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Estimating parameters from data is a fundamental problem, customarily done by minimizing a loss function between a model and observed statistics. In scattering-based analysis, researchers often employ their domain expertise to select a…

We describe a computational framework linking Uncertainty Quantification (UQ) methods for continuum problems depending on random parameters with Equation-Free (EF) methods for performing continuum deterministic numerics by acting directly…

Most uncertainty quantification (UQ) approaches provide a single scalar value as a measure of model reliability. However, different uncertainty measures could provide complementary information on the prediction confidence. Even measures…

Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of…

In modern process industries, data-driven models are important tools for real-time monitoring when key performance indicators are difficult to measure directly. While accurate predictions are essential, reliable uncertainty quantification…

Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…

Effective Uncertainty Quantification (UQ) represents a key aspect for reliable deployment of Large Language Models (LLMs) in automated decision-making and beyond. Yet, for LLM generation with multiple choice structure, the state-of-the-art…

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is…

Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…

The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining…

The advent of fabrication techniques like additive manufacturing has focused attention on the considerable variability of material response due to defects and other micro-structural aspects. This variability motivates the development of an…

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…

Over the last few years, debiased estimators have been proposed in order to establish rigorous confidence intervals for high-dimensional problems in machine learning and data science. The core argument is that the error of these estimators…

This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…

We consider optimization problems that arise when estimating a set of unknown parameters from experimental data, particularly in the context of nuclear density functional theory. We examine the cost of not having derivatives of these…

In the context of Monte Carlo (MC) simulation of particle transport Uncertainty Quantification (UQ) addresses the issue of predicting non statistical errors affecting the physical results, i.e. errors deriving mainly from uncertainties in…

Inverse Uncertainty Quantification (UQ) is a process to quantify the uncertainties in random input parameters while achieving consistency between code simulations and physical observations. In this paper, we performed inverse UQ using an…

Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian…