A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations
A physics informed neural network (PINN) incorporates the physics of a system by satisfying
its boundary value problem through a neural network's loss function. The PINN approach …
its boundary value problem through a neural network's loss function. The PINN approach …
Solving parametric PDE problems with artificial neural networks
The curse of dimensionality is commonly encountered in numerical partial differential
equations (PDE), especially when uncertainties have to be modelled into the equations as …
equations (PDE), especially when uncertainties have to be modelled into the equations as …
The random feature model for input-output maps between banach spaces
Well known to the machine learning community, the random feature model is a parametric
approximation to kernel interpolation or regression methods. It is typically used to …
approximation to kernel interpolation or regression methods. It is typically used to …
Operator learning using random features: A tool for scientific computing
Supervised operator learning centers on the use of training data, in the form of input-output
pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful …
pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful …
A deep neural network method for solving partial differential equations with complex boundary in groundwater seepage
High dimensional stochastic partial differential equations (SPDEs) attract a lot of attention
because of their application in uncertainty quantification (UQ) of ore deposits, petroleum …
because of their application in uncertainty quantification (UQ) of ore deposits, petroleum …
The physics informed neural networks for the unsteady Stokes problems
J Yue, J Li - International Journal for Numerical Methods in …, 2022 - Wiley Online Library
In this article, we develop the physics informed neural networks (PINNs) coupled with small
sample learning for solving the transient Stokes equations. Specifically, the governing …
sample learning for solving the transient Stokes equations. Specifically, the governing …
Proper orthogonal decomposition method to nonlinear filtering problems in medium-high dimension
Z Wang, X Luo, SST Yau… - IEEE Transactions on …, 2019 - ieeexplore.ieee.org
In this paper, we investigate the proper orthogonal decomposition (POD) method to
numerically solve the forward Kolmogorov equation (FKE). Our method aims to explore the …
numerically solve the forward Kolmogorov equation (FKE). Our method aims to explore the …
Exploring the locally low dimensional structure in solving random elliptic PDEs
We propose a stochastic multiscale finite element method (StoMsFEM) to solve random
elliptic partial differential equations with a high stochastic dimension. The key idea is to …
elliptic partial differential equations with a high stochastic dimension. The key idea is to …
Multiscale digital-image driven stochastic finite element modeling of chloride diffusion in recycled aggregate concrete
Y Wu, J Xiao - Construction and Building Materials, 2018 - Elsevier
For estimation of the durability of recycled aggregate concrete (RAC) in chloride-rich
environment, it is valuable to investigate the chloride diffusivity in RAC. Because RAC is …
environment, it is valuable to investigate the chloride diffusivity in RAC. Because RAC is …
Uncertainty propagation; intrusive kinetic formulations of scalar conservation laws
B Després, B Perthame - SIAM/ASA Journal on Uncertainty Quantification, 2016 - SIAM
We study two intrusive methods for uncertainty propagation in scalar conservation laws
based on their kinetic formulations. The first method uses convolutions with Jackson kernels …
based on their kinetic formulations. The first method uses convolutions with Jackson kernels …