Dana Lavacot

Echocardiography (echo) is a medical imaging technique that allows for real-time visualization of cardiac structures at the bedside. Coupled with color Doppler, echo provides useful information about the hemodynamics in the heart that is commonly used by clinicians for diagnosis and treatment planning. However, echo and Doppler images are often noisy and sparse, leading to substantial uncertainties in blood flow measurements.

This work aims to reconstruct full spatio-temporal flow fields in the heart from echo measurements using machine learning. We employ a diffusion-based probabilistic model to allow for uncertainty quantification of the flow predictions. Additionally, we enforce physical constraints to ensure the generated fields are consistent with not only the echo data but also the governing Navier-Stokes equations.

Rayleigh-Taylor (RT) instability, when a light fluid is accelerated into a heavy fluid, can occur in inertial confinement fusion (ICF) and significantly reduce energy output. Thus, it is important to accurately model RT mixing during the ICF experiment design process. This work investigates the importance of non-locality in modeling turbulent RT mixing using the Macroscopic Forcing Method, a numerical approach to determine turbulent closure operators from high-fidelity simulations.

Related publications:

• Lavacot, D. L. O.-L., Mani, A., and Morgan, B. Atwood effects on nonlocality of the scalar transport closure in Rayleigh-Taylor mixing. 2025. Phys. Rev. Fluids.
• Lavacot, D. L. O.-L., Liu, J., Williams, H., Morgan, B., and Mani, A. Non-locality of mean scalar transport in two-dimensional Rayleigh-Taylor instability using the macroscopic forcing method. 2024. J. Fluid Mech.

Physical data usually exist on irregular grids due to complex geometries encountered in real world problems. In this work, we present the Deep Differentiable Shape Layer (DDSL), which leverages the non-uniform Fourier transform to facilitate deep learning on arbitrary geometries. I derived the analytical derivative for the transform, to allow for fast backpropagation for neural network training as well as shape optimization after training. I demonstrated the utility of the DDSL in the optimization of airfoil shapes for low lift-drag ratios.

Related publications:

• Jiang, C., Lansigan, D., Niessner, M., and Marcus, P. DDSL: Deep Differentiable Simplex Layer for Learning Geometric Signals. 2019. Proceedings of ICCV.