Neural network closures for nonlinear model order reduction

• Published in: Advances in computational mathematics Vol. 44; no. 6; pp. 1717 - 1750
• Main Authors: San, Omer, Maulik, Romit
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2018; Springer Nature B.V
• Subjects: Basis functions; Bayesian analysis; Burgers equation; Closures; Computational fluid dynamics; Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Computer architecture; Dependence; Forecasting; Galerkin method; Machine learning; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Model accuracy; Model reduction; Neural networks; Nonlinear systems; Nonlinearity; Parameter robustness; Proper Orthogonal Decomposition; Reduced order models; Regularization; System effectiveness; Visualization; 37N10; 76M25; Extreme learning machine; Neural networks; 76F20; 76D99; Machine learning; Projection methods; Model order reduction; Burgers equation

Many reduced-order models are neither robust with respect to parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework for projection-based reduced-order modeling of such nonlinear a...