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Explicit quantification of uncertainty in engineering simulations is being increasingly used to inform robust and reliable design practices. In the aerospace industry, computationally-feasible analyses for design optimization purposes often…

Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with only modest progress made in the last few decades beyond the so-called `log law', which describes only the intermediate region in wall-bounded…

Nonlinear robust optimization (NRO) is widely used in different applications, including energy, control, and economics, to make robust decisions under uncertainty. One of the classical solution methods in NRO is an outer approximation…

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different…

In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a…

Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…

Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…

Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…

Model predictive control (MPC) is a powerful strategy for planning and control in autonomous mobile robot navigation. However, ensuring safety in real-world deployments remains challenging due to the presence of disturbances and measurement…

Statistical uncertainties complicate engineering design -- confounding regulated design approaches, and degrading the performance of reliability efforts. The simplest means to tackle this uncertainty is double loop simulation; a nested…

In recent work, the authors have developed a generic methodology for calibrating the noise in fluid dynamics stochastic partial differential equations where the stochasticity was introduced to parametrize subgrid-scale processes. The…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…

This work presents ReSync, a Riemannian subgradient-based algorithm for solving the robust rotation synchronization problem, which arises in various engineering applications. ReSync solves a least-unsquared minimization formulation over the…

Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N-1)- dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the "trust…

Bayesian inverse problems use data to update a prior probability distribution on uncertain parameter values to a posterior distribution. Such problems arise in many structural engineering applications, but computational solution of Bayesian…

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…

We consider the problem of reconstructing a low rank matrix from noisy observations of a subset of its entries. This task has applications in statistical learning, computer vision, and signal processing. In these contexts, "noise"…

This article addresses the challenge of learning effective regularizers for linear inverse problems. We analyze and compare several types of learned variational regularization against the theoretical benchmark of the optimal affine…

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based…