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Merten Stender

Publications and source records attributed to Merten Stender.

18 recordsLinked to original sources
arXiv2026

Deep learning-based prediction of time-resolved adhesive forces in viscoelastic Hertzian contacts

Fast prediction of the response of adhesive soft viscoelastic contacts represents a current challenge in soft robotics and for gripping and manipulation tasks. Determining the complete time-resolved force trajectory requires full numerical simulations, whose computational cost is strongly parameter-dependent, making them impractical for real-time application or design-optimization loops. In this work, we overcome this limitation by training a scalar-conditioned, stateful, sequence-to-sequence deep learning model to predict the full force evolution from a prescribed displacement history for both short- and long-range adhesion regimes. The data set spans four orders of magnitude in loading and unloading rates and includes varied dwell times, with the Tabor parameter ranging from $0.2$ to $3.2$. To enable learning across these heterogeneous time scales, we introduce a fixed-measurement-step (FMS) representation that converts variable-length trajectories into fixed-length sequences while preserving their physical-time information. Different architectures were trained, including long short-term memory (LSTM) networks, temporal convolutional neural (TCN) networks, and time-distributed dense layers with three different Tabor-conditioning mechanisms. The models were compared using global waveform and error metrics. We found that the best-performing model has an LSTM architecture with concatenated conditioning, which achieves a held-out mean-squared error of $5.0\times10^{-4}$, a median pull-off-force error of $\approx2.2\%$, and a median hysteresis error of $\approx1.1\%$. For the held-out protocols, the model predicts a complete force trajectory with a median inference time of $0.16$ s. The model is tested across unseen parameter combinations and against analytical limiting cases, providing a rapid surrogate for repeated numerical evaluations with potential use in control-oriented applications.

cs.LG↗
arXiv2025

Bridging ocean wave physics and deep learning: Physics-informed neural operators for nonlinear wavefield reconstruction in real-time

Accurate real-time prediction of phase-resolved ocean wave fields remains a critical yet largely unsolved problem, primarily due to the absence of practical data assimilation methods for reconstructing initial conditions from sparse or indirect wave measurements. While recent advances in supervised deep learning have shown potential for this purpose, they require large labelled datasets of ground truth wave data, which are infeasible to obtain in real-world scenarios. To overcome this limitation, we propose a Physics-Informed Neural Operator (PINO) framework for reconstructing spatially and temporally phase-resolved, nonlinear ocean wave fields from sparse measurements, without the need for ground truth data during training. This is achieved by embedding residuals of the free surface boundary conditions of ocean gravity waves into the loss function of the PINO, constraining the solution space in a soft manner. After training, we validate our approach using highly realistic synthetic wave data and demonstrate the accurate reconstruction of nonlinear wave fields from both buoy time series and radar snapshots. Our results indicate that PINOs enable accurate, real-time reconstruction and generalize robustly across a wide range of wave conditions, thereby paving the way for operational, data-driven wave reconstruction and prediction in realistic marine environments.

cs.LG↗
arXiv2025

Dynamics-Informed Reservoir Computing with Visibility Graphs

Accurate prediction of complex and nonlinear time series remains a challenging problem across engineering and scientific disciplines. Reservoir computing (RC) offers a computationally efficient alternative to traditional deep learning by training only the read-out layer while employing a randomly structured and fixed reservoir network. Despite its advantages, the largely random reservoir graph architecture often results in suboptimal and oversized networks with poorly understood dynamics. Addressing this issue, we propose a novel Dynamics-Informed Reservoir Computing (DyRC) framework that systematically infers the reservoir network structure directly from the input training sequence. This work proposes to employ the visibility graph (VG) technique, which converts time series data into networks by representing measurement points as nodes linked by mutual visibility. The reservoir network is constructed by directly adopting the VG network from a training data sequence, leveraging the parameter-free visibility graph approach to avoid expensive hyperparameter tuning. This process results in a reservoir that is directly informed by the specific dynamics of the prediction task under study. We assess the DyRC-VG method through prediction tasks involving the canonical nonlinear Duffing oscillator, evaluating prediction accuracy and consistency. Compared to an Erd\H{o}s-R\'enyi (ER) graph of the same size, spectral radius, and fixed density, we observe higher prediction quality and more consistent performance over repeated implementations in the DyRC-VG. An ER graph with density matched to the DyRC-VG can in some conditions outperform both approaches.

cs.LG↗
arXiv2025

Pull-off force prediction in viscoelastic adhesive Hertzian contact by physics augmented machine learning

