Andrey A Popov
I am currently looking for postdoc opportunities!
I am a Ph.D. candidate under Prof. Adrian Sandu at the Computational Science Lab in the department of Computer Science at Virginia Tech.
Research Interests
My chief research interest is to bridge the gap between theory-guided and data-driven methods for computational science. While many people who perform research view theory and physics augmentations to conventional data-driven methods such as deep learning, I approach the task from the other side. I believe that it is the role of data-driven methods to augment conventional methods in physics and mathematics.
To this end I developed the multifidelity ensemble Kalman filter to perform Bayesian inference on a hierarchy of models. At the top of this hierarchy are physics-driven models such as those powering modern numerical weather prediction systems. At the bottom would be conventional data-driven methods such as autoencoder-based surrogates to these large-scale physical dynamical systems. As the data-driven methods lie on the bottom o the hierarchy, their influence is naturally constrained by the physics without their explicit enforcement. This method has the best of both worlds: speed and physical accuracy.
Another one of my goals is to examine conventional machine-learning methods and ask a simple question: does this method accomplish its intent? I recently examined autoencoders for their use in dimensionality reduction tasks for scientific computing and came to the conclusion that in their current form, they do not. I have identified several issues with the conventional autoencoder formulation that prevents it from performing its duties as a tool for dimensionality reduction. I then proposed a new formulation of the autoencoder problem through a meta-learning approach that explicitly accounts for the reduced dimension representation of the state as an explicit constraint. I have strong reason to believe that my formulation of the autoencoder problem is the first to perform dimensionality reduction through machine learning in a mathematically correct fashion, and will be of great interest to a wide array of data-driven scientific applications.
apopov@vt.eduPublications
- Popov, Andrey A; Sandu, Adrian; , Multifidelity Data Assimilation for Physical Systems, Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. IV), 2022
- Popov, Andrey A; Sandu, Adrian; , Multifidelity Ensemble Kalman Filtering using surrogate models defined by Physics-Informed Autoencoders, arXiv preprint arXiv:2102.13025, 2021
- Popov, Andrey A; Mou, Changhong; Sandu, Adrian; Iliescu, Traian; , A multifidelity ensemble Kalman filter with reduced order control variates, SIAM Journal on Scientific Computing, 2021
- Cooper, Rachel; Popov, Andrey A; Sandu, Adrian; , Investigation of Nonlinear Model Order Reduction of the Quasigeostrophic Equations through a Physics-Informed Convolutional Autoencoder, arXiv preprint arXiv:2108.12344, 2021
- Popov, Andrey A; Subrahmanya, Amit N; Sandu, Adrian; , A Stochastic Covariance Shrinkage Approach to Particle Rejuvenation in the Ensemble Transform Particle Filter, Nonlinear Processes in Geophysics Discussions, 2021
- Chennault, Austin; Popov, Andrey A; Subrahmanya, Amit N; Cooper, Rachel; Karpatne, Anuj; Sandu, Adrian; , Adjoint-Matching Neural Network Surrogates for Fast 4D-Var Data Assimilation, arXiv preprint arXiv:2111.08626, 2021
- Subrahmanya, Amit N; Popov, Andrey A; Sandu, Adrian; , An Ensemble Variational Fokker-Planck Method for Data Assimilation, arXiv preprint arXiv:2111.13926, 2021
- Popov, Andrey A; Sandu, Adrian; Nino-Ruiz, Elias D; Evensen, Geir; , A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering, arXiv preprint arXiv:2003.00354, 2020
- Popov, Andrey A; Sandu, Adrian; , An Explicit Probabilistic Derivation of Inflation in a Scalar Ensemble Kalman Filter for Finite Step, Finite Ensemble Convergence, arXiv preprint arXiv:2003.13162, 2020
- Roberts, Steven; Popov, Andrey A; Sarshar, Arash; Sandu, Adrian; , A fast time-stepping strategy for dynamical systems equipped with a surrogate model, arXiv preprint arXiv:2011.03688, 2020
- Roberts, Steven; Popov, Andrey A; Sarshar, Arash; Sandu, Adrian; , ODE Test Problems: a MATLAB suite of initial value problems, arXiv preprint arXiv:1901.04098, 2019
- Popov, Andrey A; Sandu, Adrian; , A Bayesian approach to multivariate adaptive localization in ensemble-based data assimilation with time-dependent extensions, Nonlinear Processes in Geophysics, 2019
- Popov, AA; Lee, S-C; Kuksa, PP; Glickson, JD; Shestov, AA; , Fast Parallel Algorithm for Large Fractal Kinetic Models with Diffusion, bioRxiv, 2018
- Kachur, Alexander V; Popov, Andrey A; Delikatny, E James; Karp, Joel S; Popov, Anatoliy V; , Synthesis of 18F-labeled phenolphthalein and naphtholphthalein, Journal of fluorine chemistry, 2013
- Popov, Anatoliy V; Delikatny, E James; Karp, Joel S; Popov, Andrey A; Kachur, Alexander V; , Synthesis and NMR study of fluorinated aryl (sulfone) phthaleins, ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY, 2013