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

Goal‐Oriented Two‐Layered Kernel Models as Automated Surrogates for Surface Kinetics in Reactor Simulations

“…In order to adapt the kernel to the considered dataset (X N , Y N ), recently two-layered kernels were introduced [7,8], which can be understood as a generalization of standard shape parameter-tuned kernels. Indeed, such a twolayered kernel is given by…”

“…An overview of available greedy methods and an analysis of their convergence properties are provided in [42]. The combination of the two-layered kernel optimization in conjunction with a greedy selection of suitable center points was implemented in the 2L-VKOGA algorithm [7,8]. 1)…”

“…(3). For the kernel optimization, i.e., the optimization of the first-layer matrix A q , we make use of the mini-batch training described in [7,8]: It uses a mini-batch gradient descent on an efficiently computed cross-validation loss, whereby the mini-batches of size 64 are randomly drawn from the whole training data set of size 25 000.…”

“…The recently developed two-layered kernel is a data-efficient modeling tool [7,8] that is well suited for high-dimensional problems. Here, the common kernel layer is extended by an additional linear layer, which adjusts the kernel to the magnitude and importance of the features (here: reaction conditions) and thereby significantly increases the model accuracy.…”

“…We show that, in contrast to standard machine learning methods, the VKOGA reduces the demand for costly training data and provides accurate predictions, even outside the training range. To do so, we apply the recently developed two-layer kernels [7,8] and extend the VKOGA procedure by goal-oriented selection criteria.…”