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Neutrino mass constraints are a primary focus of current and future large-scale structure (LSS) surveys. Non-linear LSS models rely heavily on cosmological simulations -- the impact of massive neutrinos should therefore be included in these…

We propose an efficient matrix rank reduction method for non-negative matrices, whose time complexity is quadratic in the number of rows or columns of a matrix. Our key insight is to formulate rank reduction as a mean-field approximation by…

We study deep learning approaches to inferring numerical coordinates for points of interest in an input image. Existing convolutional neural network-based solutions to this problem either take a heatmap matching approach or regress to…

We study the second-order quantum phase-transition of massive real scalar field theory with a quartic interaction ($\phi^4$ theory) in (1+1) dimensions on an infinite spatial lattice using matrix product states (MPS). We introduce and apply…

A new knowledge-based and machine learning hybrid modeling approach, called conditional Gaussian neural stochastic differential equation (CGNSDE), is developed to facilitate modeling complex dynamical systems and implementing analytic…

We are concerned with the numerical solution of a class integro-differential equations, known as Neural Field Equations, which describe the large-scale dynamics of spatially structured networks of neurons. These equations have many…

Machine learning (ML) tools such as encoder-decoder convolutional neural networks (CNN) can represent incredibly complex nonlinear functions which map between combinations of images and scalars. For example, CNNs can be used to map…

As neural networks grow in scale, their training becomes both computationally demanding and rich in dynamics. Amidst the flourishing interest in these training dynamics, we present a novel observation: Parameters during training exhibit…

Modern buildings encompass complex dynamics of multiple electrical, mechanical, and control systems. One of the biggest hurdles in applying conventional model-based optimization and control methods to building energy management is the huge…

We propose a numerical method based on the master field for large-$N$ reduced matrix models. While the master field is originally an infinite-dimensional matrix, in this method it is regularized to a finite dimension, with the requirement…

This paper wants to increase our understanding and computational know-how for time--varying matrix problems and Zhang Neural Networks (ZNNs). These neural networks were invented for time or single parameter--varying matrix problems around…

Accurate spatiotemporal image reconstruction methods are needed for a wide range of biomedical research areas but face challenges due to data incompleteness and computational burden. Data incompleteness arises from the undersampling often…

We introduce an efficient optimization-based meta-learning technique for large-scale neural field training by realizing significant memory savings through automated online context point selection. This is achieved by focusing each learning…

Real-world time series often exhibit complex interdependencies that cannot be captured in isolation. Global models that model past data from multiple related time series globally while producing series-specific forecasts locally are now…

Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…

Deep neural networks (DNNs) have achieved significant success in a variety of real world applications, i.e., image classification. However, tons of parameters in the networks restrict the efficiency of neural networks due to the large model…

A new model is presented for multisite statistical downscaling of temperature and precipitation using convolutional conditional neural processes (convCNPs). ConvCNPs are a recently developed class of models that allow deep learning…

While deep learning techniques have become extremely popular for solving a broad range of optimization problems, methods to enforce hard constraints during optimization, particularly on deep neural networks, remain underdeveloped. Inspired…

As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless…

We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. The approach is…