFSI: A GPU-optimized differentiable CFD platform for high-fidelity turbulence and FSI simulations

  2026cites this paper
• Physics-constrained deep learning bias correction of CMIP6 solar radiation over Africa and its implications for solar power planning in a changing climate

  2026cites this paper
• Development of a Parametric Multi-Material Physics-Informed Neural Network for real-time heat transfer prediction in spherical tokamak divertor under transient heat loads

  2026cites this paper
• Physics-enhanced machine learning surrogate modelling for real-time seismic fragility assessment of reinforced concrete bridges

  2026cites this paper
• Dual-phase evaluation framework of physics-informed machine learning model for building dynamics modeling and advanced control

  2026cites this paper
• Kernelized Deep Unfolding Network With Joint Physical Constraints for Electromagnetic Inverse Scattering Imaging

  2026cites this paper
• Thermal-structural analysis of a spatial thin-walled cantilever tube structure under different solar heat radiations based on an improved physics-informed neural network

  2026cites this paper
• Low Earth Orbit Satellite (LEOS)-Assisted Integrated Access and Backhauling in xG Wireless Communication: A Generalizable RL Framework

  2026cites this paper
• Operator learning-based springback behavior prediction for complex-shaped tube free-bending forming

  2026cites this paper
• MFPINN-DIC: Multi-scale Fourier feature encoding physics-informed neural network enhanced digital image correlation method

  2026cites this paper
• A novel physics-guided approach for time-varying mesh stiffness estimation and data generation in gear fault diagnosis under imbalanced data

  2026cites this paper
• Using physics-informed machine learning for improving predictive capability of two-phase flow drift flux modeling

  2026cites this paper
• Physics-based feature engineering for machine learning in terminal velocity prediction of fractal aggregates formed during flocculation

  2026cites this paper
• Physics-Informed Neural Network for Real-Time Imaging and Evaluation of Defect Based on High-Definition ACFM Probe

  2026cites this paper
• Physics-informed identification of stress fields and thermo-viscoplastic model parameters for metals from full-field data under impact loading

  2026cites this paper
• An adaptive residual-structured and scheduled loss weighting framework for enhancing physics-informed neural networks in solving partial differential equations

  2026cites this paper
• A Feature-Enhanced Physics Informed Neural Network for trajectory simulation of charged particles

  2026cites this paper
• A novel knowledge-informed quadratic neurons residual network for explainable fault diagnosis in few-shot scenarios

  2026cites this paper
• Coupled data-driven and experience-informed neural networks for prediction of pile base resistance with consideration of data limitation

  2026cites this paper
• A novel Sigmexd activation function to enhance Physics-Informed Neural Networks (PINNs) for differential equations with a perspective on the role of activation functions in PINNs

  2026cites this paper
• Physics-informed neural networks with continuous-time thermal modelling for model predictive control of building energy systems in demand response

  2026cites this paper
• Applied mathematical and computational frameworks in materials science: a comprehensive review

  2026cites this paper
• A hybrid MWD-acoustic deep learning method for in-situ stress estimation in tunnel

  2026cites this paper
• Duffing system parameter estimation by inverse physics-informed neural networks with sine activation function

  2026cites this paper
• Physics-Guided Intelligent Tomography Sensing System for Non-Destructive Testing Based on Neuromorphic Eddy Current Circuit Array and Physical Electromagnetic Dynamics Model

  2026cites this paper
• Hyperspectral Remote Sensing for Monitoring Crop Disease: Applications, challenges, and perspectives

  2026cites this paper
• Experimental data-driven gradient-informed neural network modeling of bio-inspired flow separation control

  2026cites this paper
• Physics-informed learning-based distributed cooperative tracking control for multiple Euler-Lagrange systems

  2026cites this paper
• Development of Convolutional Neural Network-based Physics-Informed Neural networks for solving the neutron diffusion equation

