Results 11 to 20 of about 2,172 (181)

Accuracy and stability of filters for dissipative PDEs [PDF]

, 2013
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation algorithms designed to
Scott, M. R., K F Lam (16229219), Brett, C. E. A., Lam, K. F., Brett, Charles E. A., M R Scott (16229225), C E A Brett (16229216), McCormick, D. S., Scott, Michael R., Law, K. J. H., D S McCormick (16229222), A M Stuart (13396491), Stuart, A. M., K J H Law (16170239), Lam, Kei Fong   +14 more
core   +2 more sources

Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics [PDF]

, 2012
We show how to extend a recently proposed multi-level Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the system to a ...
Anderson, David, David F. Anderson, Higham, Desmond, Desmond J. Higham   +3 more
core   +1 more source

Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs [PDF]

, 2021
In this paper we present some heuristic strategies to compute rapid and reliable approximations to stability factors in nonlinear, inf-sup stable parametrized PDEs.
Negri, Federico, Manzoni, Andrea
core  

Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs

, 2022
Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique continuation ...
Mishra, Siddhartha, Molinaro, Roberto
core   +1 more source

Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs

, 2015
In this paper we present some heuristic strategies to compute rapid and reliable approximations to stability factors in nonlinear, inf-sup stable parametrized PDEs.
Negri, Federico, Manzoni, Andrea
core   +2 more sources

An Input-to-State Safety Approach Towards Safe Control of a Class of Parabolic PDEs Under Disturbances

, 2023
Distributed Parameter Systems (DPSs), modelled by partial differential equations (PDEs), are increasingly vulnerable to disturbances arising from various sources.
Knichel, Ashley, Dey, Satadru, Roy, Tanushree   +2 more
core   +1 more source

High order linearly implicit methods for semilinear evolution PDEs

, 2023
This paper considers the numerical integration of semilinear evolution PDEs using the high order linearly implicit methods developped in a previous paper in the ODE setting.
Lacroix-Violet, Ingrid, Dujardin, Guillaume   +1 more
core   +1 more source

Finite Element Error Analysis and Solution Stability of Affine Optimal Control Problems [PDF]

, 2023
We consider affine optimal control problems subject to semilinear elliptic PDEs. The results are two-fold; first, we continue the analysis of solution stability of control problems under perturbations appearing jointly in the objective functional and the
Jork, Nicolai Alexander
core   +1 more source

Multiscale Geometric Integration of Deterministic and Stochastic Systems [PDF]

, 2011
In order to accelerate computations and improve long time accuracy of numerical simulations, this thesis develops multiscale geometric integrators. For general multiscale stiff ODEs, SDEs, and PDEs, FLow AVeraging integratORs (FLAVORs) have been ...
Tao, Molei
core   +1 more source

Poisson Structures for PDEs Associated with Diffeomorphism Groups [PDF]

, 2004
We study Poisson and Lie-Poisson structures on the diffeomorphism groups with a smooth metric spray in connection with dynamics of nonlinear PDEs. In particular, we provide a precise analytic sense in which the time t map for the Euler equations of an ...
Vasylkevych, Sergiy
core   +1 more source