An overview on deep learning-based approximation methods for partial differential equations
It is one of the most challenging problems in applied mathematics to approximatively solve
high-dimensional partial differential equations (PDEs). Recently, several deep learning …
high-dimensional partial differential equations (PDEs). Recently, several deep learning …
Physics-informed neural network (PINN) evolution and beyond: A systematic literature review and bibliometric analysis
This research aims to study and assess state-of-the-art physics-informed neural networks
(PINNs) from different researchers' perspectives. The PRISMA framework was used for a …
(PINNs) from different researchers' perspectives. The PRISMA framework was used for a …
When and why PINNs fail to train: A neural tangent kernel perspective
Physics-informed neural networks (PINNs) have lately received great attention thanks to
their flexibility in tackling a wide range of forward and inverse problems involving partial …
their flexibility in tackling a wide range of forward and inverse problems involving partial …
PINN-FORM: a new physics-informed neural network for reliability analysis with partial differential equation
The first-order reliability method (FORM) is commonly used in the field of structural reliability
analysis, which transforms the reliability analysis problem into the solution of an optimization …
analysis, which transforms the reliability analysis problem into the solution of an optimization …
Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios
Recently, a class of machine learning methods called physics-informed neural networks
(PINNs) has been proposed and gained prevalence in solving various scientific computing …
(PINNs) has been proposed and gained prevalence in solving various scientific computing …
Monte Carlo fPINNs: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations
We introduce a sampling-based machine learning approach, Monte Carlo fractional physics-
informed neural networks (MC-fPINNs), for solving forward and inverse fractional partial …
informed neural networks (MC-fPINNs), for solving forward and inverse fractional partial …
Meta-learning PINN loss functions
We propose a meta-learning technique for offline discovery of physics-informed neural
network (PINN) loss functions. We extend earlier works on meta-learning, and develop a …
network (PINN) loss functions. We extend earlier works on meta-learning, and develop a …
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks
The Fokker--Planck (FP) equation governing the evolution of the probability density function
(PDF) is applicable to many disciplines, but it requires specification of the coefficients for …
(PDF) is applicable to many disciplines, but it requires specification of the coefficients for …
Enhancing PINNs for solving PDEs via adaptive collocation point movement and adaptive loss weighting
J Hou, Y Li, S Ying - Nonlinear Dynamics, 2023 - Springer
Physics-informed neural networks (PINNs) are an emerging method for solving partial
differential equations (PDEs) and have been widely applied in the field of scientific …
differential equations (PDEs) and have been widely applied in the field of scientific …
Data-driven physics-informed constitutive metamodeling of complex fluids: A multifidelity neural network (MFNN) framework
In this work, we introduce a comprehensive machine-learning algorithm, namely, a
multifidelity neural network (MFNN) architecture for data-driven constitutive metamodeling of …
multifidelity neural network (MFNN) architecture for data-driven constitutive metamodeling of …