Related papers: Acquisition-Independent Deep Learning for Quantita…
Purpose: The clinical feasibility and translation of many advanced quantitative MRI (qMRI) techniques are inhibited by their restriction to 'research mode', due to resource-intensive, offline parameter estimation. This work aimed to achieve…
The feasibility of variational quantum algorithms, the most popular correspondent of neural networks on noisy, near-term quantum hardware, is highly impacted by the circuit depth of the involved parametrized quantum circuits (PQCs). Higher…
The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over…
Quantum embedding is a fundamental prerequisite for applying quantum machine learning techniques to classical data, and has substantial impacts on performance outcomes. In this study, we present Neural Quantum Embedding (NQE), a method that…
Neural Controlled Differential Equations (Neural CDEs, NCDEs) are a unique branch of methods, specifically tailored for analysing temporal sequences. However, they come with drawbacks, the main one being the number of parameters, required…
Neural networks inspired by differential equations have proliferated for the past several years. Neural ordinary differential equations (NODEs) and neural controlled differential equations (NCDEs) are two representative examples of them. In…
Quantitative susceptibility mapping (QSM) is an MRI phase-based post-processing method that quantifies tissue magnetic susceptibility distributions. However, QSM acquisitions are relatively slow, even with parallel imaging. Incoherent…
Purpose: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cram\'er-Rao bound. Theory and Methods: We generalize the mean squared error loss to control the bias and…
Neural Controlled Differential Equations (NCDEs) are a state-of-the-art tool for supervised learning with irregularly sampled time series (Kidger, 2020). However, no theoretical analysis of their performance has been provided yet, and it…
Deep learning (DL) is gaining popularity as a parameter estimation method for quantitative MRI. A range of competing implementations have been proposed, relying on either supervised or self-supervised learning. Self-supervised approaches,…
Background: MRI is the modality of choice for cartilage imaging; however, its diagnostic performance is variable and significantly lower than the gold standard diagnostic knee arthroscopy. In recent years, deep learning has been used to…
We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…
The increasing focus on long-term time series prediction across various fields has been significantly strengthened by advancements in quantum computation. In this paper, we introduce a data-driven method designed for time series prediction…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
We consider estimating a low-dimensional parameter in an estimating equation involving high-dimensional nuisances that depend on the parameter. A central example is the efficient estimating equation for the (local) quantile treatment effect…
Magnetic resonance imaging (MRI) offers superior soft tissue contrast and is widely used in biomedicine. However, conventional MRI is not quantitative, which presents a bottleneck in image analysis and digital healthcare. Typically,…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
The rapid advancements in quantum computing (QC) and machine learning (ML) have led to the emergence of quantum machine learning (QML), which integrates the strengths of both fields. Among QML approaches, variational quantum circuits…
Quantum error mitigation (QEM) provides a practical route for estimating reliable observables on noisy intermediate-scale quantum (NISQ) devices. Traditional QEM strategies, including zero-noise extrapolation (ZNE) and Clifford data…
The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…