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We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can…

Renewable energy is essential for energy security and global warming mitigation. However, power generation from renewable energy sources is uncertain due to volatile weather conditions and complex equipment operations. To improve…

Transformers have recently gained prominence in long time series forecasting by elevating accuracies in a variety of use cases. Regrettably, in the race for better predictive performance the overhead of model architectures has grown…

In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

Time series forecasting is a critical task in various domains, where accurate predictions can drive informed decision-making. Traditional forecasting methods often rely on current observations of variables to predict future outcomes,…

Projecting climate change is a generalization problem: we extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller…

This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improve the modeling of physical processes. Specifically, we show that a…

Global climate models represent small-scale processes such as clouds and convection using quasi-empirical models known as parameterizations, and these parameterizations are a leading cause of uncertainty in climate projections. A promising…

Conformal prediction can yield statistically valid prediction intervals for any regression model, with no model modifications and small computational costs. To assess its practical value, we apply conformal methods to quantify uncertainty…

Physics-based climate projections using general circulation models are essential for assessing future risks, but their coarse resolution limits regional decision-making. Statistical downscaling can efficiently add detail, yet many methods…

Quantile regression is a powerful tool for inferring how covariates affect specific percentiles of the response distribution. Existing methods either estimate conditional quantiles separately for each quantile of interest or estimate the…

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…

A central challenge in climate science and applied mathematics is developing data-driven models of multiscale systems that capture both stationary statistics and responses to external perturbations. Current neural climate emulators aim to…

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…

Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…

In this article, we present a novel approach to multivariate probabilistic forecasting. Our approach is based on an extension of single-output quantile regression (QR) to multivariate-targets, called quantile surfaces (QS). QS uses a simple…

``Online" data assimilation (DA) is used to generate a new seasonal-resolution reanalysis dataset over the last millennium by combining forecasts from an ocean--atmosphere--sea-ice coupled linear inverse model with climate proxy records.…

Accurate and efficient temperature prediction is critical for optimizing the preheating process of PET preforms in industrial microwave systems prior to blow molding. We propose a novel deep learning framework for generalized temperature…

The low frequency variability of the extratropical atmosphere involves hemispheric-scale recurring, often persistent, states known as teleconnection patterns or regimes, which can have profound impact on predictability on intra-seasonal and…