Alexander Grimm

Alexander Grimm, Christopher Beattie, Zlatko Drmač et al.

Given a set of response observations for a parametrized dynamical system, we seek a parametrized dynamical model that will yield uniformly small response error over a range of parameter values yet has low order. Frequently, access to internal system dynamics or equivalently, to realizations of the original system is either not possible or not practical; only response observations over a range of parameter settings might be known. Respecting these typical operational constraints, we propose a two phase approach that first encodes the response data into a high fidelity intermediate model of modest order, followed then by a compression stage that serves to eliminate redundancy in the intermediate model. For the first phase, we extend non-parametric least-squares fitting approaches so as to accommodate parameterized systems. This results in a (discrete) least-squares problem formulated with respect to both frequency and parameter that identifies "local" system response features. The second phase uses an $\mathbf{\mathcal{H}}_2$-optimal model reduction strategy accommodating the specialized parametric structure of the intermediate model obtained in the first phase. The final compressed model inherits the parametric dependence of the intermediate model and maintains the high fidelity of the intermediate model, while generally having dramatically smaller system order. We provide a variety of numerical examples demonstrating our approach.

Alexander Dallmann, Alexander Grimm, Christian Pölitz et al.

Recently, Recurrent Neural Networks (RNNs) have been applied to the task of session-based recommendation. These approaches use RNNs to predict the next item in a user session based on the previ- ously visited items. While some approaches consider additional item properties, we argue that item dwell time can be used as an implicit measure of user interest to improve session-based item recommen- dations. We propose an extension to existing RNN approaches that captures user dwell time in addition to the visited items and show that recommendation performance can be improved. Additionally, we investigate the usefulness of a single validation split for model selection in the case of minor improvements and find that in our case the best model is not selected and a fold-like study with different validation sets is necessary to ensure the selection of the best model.