Recent Advances in Uncertainty Quantification and Scientific Machine Learning with Applications to Complex Dynamical Systems
 Organizer(s):
Name:
Affiliation:
Country:
Marios Andreou
University of Wisconsin-Madison
USA
Konstantinos Zygalakis
University of Edinburgh
Scotland
Nan Chen
University of Wisconsin-Madison
USA
 Introduction:  
  Turbulent dynamics prevail in many complex nonlinear dynamical systems, stochastic or not, used to model phenomena in geophysics, fluids, engineering, and neuroscience. Such systems are characterized by their high-dimensional state space and multiscale spatiotemporal features. In recent years, uncertainty quantification (for both forward and inverse problems) and scientific machine learning have been increasingly applied for their effective state estimation, parameter inference, optimal control, and system design. These methods enhance robustness, data completeness, and predictive skill in complex systems. They advance frameworks that utilize probabilistic approaches as computationally efficient surrogates for solving practical problems. This further enables the rigorous mathematical study and analysis of the model and forecast errors, facilitating their mitigation, optimization, and tuning. This special session will highlight recently developed fundamental mathematical theories and numerical algorithms for uncertainty quantification and machine-learning-assisted methods. A focal point will be their applications to various aspects of the study of complex dynamical systems.