  2026cites this paper
• Developing empirical indices for structural engineering problems via machine learning

  2026cites this paper
• Physics-informed neural network with equation adaption for 220Rn progeny concentration prediction

  2026influential citation
• Three-Dimensional High-Fidelity Surrogate Modeling of Frequency-Domain Airborne Electromagnetics Based on Hybrid DeepONet-Fourier Neural Operator

  2026cites this paper
• LT-PINN: Lagrangian topology-conscious physics-informed neural network for boundary-focused engineering optimization

  2026cites this paper
• A machine learning-based constitutive model incorporating history-dependent features for cyclic plasticity

  2026cites this paper
• Domain-embedded deep learning frameworks for topology optimization: Enhancing structural performance under data scarce environments

  2026cites this paper
• Physics-informed neural network (PINN) for predicting the temperature field in high geothermal tunnels

  2026cites this paper
• Optimization of parameters for self-inductive angle-of-rotation sensor structure using neural network and multi-objective genetic algorithm

  2026cites this paper
• A physics-informed piecewise continuity network for solving the non-linear jerk equation: PiPC-Net

  2026cites this paper
• A Cross-Channel Parametric CNN Framework for Microwave Topology Modeling

  2026cites this paper
• Municipal solid waste gasification predictions using hybrid-data physics-informed neural networks

  2026cites this paper
• A physics-informed neural network workflow for forward and inverse modeling of unsaturated flow and root water uptake from hydrogeophysical data

  2026cites this paper
• Physics-informed neural network based on layerwise theory for bending analysis of laminated plates

  2026cites this paper
• Advances and challenges in Artificial Intelligence-driven flood and drought risk management: A comprehensive review

  2026cites this paper
• A self-adaptive transformer-enhanced physics-informed neural network for railway dynamics system

  2026cites this paper
• Learning constrained static equilibrium for thrust network inverse form-finding via physics-informed geometric deep learning on CW complexes

  2026cites this paper
• Dynamic response of a floating elastic plate supported on a viscoelastic foundation under moving periodic load: Analytical and neural modelling

  2026cites this paper
• Unlocking the value of retired EV batteries: Technologies, application, and commercial models for second-life energy storage in power systems

  2026cites this paper
• Gaussian mixture variational autoencoder with prior knowledge and distribution alignment for few-shot defect quantification evaluation based on ultrasonic simulation

  2026cites this paper
• Autonomous agentic AI with policy adaptation for physics-informed spectral learning in Structural Health Monitoring

  2026cites this paper
• Hyperspectral image reconstruction algorithms for broadband spectral modulation: a comprehensive review

  2026cites this paper
• Digital twin technology in AI-operated metaverse for food processing: A pathway to sustainability, efficiency and innovation

  2026cites this paper
• A 2D temperature distribution prediction method for onboard auxiliary transformers

  2026cites this paper
• Recent advances in uncertainty analysis for prognostics and remaining useful life prediction: A review

  2026cites this paper
• Physics-informed band structure-integrated Continuous-time inhomogeneous Markov chains for stochastic occupancy modeling

  2026cites this paper
• Embedding Physics into Machine Learning: A Review of Physics Informed Neural Networks as Partial Differential Equation Forward Solvers

  2026cites this paper
• Finite-element Gaussian processes for the machine learning of steady-state linear partial differential equations

  2026cites this paper
• Quantasio: A Generalized Neural Framework for Solving 3-D Navier–Stokes Dynamics

  2026influential citation
• Adaptable Parameters Estimation for Microgrid Distributed Energy Resources Using Modified Physics-Informed Neural Network

  2026cites this paper
• Physics-Guided Meta-Learning for Surface Roughness Prediction Under Various Working Conditions With Limited Data

  2026cites this paper
• Gearbox bearing crack growth prognostics and uncertainty quantification with physics-informed machine learning

  2026influential citation
• Evaluation of COBRA-TF prediction performance enhanced by machine learning-based CHF models

  2026cites this paper
• What can artificial intelligence do for soil health in agriculture?

