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Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…
Deep neural networks are used to model the magnetization dynamics in magnetic thin film elements. The magnetic states of a thin film element can be represented in a low dimensional space. With convolutional autoencoders a compression ratio…
This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
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…
Machine learning (ML) is a subfield of artificial intelligence. The term applies broadly to a collection of computational algorithms and techniques that train systems from raw data rather than a priori models. ML techniques are now…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
This paper explores machine learning (ML) models for classifying lung cancer levels to improve diagnostic accuracy and prognosis. Through parameter tuning and rigorous evaluation, we assess various ML algorithms. Techniques like minimum…
Model Agnostic Meta Learning or MAML has become the standard for few-shot learning as a meta-learning problem. MAML is simple and can be applied to any model, as its name suggests. However, it often suffers from instability and…
In this article, we discuss some of the recent developments in applying machine learning (ML) techniques to nonlinear dynamical systems. In particular, we demonstrate how to build a suitable ML framework for addressing two specific…
Machine learning (ML) is a promising approach for performing challenging quantum-information tasks such as device characterization, calibration and control. ML models can train directly on the data produced by a quantum device while…
Recent developments in applied mathematics increasingly employ machine learning (ML)-particularly supervised learning-to accelerate numerical computations, such as solving nonlinear partial differential equations. In this work, we extend…
The significant amount of training data required for training Convolutional Neural Networks has become a bottleneck for applications like semantic segmentation. Few-shot semantic segmentation algorithms address this problem, with an aim to…
The deployment of Quantized Neural Networks (QNNs) on resource-constrained edge devices, such as microcontrollers (MCUs), introduces fundamental challenges in balancing model performance, computational complexity, and memory constraints.…
Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…
In this paper, we study the feature learning ability of two-layer neural networks in the mean-field regime through the lens of kernel methods. To focus on the dynamics of the kernel induced by the first layer, we utilize a two-timescale…
We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…
There is growing interest in using machine learning (ML) methods for structural metamodeling due to the substantial computational cost of traditional simulations. Purely data-driven strategies often face limitations in model robustness,…
Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the…