Physics-Augmented Modeling and Optimization of Complex Systems: Healthcare Applications

The rapid advances in sensing technology have created a data-rich environment that tremendously

benefits predictive modeling and decision-making for complex systems. Harnessing

the full potential of this complexly-structured sensing data requires the development of

novel and reliable analytical models and tools for system informatics. Such advancements in

sensing present unprecedented opportunities to investigate system dynamics and optimize

decision-making processes for smart health. Nevertheless, sensing data is typically

characterized by high dimensionality and intricate structures. To fully unlock the potential of

this data, we significantly rely on innovative analytical methods and tools that can effectively

process information.

The objective of this dissertation is to develop innovative physics-augmented methodologies

for modeling, monitoring, and optimizing complex systems. Specifically, the research

focuses on the development of physics-augmented machine learning models that facilitate

optimal decision-making in complex healthcare systems. This research will enable 1) robust

predictive modeling of spatiotemporal systems; 2) extracting important feature information

about system dynamics; 3) optimizing decision-making under uncertainty and sparse sensor

observations. My research accomplishments include:

• Physics-constrained deep learning for robust inverse modeling of spatiotemporal systems:

In Chapter 2, we developed a physics-constrained machine learning framework

to address the high-dimensional inverse problem. This method integrates physics-based

principles with the advanced deep learning infrastructure to predict the spatiotemporal

system dynamics based on indirect and noisy sensor observations. This methodology

is implemented in inverse electrocardiography (ECG) modeling.

• Physics-constrained active learning and sequential design in 3D spatiotemporal systems:

In Chapter 3, a novel physics-constrained strategy for optimal sensor placement

is proposed to actively explore and model the dynamics of 3D complex-structured

systems. This active learning scheme combines uncertainty estimation in deep learning

and space-filling design over the complex geometry, enabling effective learning of system

dynamics from limited sensor exploration.

• Defects identification in 3D heterogeneous complex systems: In Chapter 4, we designed

a new framework to characterize the location and extent of diseased cardiac tissue

from indirect and noisy body sensor observations. Specifically, a hierarchical Gaussian

Process-based active learning framework was developed to reliably identify the defect

location and further extract spatial-varying properties in a complex 3D system.