Wedler, M., Stender, M., Klein, M., & Hoffmann, N. (2023). Machine learning simulation of one-dimensional deterministic water wave propagation. In Ocean Engineering (Bd. 284, S. 115222). Elsevier BV. https://doi.org/10.1016/j.oceaneng.2023.115222

Deterministic phase-resolved prediction of the evolution of surface gravity waves in water is challenging due to their complex spatio-temporal dynamics. Physics-based methods of varying complexity are available, but the conflicting objectives of numerical efficiency and accuracy impede real-time wave prediction. Data-driven methods may be able to overcome this challenge by using training data generated by complex numerical methods. This work explores the potential of a machine learning (ML) approach based on a fully convolutional encoder–decoder architecture for the efficient and accurate prediction of water waves. The high-order spectral (HOS) method forms the foundation for the generation of the training data. The HOS method is applied for different, consecutive orders of nonlinearity starting from first order up to fourth order. The JONSWAP wave energy spectrum serves as the basis for modeling the one-dimensional irregular sea states. The overall objective of this work is to evaluate whether the complex non-linear physical processes can be identified and learned by the ML approach. The trained ML flow mapper is used to perform time integration of an initial sea state. The results indicate that the proposed ML approach is able to reproduce the distinctive physical processes of the different orders of nonlinearities. It is shown that the ML approach enables fast and accurate predictions of one-dimensional waves over a time horizon that spans multiple peak periods.

Wedler, M., Stender, M., Klein, M., Ehlers, S., & Hoffmann, N. (2022). Surface similarity parameter: A new machine learning loss metric for oscillatory spatio-temporal data. In Neural Networks (Bd. 156, S. 123–134). Elsevier BV. https://doi.org/10.1016/j.neunet.2022.09.023

Supervised machine learning approaches require the formulation of a loss functional to be minimized in the training phase. Sequential data are ubiquitous across many fields of research, and are often treated with Euclidean distance-based loss functions that were designed for tabular data. For smooth oscillatory data, those conventional approaches lack the ability to penalize amplitude, frequency and phase prediction errors at the same time, and tend to be biased towards amplitude errors. We introduce the surface similarity parameter (SSP) as a novel loss function that is especially useful for training machine learning models on smooth oscillatory sequences. Our extensive experiments on chaotic spatio-temporal dynamical systems indicate that the SSP is beneficial for shaping gradients, thereby accelerating the training process, reducing the final prediction error, increasing weight initialization robustness, and implementing a stronger regularization effect compared to using classical loss functions. The results indicate the potential of the novel loss metric particularly for highly complex and chaotic data, such as data stemming from the nonlinear two-dimensional Kuramoto–Sivashinsky equation and the linear propagation of dispersive surface gravity waves in fluids.

Klein, M., Stender, M., Wedler, M., Ehlers, S., Hartmann, M., Desmars, N., Pick, M.-A., Seifried, R., & Hoffmann, N. (2022). Application of Machine Learning for the Generation of Tailored Wave Sequences. In Volume 5B: Ocean Engineering; Honoring Symposium for Professor Günther F. Clauss on Hydrodynamics and Ocean Engineering. ASME 2022 41st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers. https://doi.org/10.1115/omae2022-78601

This paper explores the applicability of machine learning techniques for the generation of tailored wave sequences. For this purpose, a fully convolutional neural network was implemented for relating the target wave sequence at the target location in time domain to the respective wave sequence at the wave board. The synthetic training and validation data were acquired by applying the high-order spectral (HOS) method. The HOS method is a very accurate method for modeling non-linear wave propagation and its numerical efficiency allows the generation of large synthetic data sets. The training data featured wave groups of short duration based on JONSWAP spectra. The sea state parameters wave steepness, wave period and enhancement factor were systematically varied. At the end of the training process, the trained models were able to predict the wave sequences at the wave board based on the time series of the target wave defined for a specific target location in the wave tank. The accuracy of the trained models were evaluated by means of unseen validation data. In addition, the predictive accuracy of the trained models was compared with the classical linear transformation approach.

Stender, M., Wedler, M., Hoffmann, N., & Adams, C. (2021). Explainable machine learning: A case study on impedance tube measurements. In INTER-NOISE and NOISE-CON Congress and Conference Proceedings (Bd. 263, Issue 3, S. 3223–3234). Institute of Noise Control Engineering (INCE). https://doi.org/10.3397/in-2021-2342

Machine learning techniques allow for finding hidden patterns and signatures in data. Currently, these methods are gaining increased interest in engineering in general and in vibroacoustics in particular. Although ML methods are successfully applied, it is hardly understood how these black-box-type methods make their decisions. Explainable machine learning aims at overcoming this issue by deepen the understanding on the decision making process through perturbation-based model diagnosis. This paper introduces machine learning methods and reviews recent techniques for explainability and interpretability. These methods are exemplified on sound absorption coefficient spectra of one sound absorbing foam material measured in an impedance tube. Variances of the absorption coefficients measurements as a function of the specimen thickness and the operator are modeled by univariate and multivariate machine learning models. In order to identify the driving patterns, i.e., how and in which frequency regime the measurements are affected by the setup specifications, Shapley additive explanations are derived for the ML models. It is demonstrated how explaining machine learning models can be used to discover and express complicated relations in experimental data, thereby paving the way to novel knowledge discovery strategies in evidence-based modeling.

Stender, M., Adams, C., Wedler, M., Grebel, A., & Hoffmann, N. (2021). Explainable machine learning determines effects on the sound absorption coefficient measured in the impedance tube. In The Journal of the Acoustical Society of America (Bd. 149, Issue 3, S. 1932–1945). Acoustical Society of America (ASA). https://doi.org/10.1121/10.0003755

Measurements of acoustic properties of sound absorbing materials in impedance tubes show poor reproducibility, which was demonstrated in round robin tests. The impedance tube measurements are standardized but lack precise definitions of the actual measurement setup, specimen preparation, and other factors that introduce uncertainty in practice. In this paper, machine learning models identify those factors that mostly affect the sound absorption coefficient from a large data set of more than 3000 absorption spectra measured in one impedance tube. The specimens are manufactured from one polyurethane foam, and different cutting technologies, different operators, different specimen diameters, different specimen thicknesses, and two different approaches to mount the specimens in the impedance tube are considered. Explainable machine learning techniques allow the identification and quantification of the most influential factors and, furthermore, the frequency ranges that are the most affected by the choice of these setup factors. The results indicate that besides the specimen thickness, also the operator affects the absorption coefficient by a directional and non-random relationship. Hence, it needs to be controlled carefully. The method proves to be a promising pathway for knowledge discovery from acoustic measurement data using explainability approaches for machine learning models.