Research Program

Thrust A: Inverse scattering in complex and uncertain media

Inverse scattering aims to uncover geometrical and physical properties of hidden objects in a medium from remote observations of scattered waveforms. Intelligent platforms for imaging and characterization in uncertain environments (such as metal printing chambers, aging structures, and subsurface energy systems) enable real-time monitoring of additive manufacturing (AM), early anomaly detection in safety-critical components, and efficient energy extraction and storage. Existing approaches, however, mostly rely on oversimplified background structure and properties, yielding uncertain baseline models. When coupled with partial/one-sided apertures and noisy data, this makes conventional gradient-based waveform inversion brittle, slow, and calibration-intensive. We are developing a mathematically grounded, fast, and robust remote sensing platform for spatiotemporal tracking of natural and engineered processes in complex systems. This will be accomplished by building on advances in sampling-based approaches to inverse scattering, optimal experimental design, deep learning, and uncertainty quantification. Signature results

• Differential imaging of advancing fractures in uncertain components — SIIMS, 2020.
  Establishes the differential evolution indicators for ultrasonic imaging of propagating fractures in specimens with uncertain micro/macrostructure. Sequential boundary data are used to design an imaging functional that is invariant to (unknown) stationary features of the domain.
• Extension to highly heterogeneous composites — PRSA, 2023.
  Extends the differential indicators to randomly heterogeneous composites for exclusive tomography of elastic transformation and fracturing in real-world materials and structures of arbitrary complexity.
• Laboratory validation via laser vibrometry — MSSP, 2021.
  First experimental demonstration of the differential evolution indicators; images the fracturing process.

Thrust B: Data-driven modeling and inverse design

Operator learning on full-field measurements enables data-driven discovery of the mechanics of materials with complex micro–meso–macro structure, especially in dynamic regimes where scale-separated homogenization fails and effective governing equations remain poorly understood. Laser ultrasonics and laser speckle interferometry pave the way by providing high-resolution, full-field measurements across a wide frequency range. We aim to learn and experimentally validate, with quantified uncertainty, the governing operators of hierarchical/particulate materials by: (i) identifying particle-to-continuum laws and closures; (ii) learning a hierarchy-to-dynamics map that remains predictive across scales; and (iii) delivering fast, physics-based surrogates that extrapolate beyond training. These developments enable predictive modeling of advanced materials, such as dense porous foams, metamaterials and metastructures, metallic-powder AM builds, and densely packed particle beds – and facilitate inverse design of next-generation metamaterials that expand achievable dynamics and unlock previously inaccessible functions. Signature results

• Ensemble WSINDy for experimental PDE discovery — MSSP, 2024 (under revision).
  Weak-form sparse regression with ensemble UQ on laser vibrometry measurements; Recovers governing PDEs and affiliated parameters for bonded granular specimens at low frequencies.
• Micropolar Deep Material Networks — CMAME, 2025.
  Establishes physics-based neuron operators in a binary-tree hierarchical surrogate for micropolar continua, capturing micro-rotations/couple-stresses and microstructure-dependent size effects; Accurately predicts mesoscale homogenized response with runtime far below that of full-field solvers.
• Deep learning for full-field ultrasonic characterization — MSSP, 2023.
  Introduces wavenumber-adaptive Sobolev losses and learned regularization for training on highly oscillatory and multi-fidelity measurements. Enables accurate neural characterization of discontinuous and heterogeneous composites from full waveform test data.

Thrust C: Data-driven discovery of interfacial mechanics

Interface operators govern the behavior of composites, AM bonds, layered builds, and fractured geomaterials, yet remain poorly characterized under realistic loads and bandwidths. Full-field, near-interface measurements enable experimental discovery and validation of multiscale, nonlinear, and rate-dependent behaviors that common contact models miss. We aim to uncover and experimentally validate the governing operators of frictional and cohesive interfaces by: (i) learning the effective traction–separation and rate-and-state slip weakening laws from wideband measurements with quantified uncertainty; and (ii) upscaling roughness and microstructure into effective dynamics across rates and frequencies. These developments enable predictive modeling and control of interfacial and effective-medium behavior in critical materials and energy systems. Signature results

• On the elastic anatomy of heterogeneous fractures in rock — IJRMMS, 2018.
  Nonparametric recovery of fracture geometry and heterogeneous shear/normal specific stiffnesses from full-field laser vibrometry data.
• Nonlinear model identification of a frictional contact support — MSSP, 2010.
  Identifies nonlinear friction laws and parameters for a contact support via reduced-order system identification; Accurately predicts structural dynamics and hysteretic slip–stick behavior from vibration data.
• A synoptic approach to the seismic sensing of heterogeneous fractures: From geometric reconstruction to interfacial characterization — CMAME, 2017.
  A unified, non-iterative pipeline that reconstructs interfacial stiffness from remote data by first performing geometric reconstruction and then inverting boundary-integral equations with proper regularization.

Laser ultrasonics & Laser vibrometry

We develop and deploy two types of non-contact, laser-based testing setups: laser ultrasonics (LU), which uses a pulsed laser for broadband ultrasound generation with interferometric detection, and laser Doppler vibrometry (LDV) paired with piezoelectric transducers for excitation. Together, these setups deliver wideband excitation and high-resolution, full-field measurements. The resulting dense spatiotemporal data and repeatable experiments power Thrust A (inverse scattering in complex, uncertain media), Thrust B (operator learning and inverse design), and Thrust C (data-driven discovery of interfacial mechanics). They enable flexible near- and far-field measurements, uncertainty-aware validation, and rapid iteration between models and experiments across rates and frequency ranges. Signature results

• Laser ultrasonic imaging of subsurface defects with the linear sampling method — Optics Express, 2023.
  Integrates the multi-frequency LSM indicator into laser ultrasonics and demonstrates state-of-the-art performance by achieving super-resolution and accurate shape reconstruction below the diffraction limit.