Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre–Green–Naghdi equations

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

(2021) Shengze Cai et al.   JOURNAL OF FLUID MECHANICS

A Physics-Informed Neural Network for Quantifying the Microstructural Properties of Polycrystalline Nickel Using Ultrasound Data: A promising approach for solving inverse problems

(2021) Khemraj Shukla et al.   IEEE SIGNAL PROCESSING MAGAZINE

Parallel physics-informed neural networks via domain decomposition

(2021) Khemraj Shukla et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions

(2021) Ameya D. Jagtap et al.   NEUROCOMPUTING

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

(2020) Maziar Raissi et al.   SCIENCE

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

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

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

Transfer learning based multi-fidelity physics informed deep neural network

(2020) Souvik Chakraborty   JOURNAL OF COMPUTATIONAL PHYSICS

hp-VPINNs: Variational physics-informed neural networks with domain decomposition

(2020) Ehsan Kharazmi et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

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 composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

(2019) Xuhui Meng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns

(2018) Krithika Manohar et al.   IEEE CONTROL SYSTEMS MAGAZINE

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

Error Estimates for Galerkin Approximations of the Serre Equations

(2017) D. C. Antonopoulos et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

On the nonlinear dynamics of the traveling-wave solutions of the Serre system

(2017) Dimitrios Mitsotakis et al.   WAVE MOTION

A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system

(2016) D. Mitsotakis et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

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

(2016) Steven L. Brunton et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Bayesian Numerical Homogenization

(2015) Houman Owhadi   MULTISCALE MODELING & SIMULATION

On the Galerkin/Finite-Element Method for the Serre Equations

(2014) Dimitrios Mitsotakis et al.   JOURNAL OF SCIENTIFIC COMPUTING

On the Galilean Invariance of Some Nonlinear Dispersive Wave Equations

(2013) Angel Duran et al.   STUDIES IN APPLIED MATHEMATICS

Large time existence for 1D Green-Naghdi equations

(2010) Samer Israwi   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions

(2009) K.S. McFall et al.   IEEE TRANSACTIONS ON NEURAL NETWORKS

Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques

(2009) R. Shekari Beidokhti et al.   JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS