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Forecasting time series and time-dependent data is a common problem in many applications. One typical example is solving ordinary differential equation (ODE) systems $\dot{x}=F(x)$. Oftentimes the right hand side function $F(x)$ is not…

Accurate modeling of cognitive decline in Alzheimer's disease is essential for early stratification and personalized management. While tabular predictors provide robust markers of global risk, their ability to capture subtle brain changes…

Functional brain networks can change rapidly as a function of stimuli or cognitive shifts. Tracking dynamic functional connectivity is particularly challenging as it requires estimating the structure of the network at each moment as well as…

Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…

A deep latent variable model is a powerful method for capturing complex distributions. These models assume that underlying structures, but unobserved, are present within the data. In this dissertation, we explore high-dimensional problems…

Predicting the spatio-temporal progression of brain tumors is essential for guiding clinical decisions in neuro-oncology. We propose a hybrid mechanistic learning framework that combines a mathematical tumor growth model with a guided…

We conduct an imaging genetics study to explore how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer's disease and mild cognitive impairment. We develop an analysis of…

Deep learning methods are increasingly being used with neuroimaging data like structural and function magnetic resonance imaging (MRI) to predict the diagnosis of neuropsychiatric and neurological disorders. For psychiatric disorders in…

Causal inference in continuous-time sequential decision problems is challenged by hidden confounders. We show that, in latent state-space models with time-varying interventions, observability of the latent dynamics from observed data is…

This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…

Dynamic MRI reconstruction, one of inverse problems, has seen a surge by the use of deep learning techniques. Especially, the practical difficulty of obtaining ground truth data has led to the emergence of unsupervised learning approaches.…

We propose a machine-learning approach to model long-term out-of-sample dynamics of brain activity from task-dependent fMRI data. Our approach is a three stage one. First, we exploit Diffusion maps (DMs) to discover a set of variables that…

Supervised Deep-Learning (DL)-based reconstruction algorithms have shown state-of-the-art results for highly-undersampled dynamic Magnetic Resonance Imaging (MRI) reconstruction. However, the requirement of excessive high-quality…

Modeling and understanding the environment is an essential task for autonomous driving. In addition to the detection of objects, in complex traffic scenarios the motion of other road participants is of special interest. Therefore, we…

A central challenge in the computational modeling of neural dynamics is the trade-off between accuracy and simplicity. At the level of individual neurons, nonlinear dynamics are both experimentally established and essential for neuronal…

Dynamic imaging is critical for understanding and visualizing dynamic biological processes in medicine and cell biology. These applications often encounter the challenge of a limited amount of time series data and time points, which hinders…

Identifying objective neuroimaging biomarkers to forecast Alzheimer's disease (AD) progression is crucial for timely intervention. However, this task remains challenging due to the complex dysfunctions in the spatio-temporal characteristics…

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…

An unprecedented amount of existing functional Magnetic Resonance Imaging (fMRI) data provides a new opportunity to understand the relationship between functional fluctuation and human cognition/behavior using a data-driven approach. To…

Time Varying Functional Connectivity (TVFC) investigates how the interactions among brain regions vary over the course of an fMRI experiment. The transitions between different individual connectivity states can be modulated by changes in…