558 citations · 558 across the 1 of their papers we have counts for
5 papers
Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability
Shaowu Pan, Karthik Duraisamy
The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. Wh…
Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks
Yaser Afshar, Saakaar Bhatnagar, Shaowu Pan +2
An approximation model based on convolutional neural networks (CNNs) is proposed for flow field predictions. The CNN is used to predict the velocity and pressure field in unseen fl…
On the Structure of Time-delay Embedding in Linear Models of Non-linear Dynamical Systems
Shaowu Pan, Karthik Duraisamy
This work addresses fundamental issues related to the structure and conditioning of linear time-delayed models of non-linear dynamics on an attractor. While this approach has been…
Long-time predictive modeling of nonlinear dynamical systems using neural networks
Shaowu Pan, Karthik Duraisamy
We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data. Emphasis is placed on predictions at long times, with limited data…
Data-driven Discovery of Closure Models
Shaowu Pan, Karthik Duraisamy
Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called…