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Magnetic resonance imaging (MRI) is a vital diagnostic tool, but its inherently long acquisition times reduce clinical efficiency and patient comfort. Recent advancements in deep learning, particularly diffusion models, have improved…

Spectral unmixing is one of the most important quantitative analysis tasks in hyperspectral data processing. Conventional physics-based models are characterized by clear interpretation. However they may not be suitable for analyzing scenes…

Flexible spacecraft structures present significant challenges for physical and control system design due to nonlinear dynamics, mission constraints, environmental variables, and changing operational conditions. This paper presents a…

Identifying from observation data the governing differential equations of a physical dynamics is a key challenge in machine learning. Although approaches based on SINDy have shown great promise in this area, they still fail to address a…

We present a data-driven numerical approach for modeling unknown dynamical systems with missing/hidden parameters. The method is based on training a deep neural network (DNN) model for the unknown system using its trajectory data. A key…

Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…

We demonstrate the application of the Dynamic Mode Decomposition (DMD) for the diagnostic analysis of the nonlinear dynamics of a magnetized plasma in resistive magnetohydrodynamics. The DMD method is an ideal spatio-temporal matrix…

Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

Dynamic free-breathing fetal cardiac MRI is one of the most challenging modalities, which requires high temporal and spatial resolution to depict rapid changes in a small fetal heart. The ability of deep learning methods to recover…

Magnetic Particle Imaging is an emerging imaging modality through which it is possible to detect tracers containing superparamagnetic nanoparticles. The exposure of the particles to dynamic magnetic fields generates a non-linear response…

Phase mixing is a fundamental kinetic process that governs dissipation and stability in collisionless plasmas, but its inherent filamentation in velocity space creates major challenges for both high-fidelity simulations and reduced-order…

In recent studies on MRI reconstruction, advances have shown significant promise for further accelerating the MRI acquisition. Most state-of-the-art methods require a large amount of fully-sampled data to optimise reconstruction models,…

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…

There is much recent interest in techniques to accelerate the data acquisition process in MRI by acquiring limited measurements. Often sophisticated reconstruction algorithms are deployed to maintain high image quality in such settings. In…

Recently, data-driven single-view reconstruction methods have shown great progress in modeling 3D dressed humans. However, such methods suffer heavily from depth ambiguities and occlusions inherent to single view inputs. In this paper, we…

Magnetic resonance elastography is a motion-sensitive image modality that allows to measure in vivo tissue displacement fields in response to mechanical excitations. This paper investigates a data assimilation approach for reconstructing…

Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely…

This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…

Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The…