Undergraduate Course: Data Assimilation (MATH11206)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Year 5 Undergraduate)
||Availability||Not available to visiting students
|Summary||Data assimilation comprises of a variety of techniques aimed at obtaining the best probabilistic estimate of the state of the underlying dynamical system from imperfect observations and an imperfect model. The main goal of this course is to present a mathematically unified and systematic framework for data assimilation, which provides a basis for derivation and analysis of algorithmic approaches, and for implementing 'informed' approximations which are needed in practical applications.
Modern scientific applications involving time-dependent state estimation and control require integration of noisy empirical data with uncertain dynamical models for improving accuracy of the resulting predictions. Such strategies are essential in practical applications and have been applied - in an ad-hoc fashion - in engineering and weather forecasting for a few decades. More applications emerge rapidly in the financial sector, machine learning, and other areas of data science due to a rapidly increasing availability of empirical data.
Students taking the course will gain a comprehensive understanding of the mathematical underpinnings of various data assimilation techniques, and they will gain the ability to implement relevant approaches algorithmically based on a number of worked examples. The Bayesian formulation of the data assimilation procedure will allow for quantifying the uncertainty associated with the resulting estimates. Many topics in the field of data assimilation represent active areas of mathematical and applied research. The course will be accompanied by hands-on implementations of discussed concepts during workshops and assignments.
1) Motivating examples.
2) Basics of probability and probabilistic view of dynamical systems.
3) Probabilistic formulation of optimal interpolation, smoothing/variational data assimilation, and sequential data assimilation.
4) Filtering problem in discrete time.
5) Discrete-time data assimilation algorithms: Kalman filter and approximate Gaussian filters, non-Gaussian filters.
6) Long-time behaviour of data assimilation algorithms.
Entry Requirements (not applicable to Visiting Students)
|| Students MUST have passed:
||Other requirements|| Suggested courses: Applied Dynamical Systems, Applied Stochastic Differential Equations, Multi-scale Methods in Mathematical Modelling
Course Delivery Information
|Academic year 2022/23, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
Lecture Hours 20,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
||Hours & Minutes
|Main Exam Diet S2 (April/May)||2:00|
On completion of this course, the student will be able to:
- Formulate a data assimilation procedure in a Bayesian framework.
- Explain the difference between stochastic filtering, variational data assimilation, and time-sequential data assimilation.
- Implement (analytically and numerically) standard data assimilation algorithms on a suite of worked examples.
- Understand and explain the meaning of optimality and uncertainty of estimates in a filtering algorithm, and the impact of modelling errors on the optimality of data assimilation algorithms.
- Apply (analytically and numerically) approximate data assimilation algorithms to new problems encountered in practice.
|- Data assimilation: A mathematical Introduction, A.M. Stuart, K.J.H. Law, K.C. Zygalakis |
- Optimal Filtering, B.D.O. Anderson and J.B. Moore
- Fundamentals of Stochastic Filtering, A. Bain and D. Crisan
|Graduate Attributes and Skills
|Course organiser||Dr Michal Branicki
Tel: (0131 6)50 4878
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427