144 citations · 635 across the 40 of their papers we have counts for
11 papers · 1 filter
Model discovery for nonautonomous translation-invariant problems
Hongli Zhao, Daniel M. Tartakovsky
Discovery of mathematical descriptors of physical phenomena from observational and simulated data, as opposed to from the first principles, is a rapidly evolving research area. Two…
Learning Nonautonomous Systems via Dynamic Mode Decomposition
Hannah Lu, Daniel M. Tartakovsky
We present a data-driven learning approach for unknown nonautonomous dynamical systems with time-dependent inputs based on dynamic mode decomposition (DMD). To circumvent the diffi…
Model Reduction via Dynamic Mode Decomposition
Hannah Lu, Daniel M. Tartakovsky
This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), wh…
Transfer Learning on Multi-Fidelity Data
Dong H. Song, Daniel M. Tartakovsky
Neural networks (NNs) are often used as surrogates or emulators of partial differential equations (PDEs) that describe the dynamics of complex systems. A virtually negligible compu…
Extended Dynamic Mode Decomposition for Inhomogeneous Problems
Hannah Lu, Daniel M. Tartakovsky
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrat…
Dynamic Mode Decomposition for Construction of Reduced-Order Models of Hyperbolic Problems with Shocks
Hannah Lu, Daniel M. Tartakovsky
Construction of reduced-order models (ROMs) for hyperbolic conservation laws is notoriously challenging mainly due to the translational property and nonlinearity of the governing e…
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena
Hannah Lu, Daniel M. Tartakovsky
Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are two complementary singular-value decomposition (SVD) techniques that are widely used to construct red…
Estimation of distributions via multilevel Monte Carlo with stratified sampling
Søren Taverniers, Daniel M. Tartakovsky
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with…
Predictive Accuracy of Dynamic Mode Decomposition
Hannah Lu, Daniel M. Tartakovsky
Dynamic mode decomposition (DMD), which the family of singular-value decompositions (SVD), is a popular tool of data-driven regression. While multiple numerical tests demonstrated…
Causality and Bayesian network PDEs for multiscale representations of porous media
Kimoon Um, Eric Joseph Hall, Markos A. Katsoulakis +1
Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the relationship between pr…
Parallel numerical tensor methods for high-dimensional PDEs
A. M. P. Boelens, D. Venturi, D. M. Tartakovsky
High-dimensional partial-differential equations (PDEs) arise in a number of fields of science and engineering, where they are used to describe the evolution of joint probability fu…