Research

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

We 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.

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

We develop neural operators that retain fine- and coarse-scale behavior and interactions between fields. We 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.

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. We 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.

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