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Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these…

When we use simulation to assess the performance of stochastic systems, the input models used to drive simulation experiments are often estimated from finite real-world data. There exist both input model and simulation estimation…

Integrated Assessment Models (IAMs) of the climate and economy aim to analyze the impact and efficacy of policies that aim to control climate change, such as carbon taxes and subsidies. A major characteristic of IAMs is that their…

Turbulent flows are of central importance across applications in science and engineering problems. For design and analysis, scientists and engineers use Computational Fluid Dynamics (CFD) simulations using turbulence models. Turbulent…

A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian…

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…

Modern autonomous systems with machine learning components often use uncertainty quantification to help produce assurances about system operation. However, there is a lack of consensus in the community on what uncertainty is and how to…

We present a risk-aware formalism for evaluating system trajectories in the presence of uncertain interactions between the system and its environment. The proposed formalism supports reasoning under uncertainty and systematically handles…

Environmental research increasingly uses high-dimensional remote sensing and numerical model output to help fill space-time gaps between traditional observations. Such output is often a noisy proxy for the process of interest. Thus one…

Large language models (LLMs) often generate fluent but factually incorrect outputs, known as hallucinations, which undermine their reliability in real-world applications. While uncertainty estimation has emerged as a promising strategy for…

Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…

The Bayesian uncertainty quantification technique has become well established in turbulence modeling over the past few years. However, it is computationally expensive to construct a globally accurate surrogate model for Bayesian inference…

In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…

Uncertainty is ubiquitous in real-world data, and the assumptions underlying classical linear regression models are often violated in practice. Inspired by the theory of sublinear expectation, we consider a linear regression model where the…

The understanding of methane emission and methane absorption plays a central role both in the atmosphere and on the surface of the Earth. Several important ecological processes, e.g., ebullition of methane and its natural microergodicity…

Energy systems modellers often resort to simplified system representations and deterministic model formulations (i.e., not considering uncertainty) to preserve computational tractability. However, reduced levels of detail and neglected…

Uncertainty quantification approaches have been more critical in large language models (LLMs), particularly high-risk applications requiring reliable outputs. However, traditional methods for uncertainty quantification, such as…

Controlling UAV flights precisely requires a realistic dynamic model and accurate state estimates from onboard sensors like UAV, GPS and visual observations. Obtaining a precise dynamic model is extremely difficult, as important aerodynamic…

Extreme weather is one of the main mechanisms through which climate change will directly impact human society. Coping with such change as a global community requires markedly improved understanding of how global warming drives extreme…

In the study of complex systems, evaluating physical observables often requires sampling representative configurations via Monte Carlo techniques. These methods rely on repeated evaluations of the system's energy and force fields, which can…