Related papers: Nonlinear Expectation Inference for Efficient Unce…

Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to…

The calibration of a reservoir model with observed transient data of fluid pressures and rates is a key task in obtaining a predictive model of the flow and transport behaviour of the earth's subsurface. The model calibration task, commonly…

The ability to make accurate predictions with quantified uncertainty provides a crucial foundation for the successful management of a geothermal reservoir. Conventional approaches for making predictions using geothermal reservoir models…

Accurate overland runoff and infiltration predictions are critical for effective water resources management, in particular for urban flood management. However, the inherent uncertainty in rainfall patterns, soil properties, and initial…

We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…

Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art…

Sequential probabilistic inference from streaming observations requires modeling distributions over future trajectories as new observations arrive. Although diffusion and flow-matching models are effective at capturing high-dimensional,…

In this article, we extend the a posteriori error estimates for hierarchical mixed-dimensional elliptic equations developed in [Varela et al., J. Numer. Math., 48 (2023), pp. 247-280] to the setting of non-matching mixed-dimensional grids.…

A critical limitation of current methods based on Neural Radiance Fields (NeRF) is that they are unable to quantify the uncertainty associated with the learned appearance and geometry of the scene. This information is paramount in real…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

A computational method based on the non-linear Gaussian process (GP), known as deep Gaussian processes (deep GPs) for uncertainty quantification & propagation in modelling of flow through heterogeneous porous media is presented. The method…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior…

In many scientific applications, uncertainty of estimates from an earlier (upstream) analysis needs to be propagated in subsequent (downstream) Bayesian analysis, without feedback. Cutting feedback methods, also termed cut-Bayes, achieve…

Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…

Many applications in computational sciences and statistical inference require the computation of expectations with respect to complex high-dimensional distributions with unknown normalization constants, as well as the estimation of these…

Quantification of uncertainty in production/injection forecasting is an important aspect of reservoir simulation studies. Conventional approaches include intrusive Galerkin-based methods (e.g., generalized polynomial chaos (gPC) and…

Seismic full waveform inversion (FWI) is a powerful technique to generate high resolution images of the Earth's interior. However, significant uncertainty exists in all FWI solutions due to imperfect acquisition geometries, inherent noise…

Reservoir engineers use large-scale numerical models to predict the production performance in oil and gas fields. However, these models are constructed based on scarce and often inaccurate data, making their predictions highly uncertain. On…

Simulating Darcy flows in porous media is fundamental to understand the future flow behavior of fluids in hydrocarbon and carbon storage reservoirs. Geological models of reservoirs are often associated with high uncertainly leading to many…