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Current climate models often struggle with accuracy because they lack sufficient resolution, a limitation caused by computational constraints. This reduces the precision of weather forecasts and long-term climate predictions. To address…

Machine Learning (ML) is accelerating the progress of materials prediction and classification, with particular success in CGNN designs. While classical ML methods remain accessible, advanced deep networks are still challenging to build and…

Machine Learning (ML) techniques are revolutionizing the way to perform efficient materials modeling. Nevertheless, not all the ML approaches allow for the understanding of microscopic mechanisms at play in different phenomena. To address…

Forecasting meteorological variables is challenging due to the complexity of their processes, requiring advanced models for accuracy. Accurate precipitation forecasts are vital for society. Reliable predictions help communities mitigate…

Recently, there has been a growing interest in applying machine learning methods to problems in engineering mechanics. In particular, there has been significant interest in applying deep learning techniques to predicting the mechanical…

Quantifying forecast uncertainty is a key aspect of state-of-the-art numerical weather prediction and data assimilation systems. Ensemble-based data assimilation systems incorporate state-dependent uncertainty quantification based on…

This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that…

Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression…

A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…

Unveiling the evolutionary history of galaxies necessitates a precise understanding of their physical properties. Traditionally, astronomers achieve this through spectral energy distribution (SED) fitting. However, this approach can be…

Informed Machine Learning has emerged as a viable generalization of Machine Learning (ML) by building a unified conceptual and algorithmic setting for constructing models on a unified basis of knowledge and data. Physics-informed ML…

We discuss an approach to probabilistic forecasting based on two chained machine-learning steps: a dimensional reduction step that learns a reduction map of predictor information to a low-dimensional space in a manner designed to preserve…

Knowledge distillation (KD) is an effective model compression method that can transfer the internal capabilities of large language models (LLMs) to smaller ones. However, the multi-modal probability distribution predicted by teacher LLMs…

A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert…

Systems exhibiting nonlinear dynamics, including but not limited to chaos, are ubiquitous across Earth Sciences such as Meteorology, Hydrology, Climate and Ecology, as well as Biology such as neural and cardiac processes. However, System…

This work presents a distributed algorithm for nonlinear adaptive learning. In particular, a set of nodes obtain measurements, sequentially one per time step, which are related via a nonlinear function; their goal is to collectively…

Kernel embeddings of distributions have recently gained significant attention in the machine learning community as a data-driven technique for representing probability distributions. Broadly, these techniques enable efficient computation of…

Accurate cyclone forecasting is essential for minimizing loss of life, infrastructure damage, and economic disruption. Traditional numerical weather prediction models, though effective, are computationally intensive and prone to error due…

This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…

In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…