Philipp Krah

Beata Zorawski, Shubhaditya Burela, Philipp Krah et al.

This paper presents a neural network-based methodology for the decomposition of transport-dominated fields using the shifted proper orthogonal decomposition (sPOD). Classical sPOD methods typically require an a priori knowledge of the transport operators to determine the co-moving fields. However, in many real-life problems, such knowledge is difficult or even impossible to obtain, limiting the applicability and benefits of the sPOD. To address this issue, our approach estimates both the transport and co-moving fields simultaneously using neural networks. This is achieved by training two sub-networks dedicated to learning the transports and the co-moving fields, respectively. Applications to synthetic data and a wildland fire model illustrate the capabilities and efficiency of this neural sPOD approach, demonstrating its ability to separate the different fields effectively.

Antoine Oriou, Philipp Krah, Julian Koellermeier

This paper introduces the Intrinsic Dimension Estimating Autoencoder (IDEA), which identifies the underlying intrinsic dimension of a wide range of datasets whose samples lie on either linear or nonlinear manifolds. Beyond estimating the intrinsic dimension, IDEA is also able to reconstruct the original dataset after projecting it onto the corresponding latent space, which is structured using re-weighted double CancelOut layers. Our key contribution is the introduction of the projected reconstruction loss term, guiding the training of the model by continuously assessing the reconstruction quality under the removal of an additional latent dimension. We first assess the performance of IDEA on a series of theoretical benchmarks to validate its robustness. These experiments allow us to test its reconstruction ability and compare its performance with state-of-the-art intrinsic dimension estimators. The benchmarks show good accuracy and high versatility of our approach. Subsequently, we apply our model to data generated from the numerical solution of a vertically resolved one-dimensional free-surface flow, following a pointwise discretization of the vertical velocity profile in the horizontal direction, vertical direction, and time. IDEA succeeds in estimating the dataset's intrinsic dimension and then reconstructs the original solution by working directly within the projection space identified by the network.

Henry Sallandt, Philipp Krah, Mathias Lemke

This manuscript presents an approach for multi zone sound field reproduction using supervised learning. Traditional multi zone sound field reproduction methods assume constant speed of sound, neglecting nonlinear effects like wind and temperature stratification. We show how to overcome these restrictions using supervised learning of transfer functions. The quality of the solution is measured by the acoustic contrast and the reproduction error. Our results show that for the chosen setup, even with relatively small wind speeds, the acoustic contrast and reproduction error can be improved by up to 16 dB, when wind is considered in the trained model.