AM Seminar: Dimensionality reduction for sensor-actuator placement and forecasting

Speaker Name: 
Krithika Manohar
Speaker Title: 
Postdoctoral fellow
Speaker Organization: 
Caltech
Start Time: 
Monday, April 1, 2019 - 4:00pm
End Time: 
Monday, April 1, 2019 - 5:00pm
Location: 
BE 372
Organizer: 
Daniele Venturi

Abstract

The increasingly high-dimensional data generated by complex systems presents a tremendous challenge for efficient prediction, estimation and control. Dimensionality reduction provides a powerful tool in the analysis of systems strictly governed by physical laws, and can uncover heavily compressed representations of the underlying dynamics. The first part of my talk describes using linear dimensionality reduction, such as PCA and balanced model reduction, to efficiently optimize sensor and actuator placements. This method bypasses the combinatorially complex brute-force search through all possible candidate placements, and generalizes to actuator placement for control using observability and controllability metrics. The resulting sensors are used to reconstruct flow fields and imaging data with many thousands of candidate locations. I will also discuss ongoing work using nonlinear dimensionality reduction with diffusion kernels to forecast macroscale dynamics in slow-fast systems. This approach is particularly useful for systems in oceanography and climate which exhibit scale separation.

Bio

Krithika Manohar is NSF postdoctoral fellow and von Karman instructor in Computing & Mathematical Sciences at the California Institute of Technology. She received the dual B.S. degree in Mathematics and Computer Science from University of Massachusetts Lowell, and the Ph.D. degree in Applied Mathematics from University of Washington. She is a recipient of the Boeing Award for Excellence in Research for her work on data-driven sensor placement methods, and was awarded the NSF Mathematical Sciences Postdoctoral Research Fellowship in 2018. Her research leverages data-driven learning for prediction, estimation and control of high-dimensional complex systems.