Research

Research Areas

Advanced data assimilation for high-fidelity simulation in the era of data — inferring the hidden state of turbulent and nonlinear systems from limited measurements.

Lifted hyperbolic dynamics projected to observation space — Deterministic hyperbolic dynamics in an extended space project to irreversible, memory-bearing diffusion in the observation space.

Inverse Problem in Lifted Hyperbolic Dynamics

Complex, irreversible behavior in a low-dimensional observation space can be explained as the projection of simple hyperbolic dynamics from a larger space. We infer latent, lifted dynamics from partial observations.

Source-location probability with linear and quadratic sensitivity — Source-location probability P(x_s) with linear vs. quadratic measurement sensitivity and adjoint sensitivity fields.

Measurement Attention & Physics-informed Positional Embedding

A framework for localized source detection in systems governed by nonlinear PDEs, using first- and second-order sensitivity analysis, generalized toward fully nonlinear neural networks.

Scalar source in a turbulent channel and its localization — A localized scalar source φ(x) in a turbulent channel, and its reconstructed probable location.

Scalar Source Reconstruction in Turbulent Environments

How turbulent dispersion and molecular diffusion affect reconstruction quality when sensor measurements are highly correlated during source shifts.NSF-funded

Pressure field and sensitivity curves around an airfoil — Pressure field with sensitivity curves used to place sensors for source search.

Optimal Sensor Placement

Minimizing condition numbers in source-search problems — placing sensors at scalar-plume edges markedly improves the ability to distinguish sources.

Adjoint iso-surfaces representing the domain of dependence — Adjoint iso-surfaces (ρ†, u†, v†, w†, T†, p†) — the domain of dependence of a wall measurement.

Domain of Dependence for Wall Measurements

Adjoint-variable iso-surfaces from different measurement kernels at the wall reveal the domain of dependence for measurements in compressible and incompressible flows.

Domain of Dependence for Dangerous Events

Adjoint methods for parameter-space searches that identify precursors of dangerous events in low-dimensional settings.

Tracer particles in a turbulent channel velocity field, as used for PIV-based assimilation.

Hierarchical Adjoint-based Assimilation with PIV

Multi-fidelity models for efficient adjoint-based data assimilation of particle-image velocimetry measurements.NSF-funded

Reconstructed 2D turbulence under different control variables — 2D turbulence reconstructed from different control variables and Sobolev regularization.

Preconditioned-Adjoint Methods

Redefining the inner products of adjoint operators to accelerate inverse problems for turbulence, including two-dimensional decaying isotropic turbulence.

Auto-encoder input versus output reconstruction — Auto-encoder input vs. reconstructed output for channel-flow velocity fields.

CNN-based Auto-Encoder for Turbulent Channel Flow

Coupling data assimilation with nonlinear reduced-order models learned by convolutional auto-encoders.

Reconstructed pressure fields — Pressure fields reconstructed from error-embedded measurements via omnidirectional integration.

ODI-aided Data Assimilation

Parallel-Ray Omnidirectional Integration built into an in-house Navier–Stokes solver, improving pressure-field reconstruction from error-embedded measurements.

Reconstructed particle forcing with uncertainty and convergence — Reconstructed forcing on finite-size particles, with uncertainty band and convergence history.

Particle Forcing Reconstruction

When particle-location measurements are sparse, adjoint-based assimilation recovers the forcing on finite-size particles by matching measured and predicted trajectories.AFOSR-funded

GPR versus Green's-function integration for pressure — Gaussian Process Regression vs. Green's-function integration for a dipole pressure field.

Gaussian Process Regression for Pressure Reconstruction

A probabilistic, intrinsically de-noising alternative to the Pressure-Poisson solver — a Gaussian-process generalization of Green's-function integration.

Forward and inverse advection-diffusion of a scalar plume — Score-based reverse physics: forward vs. inverse advection–diffusion of a scalar plume in turbulence.

Diffusion Model for Reverse Physics

Physics-constrained generative diffusion models for ill-posed inverse problems in physics. NSF 2431610