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The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…

The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…

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…

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,…

Regression is an essential and fundamental methodology in statistical analysis. The majority of the literature focuses on linear and nonlinear regression in the context of the Euclidean space. However, regression models in non-Euclidean…

This paper discusses several modern approaches to regression analysis involving time series data where some of the predictor variables are also indexed by time. We discuss classical statistical approaches as well as methods that have been…

Recent advances have introduced diffusion models for probabilistic streamflow forecasting, demonstrating strong early flood-warning skill. However, current implementations rely on recurrent Long Short-Term Memory (LSTM) backbones and…

A recent study in turbulent flow simulation demonstrated the potential of generative diffusion models for fast 3D surrogate modeling. This approach eliminates the need for specifying initial states or performing lengthy simulations,…

We consider modeling of angular or directional data viewed as a linear variable wrapped onto a unit circle. In particular, we focus on the spatio-temporal context, motivated by a collection of wave directions obtained as computer model…

The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…

Machine Learning is beginning to provide state-of-the-art performance in a range of environmental applications such as streamflow prediction in a hydrologic basin. However, building accurate broad-scale models for streamflow remains…

Modeling the time-varying 3D appearance of plants during growth poses unique challenges: unlike most dynamic scenes, plants continuously generate new geometry as they expand, branch, and differentiate. Existing dynamic scene representations…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…

Recent advances in time series research facilitate the development of foundation models. While many state-of-the-art time series foundation models have been introduced, few studies examine their effectiveness in specific downstream…

We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…

In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

We consider the use of probabilistic neural networks for fluid flow {surrogate modeling} and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the…

This work introduces a novel approach for generating conditional probabilistic rainfall forecasts with temporal and spatial dependence. A two-step procedure is employed. Firstly, marginal location-specific distributions are jointly…

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…