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We introduce a unified framework -- Quantum Neural Ordinary and Partial Differential Equations (QNODEs and QNPDEs) -- which extends the continuous-time formalism of classical neural ordinary and partial differential equations into quantum…

Quantitative MRI (qMRI) aims to map tissue properties non-invasively via models that relate these unknown quantities to measured MRI signals. Estimating these unknowns, which has traditionally required model fitting - an often iterative…

This paper demonstrates spherical convolutional neural networks (S-CNN) offer distinct advantages over conventional fully-connected networks (FCN) at estimating scalar parameters of tissue microstructure from diffusion MRI (dMRI). Such…

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…

Quantum computing is expected to provide exponential speedup in machine learning. However, optimizing the data loading process, commonly referred to as quantum data embedding, to maximize classification performance remains a critical…

Self-supervised deep learning has accelerated 2D natural image analysis but remains difficult to translate into 3D MRI, where data are scarce and pre-trained 2D backbones cannot capture volumetric context. We present a…

This paper presents a novel deep learning-based approach named RealDiffFusionNet incorporating Neural Controlled Differential Equations (Neural CDE) - time series models that are robust in handling irregularly sampled data - and multi-head…

A longstanding computational challenge is the accurate simulation of many-body particle systems. Especially for deriving key characteristics of high-impact but complex systems such as battery materials and high entropy alloys (HEA). While…

Biophysical model fitting plays a key role in obtaining quantitative parameters from physiological signals and images. However, the model complexity for molecular magnetic resonance imaging (MRI) often translates into excessive computation…

The evaluation and treatment of acute cerebral ischemia requires a technique that can determine the total area of tissue at risk for infarction using diagnostic magnetic resonance imaging (MRI) sequences. Typical MRI data sets consist of…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…

Reliable MRI is crucial for accurate interpretation in therapeutic and diagnostic tasks. However, undersampling during MRI acquisition as well as the overparameterized and non-transparent nature of deep learning (DL) leaves substantial…

Partial differential equations (PDEs) play a crucial role in financial mathematics, particularly in portfolio optimization, and solving them using classical numerical or neural network methods has always posed significant challenges. Here,…

Deep equilibrium models (DEQ) have emerged as a powerful alternative to deep unfolding (DU) for image reconstruction. DEQ models-implicit neural networks with effectively infinite number of layers-were shown to achieve state-of-the-art…

This paper introduces CompressedMediQ, a novel hybrid quantum-classical machine learning pipeline specifically developed to address the computational challenges associated with high-dimensional multi-class neuroimaging data analysis.…

Magnetic resonance imaging (MRI) is a cornerstone of clinical neuroimaging, yet conventional MRIs provide qualitative information heavily dependent on scanner hardware and acquisition settings. While quantitative MRI (qMRI) offers intrinsic…

Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical…

This paper proposed a new explicit nonlinear dimensionality reduction using neural networks for image retrieval tasks. We first proposed a Quasi-curvature Locally Linear Embedding (QLLE) for training set. QLLE guarantees the linear…

The Quantum Phase Difference Estimation (QPDE) algorithm, as an extension of the Quantum Phase Estimation (QPE), is a quantum algorithm designed to compute the differences of two eigenvalues of a unitary operator by exploiting the quantum…

Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…