  2026cites this paper
• Uncovering magnetic phases with synthetic data and physics-informed training

  2026cites this paper
• Eigenvector decomposition for joint analysis of spatial characteristics in the North Atlantic from 1979 to 2024

  2026cites this paper
• High-Fidelity saturation prediction using physics-informed attention neural network

  2026cites this paper
• Micrometer: Micromechanics transformer for predicting full field mechanical responses of heterogeneous materials

  2026cites this paper
• DFS-PINN: A Dynamic Feature Separation Physics-Informed Neural Network

  2026cites this paper
• Attention-enhanced generative design of disc cutter layout for shield TBM considering multi-working conditions

  2026cites this paper
• Transfer Learnable Physics-Informed Neural Network Surrogating Grid-Tied Inverters for Renewable Power System Simulation

  2026cites this paper
• Review of physics-informed neural networks in hemodynamics

  2026cites this paper
• Deep learning-based probabilistic slope stability analysis considering spatial variability of soils and saturated seepage

  2026cites this paper
• Predicting fuel cell aging behavior under dynamic load through physics-informed machine learning for powertrain system health monitoring

  2026cites this paper
• Physics-Informed Neural Networks-Based Adaptive Optimized Control and Its Application to Automated Surface Vessels

  2026cites this paper
• Physics-informed continuous and discrete Gaussian processes for forward and inverse soil consolidation analysis: Uncertainty quantification and diffusion kernel-based multi-fidelity modeling

  2026cites this paper
• Explainable artificial intelligence-based flexural rigidity matrix estimation of bridges using spatially distributed inclinometers

  2026cites this paper
• Physics informed machine learning based predictive control for intelligent operation of edge datacenters

  2026cites this paper
• Autonomous robotic screwdriving for high-mix manufacturing

  2026cites this paper
• A Fast and Intelligent Monitoring of Solder Layer Degradation in Multichip IGBT Modules Based on Copper Substrate Temperature Field Reconstruction

  2026cites this paper
• On the under-reaching phenomenon in message passing neural PDE solvers: Revisiting the CFL condition

  2026cites this paper
• An efficient and physics-informed regional maize yield estimation scheme by combining data assimilation and machine learning

  2026cites this paper
• Introdução às redes neurais para Físicos

  2026cites this paper
• A novel boundary-based machine learning approach for 2D crack analysis in elastic and piezoelectric materials

  2026cites this paper
• A physics-informed machine learning framework for inverse multi-solution problems

  2026cites this paper
• Forecasting of spatiotemporal nonlinear dynamic systems by Physics-informed neural networks with ResNet blocks

  2026cites this paper
• High-resolution subspace neural network approach for solving the singular perturbed boundary layer problem

  2026cites this paper
• Robust measurement of surface tension and contact angle using physics-informed autoencoders

  2026cites this paper
• Effect of excavation damaged zone on the long-term coupled thermo-hydro-mechanical behaviors of deep geological repositories in granitic rock masses

  2026cites this paper
• Generative artificial intelligence and marine ecological monitoring

  2026cites this paper
• Dual-LSTM-Based Inverse System Control for Laser Nonlinear Compensation

  2026cites this paper
• A multiscale review of magnetic permeability in polymer composites: Theory, simulation, and machine learning frontiers

  2026cites this paper
• Fundamental flaws of physics-informed neural networks and explainability methods in engineering systems

  2026cites this paper
• PGVAE-VBAKF: A robust strategy for complex system response prediction and noise variance estimation considering modeling errors and nonstationary noises

  2026cites this paper
• Few-shot surface roughness prediction via a novel physics-guided meta-learning framework

  2026cites this paper
• Neuro-heuristic and regression-based modeling of three-dimensional Williamson-micropolar nanofluid flow with regularization and uncertainty quantification

  2026cites this paper