Periodic Reporting for period 1 - STALDYS (Statistical Learning for Dynamical Systems)
Período documentado: 2019-02-01 hasta 2021-01-31
On the other hand, the field of machine learning is concerned with algorithms designed to accomplish a certain task, whose performance improves with the input of more data. Applications for machine learning methods include computer vision, stock market analysis, speech recognition, recommender systems and sentiment analysis in social media. The machine learning approach is invaluable in settings where no explicit model is formulated, but measurement data is available. This is frequently the case in many systems of interest, and the development of data-driven technologies is becoming increasingly important in many applications.
The purpose of the proposal is to cross-fertilise between the two fields and particularly by using kernel methods for dynamical systems.
b. Why is it important for society? Due to the prevalence of machine learning techniques in many fields and lack of understanding of why they work, approaches based on the theory of dynamical systems will definitely help understanding machine learning techniques and delineate their domain of applicability.
c. What are the overall objectives? The overall objectives is to use kernel methods for the analysis of nonlinear dynamical systems. These methods are mathematically well grounded and using them for dynamical systems is a good way of having sound mathematical results for machine learning approaches to complex systems.
b. I published several articles
• Boumediene Hamzi, Romit Maulik and Houman Owhadi (2021). Data-driven geophysical forecasting: Simple, low-cost, and accurate baselines with kernel methods, submitted, https://arxiv.org/abs/2103.10935.
• F. Colonius and B. Hamzi (2020). Entropy for practical stabilization, accepted for publication in SIAM Journal of Control and Optimization, https://arxiv.org/abs/2009.08187
• B. Haasdonk, B. Hamzi, G. Santin and D. Wittwar (2020). Kernel Methods for Center Manifold Approximation and a Data-Based Version of the Center Manifold Theorem, accepted for publication in Physica D, https://arxiv.org/abs/2012.00338
• Bittracher, S. Klus, B. Hamzi, C Sch\"utte (2021), A kernel-based method for coarse graining complex dynamical systems, Journal of Nonlinear Science, https://arxiv.org/abs/1904.08622
• Hamzi and H. Owhadi (2020). Learning dynamical systems from data: a simple cross-validation perspective, Physica D, https://arxiv.org/abs/2007.05074
• Haasdonk, B. Hamzi, G. Santin and D. Wittwar (2020). Greedy Kernel Methods for Center Manifold Approximation, in Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018, Springer Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 134), pp. 95--106, https://arxiv.org/abs/1810.11329
• S. Klus, F. N\"uske and B. Hamzi (2020). Kernel-based approximation of the Koopman generator and Schr\"odinger operator, Entropy, 22, 722, https://arxiv.org/abs/2005.13231
c. I edited a special issue in Physica D on “Machine Learning and Dynamical Systems” https://www.sciencedirect.com/journal/physica-d-nonlinear-phenomena/special-issue/100SM4JKVTD
d. I started organizing a Special Interest Group on Machine Learning and Dynamical Systems at the Alan Turing Institute, https://www.turing.ac.uk/research/interest-groups/machine-learning-and-dynamical-systems
e. I supervised MSc. Students at Imperial College London.
f. I gave several talks.
g. I created a Youtube Channel for online seminars on MLDS, https://www.youtube.com/channel/UCetvKhuAbnuU1tidgCz9g0g/videos