4 papers
Symplectic convolutional neural networks
Süleyman Yıldız, Konrad Janik, Peter Benner
We propose a new symplectic convolutional neural network (CNN) architecture by leveraging symplectic neural networks, proper symplectic decomposition, and tensor techniques. Specif…
A CFL-type Condition and Theoretical Insights for Discrete-Time Sparse Full-Order Model Inference
Leonidas Gkimisis, Süleyman Yıldız, Peter Benner +1
In this work, we investigate the data-driven inference of a discrete-time dynamical system via a sparse Full-Order Model (sFOM). We first formulate the involved Least Squares (LS)…
Structure-preserving learning for multi-symplectic PDEs
Süleyman Yıldız, Pawan Goyal, Peter Benner
This paper presents an energy-preserving machine learning method for inferring reduced-order models (ROMs) by exploiting the multi-symplectic form of partial differential equations…
Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftings
Süleyman Yildiz, Pawan Goyal, Thomas Bendokat +1
We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as no…