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Interacting defect systems are ubiquitous in materials under realistic scenarios, yet gaining an atomic-level understanding of these systems from a computational perspective is challenging - it often demands substantial resources due to the…

In the past decade the mathematical theory of machine learning has lagged far behind the triumphs of deep neural networks on practical challenges. However, the gap between theory and practice is gradually starting to close. In this paper I…

Recent advancements in both representation learning and function learning have demonstrated substantial promise across diverse domains of artificial intelligence. However, the effective integration of these paradigms poses a significant…

Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal…

One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…

Machine learning has emerged as a powerful tool in materials discovery, enabling the rapid design of novel materials with tailored properties for countless applications, including in the context of energy and sustainability. To ensure the…

An efficient technique based on low-rank separated approximations is proposed for computation of three-dimensional integrals arising in the energy deposition model that describes ion-atomic collisions. Direct tensor-product quadrature…

Two-line elements are widely used for space operations to predict the orbit with a moderate accuracy for 2-3 days. Local optimization methods, such as the nonlinear least squares method with differential corrections, can estimate a TLE as…

While robot learning has demonstrated promising results for enabling robots to automatically acquire new skills, a critical challenge in deploying learning-based systems is scale: acquiring enough data for the robot to effectively…

Loss functions are at the heart of deep learning, shaping how models learn and perform across diverse tasks. They are used to quantify the difference between predicted outputs and ground truth labels, guiding the optimization process to…

Implicit neural representation (INR) models signals as continuous functions using neural networks, offering efficient and differentiable optimization for inverse problems across diverse disciplines. However, the representational capacity of…

Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…

In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using…

Given $E_0, E_1, F_0, F_1, E$ rearrangement invariant function spaces, $a_0$, $a_1$, $b_0$, $b_1$, $b$ slowly varying functions and $0< \theta_0<\theta_1<1$, we characterize the interpolation spaces $$(\overline{X}^{\mathcal…

Quantum materials research requires co-design of theory with experiments and involves demanding simulations and the analysis of vast quantities of data, usually including pattern recognition and clustering. Artificial intelligence is a…

Estimating the current scene and understanding the potential maneuvers are essential capabilities of automated vehicles. Most approaches rely heavily on the correctness of maps, but neglect the possibility of outdated information. We…

A retrieval model should not only interpolate the training data but also extrapolate well to the queries that are different from the training data. While neural retrieval models have demonstrated impressive performance on ad-hoc search…

Lattice QCD is notorious for its computational expense. Modern lattice simulations require large-scale computational resources to handle the large number of Dirac operator inversions used to construct correlation functions. Machine learning…

Many real world data are sampled functions. As shown by Functional Data Analysis (FDA) methods, spectra, time series, images, gesture recognition data, etc. can be processed more efficiently if their functional nature is taken into account…

This paper proposes a computationally efficient methodology to predict the damage progression in solder contacts of electronic components using temperature-time curves. For this purpose, two machine learning algorithms, a Multilayer…