Special Issue "Machine Learning for Prediction, Data Assimilation, and Uncertainty Quantification of Dynamical Systems"
Deadline for manuscript submissions: closed (31 December 2020) | Viewed by 6701
Interests: data assimilation; data-driven modelling; stochastic computational methods; machine learning
Interests: geometric data analysis; spectral analysis of dynamical systems; statistical forecasting; climate dynamics
Modeling dynamical systems is ubiquitous in a large variety of applications in the sciences. As the capability to collect data advances, an important and growing challenge is to extract relevant information from large datasets in ways that can improve modeling. Recent empirical results suggest that various machine learning algorithms are effective tools in approximating the solution operator of the underlying dynamics without relying on a parametric modeling assumption, but instead leveraging the available datasets to learn the dynamics. While the empirical successes are an important first step, they naturally introduce many practical and theoretical questions.
In this Special Issue, we particularly welcome contributions that address the following problems (other contributions relevant to the topic are also welcome):
- Capabilities and Limitations of Purely Data-Driven Models: A theoretical or thorough empirical study to understand the extent to which model-free (or nonparametric) techniques can be used to improve the prediction of high-dimensional complex dynamical systems. One possible line of inquiry would be how to use criteria from information theory to determine any such limitations.
- Leveraging Information from Partial Models: Another pertinent question, particularly in scenarios with intrinsically high-dimensional dynamics, is how to efficiently augment a partial or imperfect first-principles (parametric) model with a data-driven model to correct model error or model unresolved degrees of freedom. Prominent applications include subgrid-scale modeling and closure schemes for complex systems.
- Data Assimilation: High-quality prediction requires powerful data assimilation techniques in order to determine accurate initial conditions. How can one leverage machine learning to improve data assimilation? For example, an issue that is particularly prevalent in the data assimilation community is estimating non-stationary second-order statistics, and this may be an opportunity for model-free methods. Conversely, how can one leverage modern data assimilation methods to improve model-free forecasting techniques?
- Uncertainty Quantification: It is crucially important to provide confidence in the prediction through a reliable uncertainty quantification (UQ). How can one leverage machine learning in this context? Methods of improving UQ in parametric modeling with machine learning or evaluating UQ techniques applied to model-free methods are welcomed.
Prof. Dimitrios Giannakis
Prof. John Harlim
Prof. Tyrus Berry
Manuscript Submission Information
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- model-free prediction
- nonparametric models
- model error
- machine learning
- kernel methods
- data assimilation
- Bayesian inferences
- uncertainty quantification