Research Overview

I am an applied mathematician working across scientific machine learning, biostatistics, inverse problems, dynamical systems, causal inference, uncertainty quantification, and biomedical artificial intelligence. My research develops along two complementary directions: reliable statistical learning for biomedical and population-health applications, and scientific machine learning for discovering hidden structure in dynamical systems.

Across both directions, I am interested in developing mathematically grounded and computationally scalable methods that quantify uncertainty, remain reliable under heterogeneous or incomplete data, and provide scientifically meaningful insight beyond predictive accuracy.


Graph-iPINN: Inverse Physics-Informed Learning for Sparse Network Discovery

Graph-iPINN develops an inverse physics-informed neural network framework for recovering unknown sparse interaction networks from observations of dynamical systems. The approach jointly learns system dynamics and the underlying network structure while incorporating governing-equation constraints, sparse regularization, and structural graph information.

My work includes finite-difference residual formulations, sparsity-inducing regularization, structural projections for symmetric and loop-free networks, and neural tangent kernel based monitoring and stopping strategies. I have evaluated the framework on Erdős–Rényi, Barabási–Albert, and Watts–Strogatz networks in high-dimensional systems with up to p=2000 state variables.

This work provides the foundation for my broader interests in nonlinear, stochastic, and time-varying dynamical networks, with applications to biological and population-health systems.


B-RISA: Bayesian Robust and Selective Learning for Clinical Prediction

My biostatistics and clinical AI research includes B-RISA, a Bayesian uncertainty-aware framework for robust and selective clinical prediction. The framework studies Bayesian logistic regression, Bayesian linear discriminant analysis, and Bayesian additive regression trees under variations in sample size, dimensionality, class imbalance, covariance structure, nonlinearity, label noise, missingness, and distributional differences.

Beyond discrimination and calibration, B-RISA quantifies patient-level predictive uncertainty using posterior predictive distributions, posterior standard deviations, and credible intervals. It also incorporates selective prediction, allowing a model to defer predictions when uncertainty is high, and evaluates the resulting trade-off between coverage and predictive risk.

A central component of this work is external validation across distinct clinical populations, which motivates my broader interests in transportability, generalizability, missing-data methodology, causal inference, and uncertainty-aware biomedical decision making.


HyVar-PINN-CT: Physics-Informed Computational Imaging

I am also developing HyVar-PINN-CT, a hybrid variational physics-informed neural network framework for dynamic CT reconstruction and motion estimation. This work extends my research in inverse problems and scientific machine learning to computational imaging, where physical constraints, variational regularization, and data-driven learning can be combined to recover dynamic processes from incomplete measurements.


Future Research Directions

My future research connects these areas through two complementary methodological programs.

In biostatistics and population health, I am interested in Bayesian and causal methods for transportability and generalizability, informative missingness, measurement heterogeneity, heterogeneous treatment effects, and uncertainty-aware decision making.

In scientific machine learning and dynamical systems, I plan to extend network discovery to nonlinear, stochastic, and time-varying systems and investigate applications in epidemiological mobility and transmission networks.

A longer-term goal is to connect these directions by combining statistical learning, causal inference, uncertainty quantification, and mechanistic dynamical modeling to study complex biomedical and population-health systems.


Selected Research Areas