Understanding and predicting the adhesive properties of viscoelastic Hertzian contacts is crucial for diverse engineering applications, including robotics, biomechanics, and advanced material design. The maximum adherence force of a Hertzian indenter unloaded from a viscoelastic substrate has been studied with analytical and numerical models. Analytical models are valid within their assumptions, numerical methods offer precision but can be computationally expensive, necessitating alternative solutions. This study introduces a novel physics-augmented machine learning (PA-ML) framework as a hybrid approach, bridging the gap between analytical models and data-driven solutions, which is capable of rapidly predicting the pull-off force in an Hertzian profile unloaded from a broad band viscoelastic material, with varying Tabor parameter, preload and retraction rate. Compared to previous models, the PA-ML approach provides fast yet accurate predictions in a wide range of conditions, properly predicting the effective surface energy and the work-to-pull-off. The integration of the analytical model provides critical guidance to the PA-ML framework, supporting physically consistent predictions. We demonstrate that physics augmentation enhances predictive accuracy, reducing mean squared error (MSE) while increasing model efficiency and interpretability. We provide data-driven and PA-ML models for real-time predictions of the adherence force in soft materials like silicons and elastomers opening to the possibility to integrate PA-ML into materials and interface design. The models are openly available on Zenodo and GitHub.

cond-mat.mtrl-sci↗
arXiv2025

Node pruning reveals compact and optimal substructures within large networks

The structural complexity of reservoir networks poses a significant challenge, often leading to excessive computational costs and suboptimal performance. In this study, we introduce a systematic, task specific node pruning framework that enhances both the efficiency and adaptability of reservoir networks. By identifying and eliminating redundant nodes, we demonstrate that large networks can be compressed while preserving or even improving performance on key computational tasks. Our findings reveal the emergence of optimal subnetwork structures from larger Erdos Renyi random networks, indicating that efficiency is governed not merely by size but by topological organization. A detailed analysis of network structure at both global and node levels uncovers the role of density distributions, special-radius and asymmetric input-output node distributions, among other graph-theoretic measures that enhance the computational capacity of pruned compact networks. We show that pruning leads to non-uniform network refinements, where specific nodes and connectivity patterns become critical for information flow and memory retention. This work offers fundamental insights into how structural optimization influences reservoir dynamics, providing a pathway toward designing more efficient, scalable, and interpretable machine learning architectures.

physics.comp-ph↗
arXiv2025

Denoising and Reconstruction of Nonlinear Dynamics using Truncated Reservoir Computing

Measurements acquired from distributed physical systems are often sparse and noisy. Therefore, signal processing and system identification tools are required to mitigate noise effects and reconstruct unobserved dynamics from limited sensor data. However, this process is particularly challenging because the fundamental equations governing the dynamics are largely unavailable in practice. Reservoir Computing (RC) techniques have shown promise in efficiently simulating dynamical systems through an unstructured and efficient computation graph comprising a set of neurons with random connectivity. However, the potential of RC to operate in noisy regimes and distinguish noise from the primary smooth or non-smooth deterministic dynamics of the system has not been fully explored. This paper presents a novel RC method for noise filtering and reconstructing unobserved nonlinear dynamics, offering a novel learning protocol associated with hyperparameter optimization. The performance of the RC in terms of noise intensity, noise frequency content, and drastic shifts in dynamical parameters is studied in two illustrative examples involving the nonlinear dynamics of the Lorenz attractor and the adaptive exponential integrate-and-fire system. It is demonstrated that denoising performance improves by truncating redundant nodes and edges of the reservoir, as well as by properly optimizing hyperparameters, such as the leakage rate, spectral radius, input connectivity, and ridge regression parameter. Furthermore, the presented framework shows good generalization behavior when tested for reconstructing unseen and qualitatively different attractors. Compared to the extended Kalman filter, the presented RC framework yields competitive accuracy at low signal-to-noise ratios and high-frequency ranges.

cs.LG↗
arXiv2025

Physics-informed neural networks for phase-resolved data assimilation and prediction of nonlinear ocean waves

The assimilation and prediction of phase-resolved surface gravity waves are critical challenges in ocean science and engineering. Potential flow theory (PFT) has been widely employed to develop wave models and numerical techniques for wave prediction. However, traditional wave prediction methods are often limited. For example, most simplified wave models have a limited ability to capture strong wave nonlinearity, while fully nonlinear PFT solvers often fail to meet the speed requirements of engineering applications. This computational inefficiency also hinders the development of effective data assimilation techniques, which are required to reconstruct spatial wave information from sparse measurements to initialize the wave prediction. To address these challenges, we propose a novel solver method that leverages physics-informed neural networks (PINNs) that parameterize PFT solutions as neural networks. This provides a computationally inexpensive way to assimilate and predict wave data. The proposed PINN framework is validated through comparisons with analytical linear PFT solutions and experimental data collected in a laboratory wave flume. The results demonstrate that our approach accurately captures and predicts irregular, nonlinear, and dispersive wave surface dynamics. Moreover, the PINN can infer the fully nonlinear velocity potential throughout the entire fluid volume solely from surface elevation measurements, enabling the calculation of fluid velocities that are difficult to measure experimentally.

