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

Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs

(2021) Fabian Laakmann et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

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

(2020) Ameya D. Jagtap et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A multi-level procedure for enhancing accuracy of machine learning algorithms

(2020) KJETIL O. LYE et al.   EUROPEAN JOURNAL OF APPLIED MATHEMATICS

Deep learning observables in computational fluid dynamics

(2020) Kjetil O. Lye et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Physics-Informed Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks

(2020) Khemraj Shukla et al.   JOURNAL OF NONDESTRUCTIVE EVALUATION

Machine learning for fast and reliable solution of time-dependent differential equations

(2019) F. Regazzoni et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

(2019) Ameya D. Jagtap et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Physics-informed neural networks for high-speed flows

(2019) Zhiping Mao et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A finite element data assimilation method for the wave equation

(2019) Erik Burman et al.   MATHEMATICS OF COMPUTATION

Fully discrete finite element data assimilation method for the heat equation

(2018) Erik Burman et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization

(2018) Erik Burman et al.   INVERSE PROBLEMS

An artificial neural network as a troubled-cell indicator

(2018) Deep Ray et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Hidden physics models: Machine learning of nonlinear partial differential equations

(2018) Maziar Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Solving high-dimensional partial differential equations using deep learning

(2018) Jiequn Han et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

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

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Stabilized nonconforming finite element methods for data assimilation in incompressible flows

(2017) Erik Burman et al.   MATHEMATICS OF COMPUTATION

Error bounds for approximations with deep ReLU networks

(2017) Dmitry Yarotsky   NEURAL NETWORKS

Geometric control condition for the wave equation with a time-dependent observation domain

(2017) Jérôme Le Rousseau et al.   Analysis & PDE

Stability estimates for Navier-Stokes equations and application to inverse problems

(2016) Mehdi Badra et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

Deep learning

(2015) Yann LeCun et al.   NATURE

Error estimates for stabilized finite element methods applied to ill-posed problems

(2014) Erik Burman   COMPTES RENDUS MATHEMATIQUE

Global Carleman Estimates for Waves and Applications

(2013) Lucie Baudouin et al.   COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

Recovering the initial state of an infinite-dimensional system using observers

(2010) Karim Ramdani et al.   AUTOMATICA

Optimal three-ball inequalities and quantitative uniqueness for the Stokes system

(2010) Ching-Lung Lin et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

The stability for the Cauchy problem for elliptic equations

(2009) Giovanni Alessandrini et al.   INVERSE PROBLEMS