Learning physics-based models from data: perspectives from inverse problems and model reduction
This article addresses the inference of physics models from data, from the perspectives of
inverse problems and model reduction. These fields develop formulations that integrate data …
inverse problems and model reduction. These fields develop formulations that integrate data …
Ot-flow: Fast and accurate continuous normalizing flows via optimal transport
A normalizing flow is an invertible mapping between an arbitrary probability distribution and
a standard normal distribution; it can be used for density estimation and statistical inference …
a standard normal distribution; it can be used for density estimation and statistical inference …
[图书][B] Robust numerical methods for singularly perturbed differential equations
HG Roos - 2008 - Springer
The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …
century, when approximate solutions were constructed from asymptotic expansions …
Modified Variational Iteration Algorithm‐II: Convergence and Applications to Diffusion Models
Variational iteration method has been extensively employed to deal with linear and
nonlinear differential equations of integer and fractional order. The key property of the …
nonlinear differential equations of integer and fractional order. The key property of the …
[图书][B] Computational optimization of systems governed by partial differential equations
This book provides an introduction to some modern computational techniques for
optimization problems governed by partial differential equations (PDEs). The optimization …
optimization problems governed by partial differential equations (PDEs). The optimization …
[HTML][HTML] New approach on conventional solutions to nonlinear partial differential equations describing physical phenomena
In current study, the modified variational iteration algorithm-I is investigated in the form of the
analytical and numerical treatment of different types of nonlinear partial differential …
analytical and numerical treatment of different types of nonlinear partial differential …
Adaptive space-time finite element methods for parabolic optimization problems
In this paper we derive a posteriori error estimates for space-time finite element
discretizations of parabolic optimization problems. The provided error estimates assess the …
discretizations of parabolic optimization problems. The provided error estimates assess the …
A unified convergence analysis for local projection stabilisations applied to the Oseen problem
G Matthies, P Skrzypacz, L Tobiska - … : Mathematical Modelling and …, 2007 - esaim-m2an.org
The discretisation of the Oseen problem by finite element methods may suffer in general
from two shortcomings. First, the discrete inf-sup (Babuška-Brezzi) condition can be violated …
from two shortcomings. First, the discrete inf-sup (Babuška-Brezzi) condition can be violated …
A priori error estimates for space-time finite element discretization of parabolic optimal control problems part II: problems with control constraints
This paper is the second part of our work on a priori error analysis for finite element
discretizations of parabolic optimal control problems. In the first part [SIAM J. Control Optim …
discretizations of parabolic optimal control problems. In the first part [SIAM J. Control Optim …
Regularization-robust preconditioners for time-dependent PDE-constrained optimization problems
JW Pearson, M Stoll, AJ Wathen - SIAM Journal on Matrix Analysis and …, 2012 - SIAM
In this article, we motivate, derive, and test effective preconditioners to be used with the
Minres algorithm for solving a number of saddle point systems which arise in PDE …
Minres algorithm for solving a number of saddle point systems which arise in PDE …