Abstract

Predicting future states of high-dimensional, partially observed dynamical systems - such as cardiac electrical propagation - is crucial for advancing fields like healthcare and physics. While univariate time-series forecasting is well-explored, high-dimensional time-series forecasting presents unresolved challenges. These challenges include the computational burden of processing high-dimensional data and the difficulty of accessing the system’s underlying dynamics directly. Classical optimization and analytical approaches become impractical as the dimensionality increases, leading to a growing interest in data-driven deep learning models, particularly those based on latent dynamics functions. Latent dynamics models provide an efficient way to map high-dimensional observations into lower-dimensional latent spaces, where a dynamics function learns to predict future states. The latent space acts as a coordinate system that simplifies the system’s underlying dynamics, optimizing for representations that expose simple, interpretable patterns. This transformation offers computational advantages and aligns with the theoretical assumption that many complex systems exhibit simple underlying dynamics. However, existing latent dynamics approaches typically focus on modeling individual systems under fixed training distributions, limiting their ability to adapt to related-but-different conditions at test-time. This dissertation proposes novel methods to extend latent dynamics functions to more complex forecasting scenarios, addressing the need for adaptability across heterogeneous environments. Five key research questions guide this work: (1) How can unsupervised latent dynamics functions be learned while integrating known domain knowledge? (2) How can a core latent dynamics function be adapted to downstream systems using control parameters? (3) How can models learn to generalize across environments with limited training samples? (4) How can a latent dynamics function continually adapt to new systems without forgetting previously learned dynamics? (5) How can adaptive latent dynamics functions be effectively deployed in complex clinical settings? The core contributions include: developing a unifying framework for latent dynamics, creating an unsupervised learning model with physics-informed supervision, introducing controllable latent dynamics for parameterized adaptation, extending models with meta-learning to generalize across tasks, and designing continual learning strategies to prevent catastrophic forgetting in dynamic environments. Finally, we propose a continual meta-learning framework for learning personalized neural surrogates of cardiac simulations in non-stationary environments. Together, these contributions advance the state of latent dynamics learning, equipping models to perform efficiently under complex, real-world forecasting conditions.

Library of Congress Subject Headings

Heart--Electric properties--Mathematical models; Heart--Electric properties--Forecasting; Electrophysiology--Mathematical models

Publication Date

8-2025

Document Type

Dissertation

Student Type

Graduate

Degree Name

Computing and Information Sciences (Ph.D.)

Department, Program, or Center

Computing and Information Sciences Ph.D, Department of

College

Golisano College of Computing and Information Sciences

Advisor

Linwei Wang

Advisor/Committee Member

Qi Yu

Advisor/Committee Member

Haibo Yang

Campus

RIT – Main Campus

Plan Codes

COMPIS-PHD

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