Research

Optimal Transportation methods in nonlinear filtering:

Uncertainty is, more than ever, an integral part of modern control system applications. We use models that are learned from data, fuse variety of noisy sensors, and augment machine learning modules that are inherently stochastic. Nonlinear filtering is a principled approach to quantify uncertainty and as- similate noisy sensory data in a probabilistic framework. However, existing nonlinear filtering algorithms face critical limitations due to (i) highly nonlinear and complex models (ii) curse of dimensionality; (ii) and incorrect specification of models and noise statistics. This research project is aimed at overcoming these limitations.

• Optimal Transportation Methods in Nonlinear Filtering: The feedback particle filter(arXiv)

• An Optimal Transport Formulation of Bayes’ Law for Nonlinear Filtering Algorithms

• An optimal transport formulation of the ensemble Kalman filter (arXiv)

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Interplay between optimization and sampling:

Optimization and sampling algorithms share remarkable similarities in general, as highlighted by the similarity between stochastic gradient descent and Langevin sampling. In fact, sampling can be viewed as an optimization problem on the space of probability distributions. The goal of this research is to bridge the gap between optimization and sampling by employing optimization algorithms specifically for the purpose of sampling, using the Riemannian geometry, as provided by optimal mass transport.

• Variational Wasserstein gradient flow

• Accelerated flow for probability distributions (arXiv)

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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 ressearch is to develop efficient data-driven computational algorithms that provide reliable approximations to these geometrical tools in high dimensions.

• Scalable computations of Wasserstein barycenter via input convex neural networks

• Optimal transport mapping via input-convex neural networks (arXiv)

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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. Remarkabley, these problems can be viewed as optimal control problems for probabibility distributions where optimal mass transport plays a central role.

• Energy harvesting from anisotropic fluctuations(arXiv)

• On the relation between information and power in stochastic thermodynamic engines(arXiv)

• Maximal power output of a stochastic thermodynamic engine (arXiv )