Orthogonal grid physics-informed neural networks: A neural network-based simulation tool for advection–diffusion–reaction problems

Fluid-like representation of Fickian diffusion

(2022) E. Heifetz et al.   PHYSICS OF FLUIDS

Approximate solutions of the advection–diffusion equation for spatially variable flows

(2022) Yubiao Sun et al.   PHYSICS OF FLUIDS

Physics-Informed Neural Networks for Heat Transfer Problems

(2021) Shengze Cai et al.   JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME

Inverse Modeling of Contaminant Transport for Pollution Source Identification in Surface and Groundwaters: A Review

(2021) Maryam Barati Moghaddam et al.   Groundwater for Sustainable Development

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

(2021) Sifan Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Deep learning methods for super-resolution reconstruction of turbulent flows

(2020) Bo Liu et al.   PHYSICS OF FLUIDS

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

(2020) Maziar Raissi et al.   SCIENCE

Deep learning-based method coupled with small sample learning for solving partial differential equations

(2020) Ying Li et al.   MULTIMEDIA TOOLS AND APPLICATIONS

Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with PT-symmetric harmonic potential via deep learning

(2020) Zijian Zhou et al.   PHYSICS LETTERS A

Efficient solver for a special class of convection-diffusion problems

(2019) Narain Karedla et al.   PHYSICS OF FLUIDS

An iterative strategy for contaminant source localisation using GLMA optimization and Data Worth on two synthetic 2D Aquifers

(2019) E. Essouayed et al.   JOURNAL OF CONTAMINANT HYDROLOGY

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

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

PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network

(2019) Zichao Long et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Backward Probability Model for Identifying Multiple Contaminant Source Zones Under Transient Variably‐Saturated Flow Conditions

(2019) Hyoun‐Tae Hwang et al.   WATER RESOURCES RESEARCH

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

A KDE-Based Random Walk Method for Modeling Reactive Transport With Complex Kinetics in Porous Media

(2017) Guillem Sole-Mari et al.   WATER RESOURCES RESEARCH

Estimation of river pollution source using the space-time radial basis collocation method

(2016) Zi Li et al.   ADVANCES IN WATER RESOURCES

Contaminant release history identification in 2-D heterogeneous aquifers through a minimum relative entropy approach

(2015) Fausto Cupola et al.   SpringerPlus

Identification of contaminant point source in surface waters based on backward location probability density function method

(2010) Wei Ping Cheng et al.   ADVANCES IN WATER RESOURCES

The Finite Volume-Complete Flux Scheme for Advection-Diffusion-Reaction Equations

(2010) J. H. M. ten Thije Boonkkamp et al.   JOURNAL OF SCIENTIFIC COMPUTING

Lagrangian modeling of advection-diffusion transport in open channel flow

(2009) Bishnu H. Devkota et al.   WATER RESOURCES RESEARCH