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math.DS2022★ 1 cited
A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems
Peter Benner, Pawan Goyal, Jan Heiland +1
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated…
math.DS2020
Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows
Peter Benner, Pawan Goyal, Jan Heiland +1
Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the…
math.DS2020
Space and Chaos-Expansion Galerkin POD Low-order Discretization of PDEs for Uncertainty Quantification
Peter Benner, Jan Heiland
The quantification of multivariate uncertainties in partial differential equations can easily exceed any computing capacity unless proper measures are taken to reduce the complexit…