Data-Driven Analysis and Modeling of Complex Systems
AEROSP 729, Fall 2018
Time: T Th 1:30 – 3:00 p.m. / Location: 1008 FXB
Exposure to scientific computing, adequate programming skills and basic command of linear algebra and differential equations.
Primary Instructor: Karthik Duraisamy, FXB 3009, firstname.lastname@example.org.
The objective of this course is to learn to effectively use data in the analysis and modeling of complex, real-world problems. Specifically, we will study the use of data to
1. Augment existing models to improve predictability,
2. Discover the structure of the underlying physical system,
3. Decompose the system into a simpler form to aid our understanding,
4. Develop mathematically formal reduced-order models to enable efficient prediction.
While this course is focused on applications, we will study the basics of several mathematical tools and techniques.
No text book is required. Handouts will be provided to supplement in-class teaching. Additional reading material and homework will be posted on Canvas. We will also study a few journal papers in detail. The following are excellent references:
1. Data-driven Modeling and Scientific Computation, Kutz, Oxford University Press, 2013.
2. Parameter Estimation and Inverse Problems, Aster/Borchers/Thurber, Wiley, 2013.
3. Approximation of Large-Scale Dynamical Systems, Antoulas, SIAM 2005.
Course contents (some topics may not be covered):
– Modeling, data, uncertainty & predictive science
– Overview of tools & techniques
– Functional analysis
– Linear algebra & Spectral theory
– Adjoint operators and dual space
– Least-squares and L1-regression
– Basic probability & statistics
The idea of augmenting models with data
– Sensitivity analysis using adjoints
– Parameter and function estimation
– Bayesian inversion
The idea of data-driven discovery
– Regression in feature space
– Sparse identification of dynamical systems
Dynamical systems & observables
– Phase portraits, equilibria, bifurcations
– Normal forms
– Lyapunov exponents and chaos
– Probabilistic properties of deterministic systems
– Koopman and Perron-Frobenius operators
Data-driven decompositions & modeling
– Proper orthogonal decompositions
– Dynamic mode decomposition
– Koopman decomposition
– Kernel methods
– Projection-based Model Reduction
– Balanced truncation and balanced residualization
– Techniques for Non-linear Model Reduction
Homeworks/Projects : 70 %,
Written Mid Term : 15 %,
Oral Final Exam : 15 %