Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs [PDF]
, 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
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Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs [PDF]
, 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
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An Input-to-State Safety Approach Towards Safe Control of a Class of Parabolic PDEs Under Disturbances [PDF]
, 2023 Distributed Parameter Systems (DPSs), modelled by partial differential equations (PDEs), are increasingly vulnerable to disturbances arising from various sources.
Knichel, Ashley +2 more
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High order linearly implicit methods for semilinear evolution PDEs [PDF]
, 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 +1 more
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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. +14 more
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Adaptive meshing in two dimensions : refinement, coarsening and stability [PDF]
, 2021 This thesis deals with adaptive meshes in two dimensions, which are used in, e.g., the numerical computation of solutions to partial differential equations (PDEs) and in computer graphics. This thesis consists of four research articles.
Schmidt, Anja
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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 +3 more
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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
\^A-and \^I-stability of collocation Runge-Kutta methods [PDF]
, 2023 This paper deals with stability of classical Runge-Kutta collocation methods. When such methods are embedded in linearly implicit methods as developed in [12] and used in [13] for the time integration of nonlinear evolution PDEs, the stability of these ...
Lacroix-Violet, Ingrid +1 more
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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
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