Research

I develop mathematical and AI methods to quantify structure and predict dynamics across scales. I ask how they jointly shape function, and how this understanding can guide design. Drawing on network science and physics, I study both scientific systems and AI models themselves.

Multiscale structure

Multifractal analysis
Network science
Multiscale representations

How can we quantify the organization of a complex system across scales?

I develop multiscale representations that make network organization and heterogeneity measurable. These quantities let us compare systems and investigate how structural differences relate to behavior and function.

Neuron-based Multifractal Analysis of Neuron Interaction Dynamics in Large ModelsICLR, 2025
NeuroMFA quantifies the multifractal organization of AI weight networks and tracks how it changes across training checkpoints.
Spiking dynamics of individual neurons reflect changes in the structure and function of neuronal networksNature Communications, 2025
Multifractal statistics of neuronal spiking reveal structural and functional differences in the underlying network, linking temporal measurements to network organization.
Deciphering the Generating Rules and Functionalities of Complex NetworksScientific Reports, 2021
NMFA uses node-centered box growth to quantify network organization across scales and compare structural complexity and heterogeneity.

Multiscale dynamics

Neural operators
Physics-informed AI
Multiwavelets

How can we predict physical fields and their evolution across scales?

I develop neural operators that retain fine- and coarse-scale behavior and interactions between fields. I test how predictions hold up at new resolutions and conditions, and whether they provide the information needed for decisions such as planning a flight through urban wind.

GeoWind2Plan: Mission-Time 3D Urban Wind Prediction for Energy-Efficient UAV PlanningNeurIPS, 2026 · Spotlight
GeoWind2Plan uses a geometry-conditioned neural operator to predict local 3D urban wind for energy-efficient UAV planning. Routes planned with predicted wind are evaluated under high-fidelity CFD wind, testing whether fast predictions support useful decisions.
Coupled Multiwavelet Operator Learning for Coupled Differential EquationsICLR, 2023
CMWNO learns coupled solution operators through interacting kernels in multiwavelet space, accounting for how evolving fields influence one another.
Multiwavelet-based Operator Learning for Differential EquationsNeurIPS, 2021 · Spotlight
Multiwavelet operator learning represents PDE solution operators across scales using multiwavelet bases, retaining localized information at different resolutions.

Inverse design & AI design

Network-informed materials
Neuro-inspired AI

How can we use this understanding to design for a desired function?

The design problem begins with a desired function, the variables we can change, and the constraints we must respect. I seek to use structural and dynamical understanding to guide those choices, in scientific systems and AI models alike.

Neuro-Inspired Information-Theoretic Hierarchical Perception for Multimodal LearningICLR, 2024
ITHP uses a neuro-inspired hierarchy of information bottlenecks to learn compact multimodal representations. Other modalities guide training; inference uses only the primary modality.
Biomorphic Structural Batteries for RoboticsScience Robotics, 2020
Graph and multifractal analysis guide the selection of nanofiber networks for structural batteries. Physical tests assess mechanical performance and ion transport, connecting network organization to material function.

I am extending these foundations toward physics-constrained inverse design, linking forward prediction to candidate generation and independent validation.

Questions before methods

First define the scientific question, the relevant scales and constraints, and the evidence needed to evaluate an answer. These choices guide the representation, model, and evaluation.

Forward modeling

System & conditionsmap toStructure, dynamics, or function

Define the quantity of interest and develop a model to estimate it. Depending on the question, the target may be a structural property, an evolving field, or a functional response.

Inverse design

Structures, interactions & controlsare sought to meetDesign targets & constraints

Use forward models and domain knowledge to guide the search for structures, interactions, or controls that meet a target.

Predictive accuracy alone does not establish mechanism. Inverse design requires constraints and independent validation, not simply reversing a predictor.

DUAL

These questions guide my research group at UTK. We develop methods for studying scientific systems and examine AI models as complex systems in their own right.

Research at DUAL