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View article: Goal Oriented Optimal Design of Infinite-Dimensional Bayesian Inverse Problems using Quadratic Approximations
Goal Oriented Optimal Design of Infinite-Dimensional Bayesian Inverse Problems using Quadratic Approximations Open
We consider goal-oriented optimal design of experiments for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we seek sensor placements that minimize the posterior varian…
View article: Toward real-time optimization through model reduction and model discrepancy sensitivities
Toward real-time optimization through model reduction and model discrepancy sensitivities Open
Optimization problems arise in a range of scenarios, from optimal control to model parameter estimation. In many applications, such as the development of digital twins, it is essential to solve these optimization problems within wall-clock…
View article: Preconditioned pseudo-time continuation for parameterized inverse problems
Preconditioned pseudo-time continuation for parameterized inverse problems Open
We consider parametrized variational inverse problems that are constrained by partial differential equations (PDEs). We seek to efficiently compute the solution of the inverse problem when auxiliary model parameters, which appear in the go…
View article: A control-oriented approach to optimal sensor placement
A control-oriented approach to optimal sensor placement Open
We propose a control-oriented optimal experimental design (cOED) approach for linear PDE-constrained Bayesian inverse problems. In particular, we consider optimal control problems with uncertain parameters that need to be estimated by solv…
View article: Goal oriented optimal design of infinite-dimensional Bayesian inverse problems using quadratic approximations
Goal oriented optimal design of infinite-dimensional Bayesian inverse problems using quadratic approximations Open
We consider goal-oriented optimal design of experiments for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we seek sensor placements that minimize the posterior varian…
View article: Neural network approaches for parameterized optimal control
Neural network approaches for parameterized optimal control Open
Here, we consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offlin…
View article: Glyph-Based Uncertainty Visualization and Analysis of Time-Varying Vector Fields
Glyph-Based Uncertainty Visualization and Analysis of Time-Varying Vector Fields Open
Uncertainty is inherent to most data, including vector field data, yet it is often omitted in visualizations and representations. Effective uncertainty visualization can enhance the understanding and interpretability of vector field data. …
View article: Neural Network Approaches for Parameterized Optimal Control
Neural Network Approaches for Parameterized Optimal Control Open
We consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stag…
View article: Hyper-differential sensitivity analysis with respect to model discrepancy: Posterior Optimal Solution Sampling
Hyper-differential sensitivity analysis with respect to model discrepancy: Posterior Optimal Solution Sampling Open
Optimization constrained by high-fidelity computational models has potential for transformative impact. However, such optimization is frequently unattainable in practice due to the complexity and computational intensity of the model. An al…
View article: Stochastic Deep Model Reference Adaptive Control.
Stochastic Deep Model Reference Adaptive Control. Open
In this paper, we present a Stochastic Deep Neural Network-based Model Reference Adaptive Control. Building on our work "Deep Model Reference Adaptive Control", we extend the controller capability by using Bayesian deep neural networks (DN…
View article: Enabling Hyper-Differential Sensitivity Analysis for Ill-Posed Inverse Problems
Enabling Hyper-Differential Sensitivity Analysis for Ill-Posed Inverse Problems Open
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high…
View article: MrHyDE v.1.0
MrHyDE v.1.0 Open
SAND2024-01324O MrHyDE, which stands for Multi-resolution Hybridized Differential Equations, is a general-purpose C++ package for the solution of coupled multiphysics and multiscale systems on massively parallel computing systems. MrHyDE i…
View article: Hyper-differential sensitivity analysis in the context of Bayesian inference applied to ice-sheet problems
Hyper-differential sensitivity analysis in the context of Bayesian inference applied to ice-sheet problems Open
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model which must be estimated. Although the…
View article: Hyper-differential sensitivity analysis with respect to model discrepancy: Mathematics and computation
Hyper-differential sensitivity analysis with respect to model discrepancy: Mathematics and computation Open
Model discrepancy, defined as the difference between model predictions and reality, is ubiquitous in computational models for physical systems. It is common to derive partial differential equations (PDEs) from first principles physics, but…