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Autonomous driving has the potential to significantly enhance productivity and provide numerous societal benefits. Ensuring robustness in these safety-critical systems is essential, particularly when vehicles must navigate adverse weather…

The uniform quadratic optimizatin problem (UQ) is a nonconvex quadratic constrained quadratic programming (QCQP) sharing the same Hessian matrix. Based on the second-order cone programming (SOCP) relaxation, we establish a new sufficient…

Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires…

We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the…

Existing work in scientific machine learning (SciML) has shown that data-driven learning of solution operators can provide a fast approximate alternative to classical numerical partial differential equation (PDE) solvers. Of these, Neural…

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

Uncertainty Quantification (UQ) is a key discipline for computational modeling of complex systems, enhancing reliability of engineering simulations. In crashworthiness, having an accurate assessment of the behavior of the model uncertainty…

OOD detection has become more pertinent with advances in network design and increased task complexity. Identifying which parts of the data a given network is misclassifying has become as valuable as the network's overall performance. We can…

Uncertainty quantification (UQ) is an important component of molecular property prediction, particularly for drug discovery applications where model predictions direct experimental design and where unanticipated imprecision wastes valuable…

We gain robustness on the quantification of a risk measurement by accounting for all sources of uncertainties tainting the inputs of a computer code. We evaluate the maximum quantile over a class of distributions defined only by constraints…

Modern computers enable methods for design optimization that account for uncertainty in the system---so-called optimization under uncertainty. We propose a metric for OUU that measures the distance between a designer-specified probability…

Machine learning methods are increasingly widely used in high-risk settings such as healthcare, transportation, and finance. In these settings, it is important that a model produces calibrated uncertainty to reflect its own confidence and…

We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…

As machine learning (ML) models are increasingly deployed in high-stakes domains, trustworthy uncertainty quantification (UQ) is critical for ensuring the safety and reliability of these models. Traditional UQ methods rely on specifying a…

In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within…

In this work, we propose a robust optimization approach to mitigate the impact of uncertainties in particle precipitation. Our model incorporates partial differential equations, more particular nonlinear and nonlocal population balance…

The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive…

Scientific Machine Learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques for uncovering governing equations of complex processes. Among the available approaches, Universal…

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual…

While neural networks have demonstrated impressive performance across various tasks, accurately quantifying uncertainty in their predictions is essential to ensure their trustworthiness and enable widespread adoption in critical systems.…