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Machine learning methods adapt the parameters of a model, constrained to lie in a given model class, by using a fixed learning procedure based on data or active observations. Adaptation is done on a per-task basis, and retraining is needed…

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…

Weather forecasting centers currently rely on statistical postprocessing methods to minimize forecast error. This improves skill but can lead to predictions that violate physical principles or disregard dependencies between variables, which…

Climate models are essential to understand and project climate change, yet long-standing biases and uncertainties in their projections remain. This is largely associated with the representation of subgrid-scale processes, particularly…

Deep neural network based recommendation systems have achieved great success as information filtering techniques in recent years. However, since model training from scratch requires sufficient data, deep learning-based recommendation…

We derive a linearized rotating shallow water system modeling tides, which can be discretized by mixed finite elements. Unlike previous models, this model allows for multiple layers stratified by density. Like the single-layer…

Rainfall prediction is one of the challenging and uncertain tasks which has a significant impact on human society. Timely and accurate predictions can help to proactively reduce human and financial loss. This study presents a set of…

At the heart of the Met Office climate and weather forecasting capabilities lies a sophisticated numerical model which solves the equations of large-scale atmospheric flow. Since this model uses semi-implicit time-stepping, it requires the…

This paper proposes a semi-conditional normalizing flow model for semi-supervised learning. The model uses both labelled and unlabeled data to learn an explicit model of joint distribution over objects and labels. Semi-conditional…

Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear…

Recent applications of machine learning (ML) reveal a noticeable shift from its use for predictive modeling in the sense of a data-driven construction of models mainly used for the purpose of prediction (of ground-truth facts) to its use…

In this work, we study some novel applications of conformal inference techniques to the problem of providing machine learning procedures with more transparent, accurate, and practical performance guarantees. We provide a natural extension…

Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an…

Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…

Applications of machine learning tools to problems of physical interest are often criticized for producing sensitivity at the expense of transparency. To address this concern, we explore a data planing procedure for identifying combinations…

The growing number of pretrained models in Machine Learning (ML) presents significant challenges for practitioners. Given a new dataset, they need to determine the most suitable deep learning (DL) pipeline, consisting of the pretrained…

Time series forecasts are widely used to inform decisions. Human decision-makers interpret these forecasts, incorporate prior experience and uncertainty about future outcomes, and then make a decision. In this paper, we propose a new…

Modern machine learning models are opaque, and as a result there is a burgeoning academic subfield on methods that explain these models' behavior. However, what is the precise goal of providing such explanations, and how can we demonstrate…

Fluids under nanoscale confinement differ -- and often dramatically -- from their bulk counterparts. A notorious feature of nanoconfined fluids is their inhomogeneous density profile along the confining dimension, which plays a key role in…

The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…