About me
von Karman Instructor, Caltech
Welcome! I am von Karman instructor in Computing + Mathematical Sciences at Caltech, and, starting 1/2021, Assistant Professor of Mechanical Engineering at University of Washington. Prior to this, I completed an NSF Mathematical Sciences Postdoctoral Research Fellowship, sponsored by Prof. Andrew Stuart. I received my Ph.D. in Applied Mathematics from University of Washington.
I am interested in data-driven prediction and control of complex, large-scale dynamical systems, which naturally occur in fluid dynamics, atmospheric science, biology, even engineering processes. My research focuses on interpretable machine learning and optimizing data observations for efficient modeling and control. I study these methods from an algorithmic and theoretical perspective, by exploiting tools from dimensionality reduction, operator theory and manifold learning. I apply these techniques to study complex phenomena in climate, fluid dynamics, biology and manufacturing.
Publications
Kernel Analog Forecasting: Multiscale Test Problems
D Burov, D Giannakis, K Manohar, A Stuart - arXiv:2005.06623, 2020
Data-Driven Aerospace Engineering: Reframing the Industry with Machine Learning
SL Brunton, JN Kutz, K Manohar, AY Aravkin, K Morgansen, J Klemisch, N Goebel, J Buttrick, J Poskin, A Blom-Schieber, T Hogan, D McDonald - arXiv:2008.10740, 2020
Optimal sensor and actuator placement using balanced model reduction
K Manohar, JN Kutz, SL Brunton - arXiv:1812.01574, 2018
Randomized CP tensor decomposition
NB Erichson, K Manohar, SL Brunton, JN Kutz
Machine Learning: Science and Technology 1 (2), 025012, 2020
Sparse principal component analysis using variable projection
NB Erichson, P Zheng, K Manohar, SL Brunton, JN Kutz, AY Aravkin
SIAM Journal on Applied Mathematics 80 (2), 977-1002, 2020
Optimized sampling for multiscale dynamics
K Manohar, E Kaiser, SL Brunton, JN Kutz
Multiscale Modeling & Simulation 17 (1), 117-136, 2020
Data-driven sparse sensor placement for reconstruction
K Manohar, BW Brunton, JN Kutz, SL Brunton
IEEE Control Systems Magazine 38 (3), 63-86, 2018
Predicting shim gaps in aircraft assembly with machine learning and sparse sensing
K Manohar, T Hogan, J Buttrick, AG Banerjee, JN Kutz, SL Brunton
Journal of Manufacturing Systems, 48: 87-95, 2018
Sparse-TDA: Sparse realization of topological data analysis for multi-way classification
W Guo, K Manohar, SL Brunton, AG Banerjee
IEEE Transactions on Knowledge and Data Engineering 30 (7), 1403-1408, 2018
Environment identification in flight using sparse approximation of wing strain
K Manohar, SL Brunton, JN Kutz
Journal of Fluids and Structures 70, 162-180, 2017
Overview of Courses
Computing + Mathematical Sciences, Caltech
Fall Term 2020
CMS 270: Data-driven modeling of dynamical systems
9 units (3-0-6); first term. Prerequisites: Basic differential equations, linear algebra, probability and statistics: ACM 104, ACM/EE 106 ab, ACM/EE/IDS 116 or equivalent. The explosion of data in the sciences and engineering poses new challenges for learning interpretable models using efficient algorithms. When governing equations are unavailable, the tools of dimensionality reduction and machine learning can be leveraged for data-driven pattern extraction, inference and prediction. This course covers the theory and algorithms behind data-driven modeling of dynamical systems, using concepts from operator theory, statistical computing and network science. Applications will be drawn from the physical, engineering and biological sciences. Topics include but are not limited to: Modal decompositions, Koopman operator approximation, Laplacian embeddings (diffusion maps, etc), physics-constrained neural networks, and autoencoders.
Contact Information
California Institute of Technology
1200 E. California Blvd.
MC 305-16
Pasadena, CA 91125
kmanohar [at] caltech.edu