Lupin-Jimenez, L. (AM) – Data-Driven Deep Learning for Turbulent Phenomena: Regional Ocean Prediction and Assimilation, Spectral Bias in Diffusion Models, and Equation Discovery
Deep learning models trained on simulation and reanalysis data can now emulate turbulent geophysical flows at a small fraction of the computational cost of numerical solvers.
Their scientific utility depends on physical consistency, which for the systems studied here
rests in large part on spectral fidelity, the accurate reconstruction of variance across spatial
scales. This document presents two published studies and two studies in progress that develop, analyze, and apply data-driven methods for turbulent phenomena along that thread.
The first study develops FCDS, a framework that autoregressively emulates surface ocean
dynamics over the Gulf of Mexico at 8 km resolution and simultaneously downscales and
bias-corrects the emulated fields to 4 km, with a spectral loss that keeps decadal integrations stable and statistically consistent with a high-resolution reanalysis. The second study
develops a neural-operator-conditioned denoising diffusion model that reconstructs regional
surface ocean states from Lagrangian-like observations at 99% and 99.9% sparsity without a
background dynamical model, and shows that the recovered small-scale dynamics are visible
in spectral diagnostics but not in pointwise metrics. The third study derives a signal-tonoise theory of spectral bias in diffusion models for 2D turbulence, organized around the
crossover wavenumber kc(Ļ) at which signal and noise contribute equal power, and validates
its predictions on a sweep of 28 models spanning seven forcing wavenumbers and four noise
schedulers. The fourth study develops a window-pair spectral method for discovering governing equations from single-point sensor measurements of soliton dynamics in a superfluid
wave flume, replacing noise-amplifying instantaneous derivatives with finite-time spectral
shifts and verifying the discovered equations against a measured-scalar null model. A concluding chapter summarizes the results and outlines future work on novel architectures and
methods for data-driven emulation of physical simulations.
Event Host: Leonard Lupin-Jimenez, Ph.D. Student, Applied MathematicsĀ
Advisor: Ashesh Chattopadhyay
Zoom: https://ucsc.zoom.us/j/97866640488?pwd=UJdTs3sxKfFbz5mabKLIyx5ZYF90J9.1
Passcode: 815911