- Ph.D. in Mechanical Engineering, University of Illinois at Urbana-Champaign, 2019
- M.S. in Mathematics, University of Illinois at Urbana-Champaign, 2017
- B.S. in Mechanical Engineering, Sharif University of Technology, Iran, 2013
- B.S. in Physics, Sharif University of Technology, Iran, 2013
- Postdoctoral Scholar, Department of Mechanical and Aerospace Engineering, University of California, Irvine, 2019
Uncertainty due to modeling imperfections, measurement errors, and noise in data is ubiquitous in Engineering applications and a key limiting factor in achieving optimal and reliable performance. Nowadays, in the age of big data, the gravity and urgency of coping with uncertainty have only increased. Traditionally, statistics and probability theory have provided a quantitative framework to deal with uncertainty. While both disciplines are classical, a transformative change in how we view probability distributions has taken place in recent years that brought about new elegant and powerful geometrical tools.
The context was the so-called Monge-Kantorovich problem of Optimal Mass Transportation (OMT). OMT related mathematics is rapidly impacting diverse fields such as stochastic control and estimation, machine learning, thermodynamics, and social networks.
My own work has been at the intersection of all these disciplines. My immediate goal is to design reliable and efficient computational algorithms (data assimilation and control techniques for large scale de-centralized systems), uncover new physical principles (work in stochastic thermodynamics), and expand the reach of OMT to control of interacting particle systems (which includes controlling diffusion processes in networks, modeling the dynamics of pandemics, and developing novel optimal nonlinear filtering techniques).
Data assimilation in high dimensional space
While the subject dates back to the invention of the least-squares method by Gauss, attention to fundamental limitations and the performance of data assimilation algorithms in a truly high-dimensional setting is quite recent. A new branch of data assimilation algorithms, tapping on systems of controlled interacting particles and their respective OMT flow, hold a great promise to overcome the curse of dimensionality. The objective of this research is to develop design principles for controlled interacting particle filters and efficient numerical algorithms to implement them in high-dimensional setting
Computational methodology for optimal mass transportation
There is a growing interest in application of the optimal transportation theory in machine learning and control related problems. The main reason is that the optimal transportation theory provides powerful and elegant geometrical tools to view and manipulate probability distributions. The objective of this research is to develop efficient data-driven computational algorithms that provide reliable approximations to these geometrical tools in high dimensions
Fundamental limitations in stochastic thermodynamics
Classical thermodynamics is inherently static and can not capture non-equilibrium transitions and the power that can be extracted from an engine in finite time. To this end, the framework of stochastic thermodynamics was developed in recent years to allow quantifying thermodynamic quantities in finite time transitions. The objective of this project is to study fundamental limits in dissipation and in power generation by thermodynamic processes. Remarkably, these problems can be viewed as optimal control problems for probability distributions where optimal mass transport play a central role.
- A. Taghvaei, O. Movilla Miangolarra, R.i Fu, Y. Chen, T. T. Georgiou On the relation between information and power in stochastic thermodynamic engines IEEE Control Systems Letters (L-CSS), 2021.
- A. Taghvaei, P. G. Mehta. Optimal Transportation Methods in Nonlinear Filtering: The feedback particle filter. IEEE Control Systems Magazine (CSM), 2021
- J. Fan, A. Taghvaei, Y. Chen Scalable computations of Wasserstein barycenter via input convex neural networks International Conference of Machine Learning (ICML), 2021.
- A. Taghvaei, T. T. Georgiou, L. Norton, A. R. Tannenbaum. Fractional SIR Epidemiological Models. Scientific Reports, 10(1):20882, 2020.
- R. Fu, A. Taghvaei, Y. Chen, T. T. Georgiou. Maximal power output of a stochastic thermodynamic engine. Automatica, 123:109366, 2021.
- A. Taghvaei, P. G. Mehta. An optimal transport formulation of the ensemble Kalman filter. IEEE Transactions of Automatic Control (TAC), vol. 66, no. 7, pp. 3052-3067, July 2021.
- A. Taghvaei, P. G. Mehta, S. P. Meyn. Diffusion map-based algorithm for gain function approximation in the feedback particle filter. SIAM/ASA Journal on Uncertainty Quantification, 8(3):1090–1117, 2020
- A. Taghvaei, A Makkuva, S. Oh, J. Lee. Optimal transport mapping via input-convex neural networks. International Conference on Machine Learning (ICML), 6672-6681, June 2020.
- A. Taghvaei, P. G. Mehta, Accelerated flow for probability distributions. International Conference on Machine Learning (ICML), 6076–6085, Long Beach, June 2019.