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The calibration of rheological parameters in the modeling of complex flows of non-Newtonian fluids can be a daunting task. In this paper we demonstrate how the framework of Uncertainty Quantification (UQ) can be used to improve the…

Modeling yield stress fluids in complex flow scenarios presents significant challenges, particularly because conventional rheological characterization methods often yield material parameters that are not fully representative of the…

In hydrology, modeling streamflow remains a challenging task due to the limited availability of basin characteristics information such as soil geology and geomorphology. These characteristics may be noisy due to measurement errors or may be…

Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical…

In the study of gas dynamics, theoretical modeling and numerical simulation are mostly set up with deterministic settings. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between flow-field…

Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the understanding of time lags associated with the delay between rainfall occurrence and subsequent changes…

Many applications in aerodynamics, particularly in closed-loop control, depend on sensors to estimate the evolving state of the flow. This estimation task is inherently accompanied by uncertainty due to the noisy measurements of sensors or…

Estimating the expectation of a real-valued function of a random variable from sample data is a critical aspect of statistical analysis, with far-reaching implications in various applications. Current methodologies typically assume…

In computational fluid dynamics simulations of industrial flows, models based on the Reynolds-averaged Navier--Stokes (RANS) equations are expected to play an important role in decades to come. However, model uncertainties are still a major…

Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering application. For many practical flows, the turbulence models are by far…

Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…

Predictive uncertainty in hydrological modelling is quantified by using post-processing or Bayesian-based methods. The former methods are not straightforward and the latter ones are not distribution-free (i.e. assumptions on the probability…

Uncertainty quantification is critical for ensuring robustness in high-stakes machine learning applications. We introduce HybridFlow, a modular hybrid architecture that unifies the modeling of aleatoric and epistemic uncertainty by…

Simulating turbulent flows is crucial for a wide range of applications, and machine learning-based solvers are gaining increasing relevance. However, achieving temporal stability when generalizing to longer rollout horizons remains a…

The stochastics two-layer quasi-geostrophic flow model is an intermediate system between the single-layer two dimensional barotropic flow model and the continuously stratified three dimensional baroclinic flow model. This model is widely…

Data-driven methods for improving turbulence modeling in Reynolds-Averaged Navier-Stokes (RANS) simulations have gained significant interest in the computational fluid dynamics community. Modern machine learning algorithms have opened up a…

Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions and…

The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic…

Model-form uncertainty (MFU) in assumptions made during physics-based model development is widely considered a significant source of uncertainty; however, there are limited approaches that can quantify MFU in predictions extrapolating…

To evaluate models as hypotheses, we developed the method of Flux Mapping to construct a hypothesis space based on dominant runoff generating mechanisms. Acceptable model runs, defined as total simulated flow with similar (and minimal)…