Projects
I have several ongoing academic projects as part of my doctoral research, supervised by Prasanth B. Nair. My few non-academic projects usually take the form of small, self-contained apps.
Doctoral Research
-
Multiscale Models: Certain physical systems, such as fluid flow at high Reynolds number, require the state to be resolved across a wide continuum of length and time scales. This approach imposes a scale separation between directly-resolved macroscale features and inferred microscale features and models their dynamics as a coupled pair of SDEs, allowing for efficient inference and prediction. This uses the VISDE library (see below) to infer model parameters. paper code demo
-
Reduced-Order Models: Reduced-order models are so named because they reduce the number of degrees of freedom in a dynamical system, often by orders of magnitude, allowing one to obtain faster predictions. Unlike multiscale models, this is an old and well-researched class of models. Using the VISDE library (see below), we are able to learn stochastic, non-intrusive models conditioned on parameters and time-dependent forcing. paper code demo
-
Gaussian Continuation: An optimization technique that injects and decays noise in gradient computation, allowing the optimizer to more easily escape local minima. This method, implemented for PyTorch, is designed for highly non-convex loss functions and is most effective in low-dimensional parameter spaces. paper code
Software Libraries
-
Variational Inference for Stochastic Differential Equations (VISDE): A framework for fast variational inference of latent SDE models from time-series data, developed as part of my doctoral research. It supports multiple-trajectory datasets with varying initial conditions, model parameters, and time-dependent forcing functions. It can also be conditioned on physics-informed priors. This is a general training framework, available as a PyTorch Lightning package, that can be applied to a wide variety of model architectures. code
Aerospace Projects
-
Microgravity UAV Design: Design and control of a specialized small airplane capable of simulating a zero-gravity environment. This work led to one paper so far about a design methodology that maximizes zero-gravity time and stability. The eventual goal is to build and fly a prototype. design paper
Non-Academic Projects
