20 citations · 67 across the 12 of their papers we have counts for
13 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…
Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamics
Pawan Goyal, Süleyman Yıldız, Peter Benner
Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex no…
Linearly Implicit Global Energy Preserving Reduced-order Models for Cubic Hamiltonian Systems
Süleyman Yildiz, Pawan Goyal, Peter Benner
This work discusses the model reduction problem for large-scale multi-symplectic PDEs with cubic invariants. For this, we present a linearly implicit global energy-preserving metho…
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…
Intrusive and non-intrusive reduced order modeling of the rotating thermal shallow water equation
Süleyman Yıldız, Murat Uzunca, Bülent Karasözen
In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equat…
Energy preserving reduced-order modelling of thermal shallow water equation
Suleyman Yildiz, Murat Uzunca, Bulent Karasozen
In this paper, Hamiltonian and energy preserving reduced-order models are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form wi…
Data-Driven Learning of Reduced-order Dynamics for a Parametrized Shallow Water Equation
Süleyman Yıldız, Pawan Goyal, Peter Benner +1
This paper discusses a non-intrusive data-driven model order reduction method that learns low-dimensional dynamical models for a parametrized shallow water equation. We consider th…
Reduced order modelling of nonlinear cross-diffusion systems
Bülent Karasözen, Gülden Mülayim, Murat Uzunca +1
In this work, we present a reduced-order model for a nonlinear cross-diffusion problem from population dynamics, for the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volte…
Structure-preserving reduced-order modelling of Korteweg de Vries equation
Bulent Karasozen, Murat Uzunca, Suleyman Yildiz
Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg de Vries (KdV) equations in Hamiltonian form. The KdV equation is discretized i…
Structure-preserving Reduced Order Modeling of non-traditional Shallow Water Equation
Süleyman Yıldız, Murat Uzunca, Bülent Karasözen
An energy preserving reduced order model is developed for the nontraditional shallow water equation (NTSWE) with full Coriolis force. The NTSWE in the noncanonical Hamiltonian/Pois…
Structure Preserving Model Order Reduction of Shallow Water Equations
Bülent Karasözen, Süleyman Yıldız, Murat Uzunca
In this paper, we present two different approaches for constructing reduced-order models (ROMs) for the two-dimensional shallow water equation (SWE). The first one is based on the…