# Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flows

@inproceedings{Wenzel2021StructuredDK, title={Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flows}, author={Tizian Wenzel and Marius Kurz and Andrea D. Beck and Gabriele Santin and Bernard Haasdonk}, booktitle={LSSC}, year={2021} }

Standard kernel methods for machine learning usually struggle when dealing with large datasets. We review a recently introduced Structured Deep Kernel Network (SDKN) approach that is capable of dealing with high-dimensional and huge datasets and enjoys typical standard machine learning approximation properties. We extend the SDKN to combine it with standard machine learning modules and compare it with Neural Networks on the scientific challenge of data-driven prediction of closure terms of…

## 2 Citations

### Universality and Optimality of Structured Deep Kernel Networks

- Computer ScienceArXiv
- 2021

A recent deep kernel representer theorem is leverage to connect the two approaches and understand their interplay, showing that the use of special types of kernels yield models reminiscent of neural networks that are founded in the same theoretical framework of classical kernel methods, while enjoying many computational properties of deep neural networks.

### Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds

- Computer Science, MathematicsArXiv
- 2021

This work provides a novel projection technique called symplectic manifold Galerkin (SMG), which projects the Hamiltonian system onto a nonlinear symplectic trial manifold such that the reduced model is again a HamiltonianSystem, and derives analytical results such as stability, energy-preservation and a rigorous a-posteriori error bound.

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