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Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
Real-world multi-agent systems are often dynamic and continuous, where the agents co-evolve and undergo changes in their trajectories and interactions over time. For example, the COVID-19 transmission in the U.S. can be viewed as a…
Data-driven graph learning models a network by determining the strength of connections between its nodes. The data refers to a graph signal which associates a value with each graph node. Existing graph learning methods either use simplified…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
Deep unsupervised representation learning has recently led to new approaches in the field of Unsupervised Anomaly Detection (UAD) in brain MRI. The main principle behind these works is to learn a model of normal anatomy by learning to…
Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…
Modeling dynamical systems is crucial across the science and engineering fields for accurate prediction, control, and decision-making. Recently, machine learning (ML) approaches, particularly neural ordinary differential equations (NODEs),…
Model-based design of experiments (MBDOE) is essential for efficient parameter estimation in nonlinear dynamical systems. However, conventional adaptive MBDOE requires costly posterior inference and design optimization between each…
Understanding how the brain's complex nonlinear dynamics give rise to cognitive function remains a central challenge in neuroscience. While brain functional dynamics exhibits scale-free and multifractal properties across temporal scales,…
Resting-state functional magnetic resonance imaging (rs-fMRI) can reflect spontaneous neural activities in brain and is widely used for brain disorder analysis.Previous studies propose to extract fMRI representations through diverse…
Brain decoding techniques are essential for understanding the neurocognitive system. Although numerous methods have been introduced in this field, accurately aligning complex external stimuli with brain activities remains a formidable…
Human brains lie at the core of complex neurobiological systems, where the neurons, circuits, and subsystems interact in enigmatic ways. Understanding the structural and functional mechanisms of the brain has long been an intriguing pursuit…
Brain lesion segmentation plays an essential role in neurological research and diagnosis. As brain lesions can be caused by various pathological alterations, different types of brain lesions tend to manifest with different characteristics…
Brain function is organized in coordinated modes of spatio-temporal activity (functional networks) exhibiting an intrinsic baseline structure with variations under different experimental conditions. Existing approaches for uncovering such…
The Lewy body dementia (LBD) is the second most common neurodegenerative dementia after Alzheimer's disease (AD). Early differentiation between AD and LBD is crucial because they require different treatment approaches, but this is…
Divergent brain connectivity is thought to underlie the behavioral and cognitive symptoms observed in many neurodevelopmental disorders. Quantifying divergence from neurotypical connectivity patterns offers a promising pathway to inform…
Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every…
The differential diagnosis of neurodegenerative diseases, characterized by overlapping symptoms, may be challenging. Brain imaging coupled with artificial intelligence has been previously proposed for diagnostic support, but most of these…
The brain must extract behaviorally relevant latent variables from the signals streamed by the sensory organs. Such latent variables are often encoded in the dynamics that generated the signal rather than in the specific realization of the…