Virtual Seminar Series

Abstract: In combination with the fast-improving performance of optimization software, optimization over trained neural networks (NNs) appears tractable (at least for moderate-size NNs). In this talk, we discuss recent advancements in optimization formulations and software for NN surrogate models, including OMLT, the Optimization and Machine Learning Toolkit. We will then outline applications to scheduling and control problems. For supply chain scheduling, we show how optimization over trained NN state-action value functions (i.e., a critic function) can explicitly incorporate constraints, and we describe two corresponding reinforcement algorthms. For process control, we show how optimization can be used to evaluate ‘correctness’ of NN-based controllers before deployment. 

Bio: Dr. Calvin Tsay is Assistant Professor (UK Lecturer) in the Computational Optimisation Group at the Department of Computing, Imperial College London. His research focuses on computational methods for optimisation and control, with applications in machine learning and process systems engineering. Calvin received his PhD degree in Chemical Engineering from the University of Texas at Austin, receiving the 2022 W. David Smith, Jr. Graduate Publication Award from the CAST Division of the American Institute of Chemical Engineers (AIChE). He previously received his BS/BA from Rice University (Houston, TX).

Abstract: Solving model predictive control problems in real time is still an important challenge despite of recent advances in computing hardware, optimization algorithms and tailored implementations. This challenge is even greater when uncertainty is present due to disturbances, unknown parameters or measurement and estimation errors. To enable the application of advanced control schemes to large and fast systems or on low-cost embedded hardware, we propose to approximate model predictive controllers using deep learning. The use of deep networks leads in practice to better performance than the use of traditional shallow networks. We also show how guarantees about constraint satisfaction or stability can be achieved for such approximate controllers. When detailed simulations, for example in the form of digital twins, are available, they can be used to improve the performance of the approximate controllers or to obtain closed-loop performance guarantees using probabilistic validation techniques. Finally, we discuss some open issues and ideas for future research.

Bio: Sergio Lucia received the M.Sc. degree in electrical engineering from the University of Zaragoza, Spain, in 2010, and the Dr. Ing. degree in optimization and automatic control from the TU Dortmund University, Germany, in 2014. He joined the Otto-von-Guericke Universität Magdeburg and visited the Massachusetts Institute of Technology as a Postdoctoral Fellow. He was an Assistant Professor at TU Berlin between 2017 and 2020. Since 2020, he has been a Professor at TU Dortmund University and head of the Laboratory of Process Automation Systems. His research interests include decision-making under uncertainty, distributed control, as well as the interplay between machine learning techniques and control theory. Dr. Lucia is currently Associate Editor of the Journal of Process Control and of the Journal Optimal Control Applications and Methods.

Name: Joshua Pulsipher

Date: 4/25/23

Time: 10-11am EST

Title: Stochastic Programming Inspired Modeling Techniques for Shaping Dynamic Trajectories

Abstract: Infinite-dimensional optimization (InfiniteOpt) captures problems that arise in both stochastic and dynamic optimization where the decision variables are often indexed over a continuous domain (i.e., are functions). In previous work, I developed a unifying modeling abstraction for InfiniteOpt problems which establishes unified modeling objects to capture formulations in stochastic optimization, dynamic optimization, PDE-constrained optimization, and combinations. This is conveniently implemented in the Julia package InfiniteOpt.jl. Through the lens of this abstraction, we have found that continuous-time dynamic optimization problems can be interpreted as a special case of two-stage stochastic programs. In this talk, I will present how this perspective has inspired the transfer modeling objects from stochastic programming to be used in a deterministic dynamic context. Namely, I will discuss how time-valued analogs of risk measures and chance constraints (called event constraints in this context) enable unique ways to shape dynamic trajectories. The use of these new modeling objects will be demonstrated through illustrative case studies.

Bio: Joshua is an incoming assistant professor of chemical engineering at the University of Waterloo and currently is a post-doc at Carnegie Mellon University working with Profs. Carl Laird and Ignacio Grossmann. His research focuses on developing methods in optimization under uncertainty and data science to solve problems pertaining to sustainability, energy, and the environment. He completed his Ph.D. at UW-Madison under the direction of Prof. Victor Zavala and obtained his B.Sc. at BYU, both in chemical engineering.

Website: Learn more at https://pulsipher.info.

Name: Varghese Kurian

Date: 5/30/23

Time: 10-11am EST

Title: Analysis of Potential Flow Networks: Variations in Transport Time with Discrete, Continuous, and Selfish Operation

Abstract: In potential flow networks, the flow through the edges is driven by the potential difference across them. Several natural and artificial systems fall under this definition. We consider a class of networks in which the potential loss across the edges is a polynomial function of the flow rate. In these systems, as the demands are usually not proportional to the equilibrium flow rates, flow control elements are required to satisfy consumer demands. The control elements can broadly be classified into two types – discrete and continuous. Discrete control elements can have only two operational states: fully open or fully closed. On the other hand, continuous control elements may be operated in any intermediate position in addition to the fully open and fully closed states. Naturally, with their increased flexibility, continuous control elements can provide better network performance. The less intuitive question is: To what extent? In the present work, we quantify the performance of networks based on the time required to transport a given quantum of material. We define R as the ratio of minimal operational times with either type of control element. In a class of branched networks with a single source and multiple sinks, we analytically derive lower and upper bounds on R as a function of the maximum depth of the network. The results highlight the role of network topology in the variations in operational time. An extension also highlights the variation in performance between the optimal and selfish operation of non-linear flow networks.

Bio: Dr. Varghese Kurian is a postdoctoral researcher in the Department of Chemical and Biomolecular Engineering at the University of Delaware. His current research focuses on developing mathematical models of biological systems that are useful in identifying optimal interventions/treatment strategies. Varghese received his PhD in chemical engineering from the Indian Institute of Technology Madras where he analyzed the operational performance of networks and formulated efficient scheduling problems. Previously he received his undergraduate degree from the Indian Institute of Technology Roorkee.
 

Website: https://scholar.google.co.in/citations?user=o6VVZzMAAAAJ&hl=en