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The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial…

Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model using data-driven emulators, including neural operator architectures. For chaotic systems, the inherent sensitivity to initial…

The problem of statistical learning is to construct a predictor of a random variable $Y$ as a function of a related random variable $X$ on the basis of an i.i.d. training sample from the joint distribution of $(X,Y)$. Allowable predictors…

In learning with noisy labels, the sample selection approach is very popular, which regards small-loss data as correctly labeled during training. However, losses are generated on-the-fly based on the model being trained with noisy labels,…

This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common…

We study the problem of non-Bayesian social learning with uncertain models, in which a network of agents seek to cooperatively identify the state of the world based on a sequence of observed signals. In contrast with the existing…

A Bayesian treatment of deep learning allows for the computation of uncertainties associated with the predictions of deep neural networks. We show how the concept of Errors-in-Variables can be used in Bayesian deep regression to also…

Many applications require the ability to judge uncertainty of time-series forecasts. Uncertainty is often specified as point-wise error bars around a mean or median forecast. Due to temporal dependencies, such a method obscures some…

Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…

Texture classification is a pivotal task in computer vision, presenting unique challenges due to high inter-class similarity and the sensitivity of structural patterns to scale and illumination changes. While Convolutional Neural Networks…

Accurate state estimation requires careful consideration of uncertainty surrounding the process and measurement models; these characteristics are usually not well-known and need an experienced designer to select the covariance matrices. An…

When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…

Calibration error is commonly adopted for evaluating the quality of uncertainty estimators in deep neural networks. In this paper, we argue that such a metric is highly beneficial for training predictive models, even when we do not…

We present a new method for forecasting systems of multiple interrelated time series. The method learns the forecast models together with discovering leading indicators from within the system that serve as good predictors improving the…

The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fundamental drivers of forecast accuracy. Here, we demonstrate…

Seasonal forecasting remains challenging due to the inherent chaotic nature of atmospheric dynamics. This paper introduces DeepSeasons, a novel deep learning approach designed to enhance the accuracy and reliability of seasonal forecasts.…

We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…

The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of…

Analyzing signals arising from dynamical systems typically requires many modeling assumptions and parameter estimation. In high dimensions, this modeling is particularly difficult due to the "curse of dimensionality". In this paper, we…

Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…