cs.LG↗
arXiv2024

The impact of AI on engineering design procedures for dynamical systems

Artificial intelligence (AI) is driving transformative changes across numerous fields, revolutionizing conventional processes and creating new opportunities for innovation. The development of mechatronic systems is undergoing a similar transformation. Over the past decade, modeling, simulation, and optimization techniques have become integral to the design process, paving the way for the adoption of AI-based methods. In this paper, we examine the potential for integrating AI into the engineering design process, using the V-model from the VDI guideline 2206, considered the state-of-the-art in product design, as a foundation. We identify and classify AI methods based on their suitability for specific stages within the engineering product design workflow. Furthermore, we present a series of application examples where AI-assisted design has been successfully implemented by the authors. These examples, drawn from research projects within the DFG Priority Program \emph{SPP~2353: Daring More Intelligence - Design Assistants in Mechanics and Dynamics}, showcase a diverse range of applications across mechanics and mechatronics, including areas such as acoustics and robotics.

eess.SY↗
arXiv2024

Data Publishing in Mechanics and Dynamics: Challenges, Guidelines, and Examples from Engineering Design

Data-based methods have gained increasing importance in engineering, especially but not only driven by successes with deep artificial neural networks. Success stories are prevalent, e.g., in areas such as data-driven modeling, control and automation, as well as surrogate modeling for accelerated simulation. Beyond engineering, generative and large-language models are increasingly helping with tasks that, previously, were solely associated with creative human processes. Thus, it seems timely to seek artificial-intelligence-support for engineering design tasks to automate, help with, or accelerate purpose-built designs of engineering systems, e.g., in mechanics and dynamics, where design so far requires a lot of specialized knowledge. However, research-wise, compared to established, predominantly first-principles-based methods, the datasets used for training, validation, and test become an almost inherent part of the overall methodology. Thus, data publishing becomes just as important in (data-driven) engineering science as appropriate descriptions of conventional methodology in publications in the past. This article analyzes the value and challenges of data publishing in mechanics and dynamics, in particular regarding engineering design tasks, showing that the latter raise also challenges and considerations not typical in fields where data-driven methods have been booming originally. Possible ways to deal with these challenges are discussed and a set of examples from across different design problems shows how data publishing can be put into practice. The analysis, discussions, and examples are based on the research experience made in a priority program of the German research foundation focusing on research on artificially intelligent design assistants in mechanics and dynamics.

cs.CY↗
arXiv2024

Predicting multi-parametric dynamics of externally forced oscillator using reservoir computing and minimal data

Mechanical systems exhibit complex dynamical behavior from harmonic oscillations to chaotic motion. The dynamics undergo qualitative changes due to changes to internal system parameters like stiffness and changes to external forcing. Mapping out complete bifurcation diagrams numerically or experimentally is resource-consuming, or even infeasible. This study uses a data-driven approach to investigate how bifurcations can be learned from a few system response measurements. Particularly, the concept of reservoir computing (RC) is employed. As proof of concept, a minimal training dataset under the resource constraint problem of a Duffing oscillator with harmonic external forcing is provided as training data. Our results indicate that the RC not only learns to represent the system dynamics for the external forcing seen during training, but it also provides qualitatively accurate and robust system response predictions for completely unknown multi-parameter regimes outside the training data. Particularly, while being trained solely on regular period-2 cycle dynamics, the proposed framework correctly predicts higher-order periodic and even chaotic dynamics for out-of-distribution forcing signals.

nlin.CD↗
arXiv2024

Evolution beats random chance: Performance-dependent network evolution for enhanced computational capacity

The quest to understand structure-function relationships in networks across scientific disciplines has intensified. However, the optimal network architecture remains elusive, particularly for complex information processing. Therefore, we investigate how optimal and specific network structures form to efficiently solve distinct tasks using a novel framework of performance-dependent network evolution, leveraging reservoir computing principles. Our study demonstrates that task-specific minimal network structures obtained through this framework consistently outperform networks generated by alternative growth strategies and Erd\H{o}s-R\'enyi random networks. Evolved networks exhibit unexpected sparsity and adhere to scaling laws in node-density space while showcasing a distinctive asymmetry in input and information readout nodes distribution. Consequently, we propose a heuristic for quantifying task complexity from performance-dependently evolved networks, offering valuable insights into the evolutionary dynamics of network structure-function relationships. Our findings not only advance the fundamental understanding of process-specific network evolution but also shed light on the design and optimization of complex information processing mechanisms, notably in machine learning.

nlin.AO↗
arXiv2024

Data assimilation and parameter identification for water waves using the nonlinear Schr\"{o}dinger equation and physics-informed neural networks

The measurement of deep water gravity wave elevations using in-situ devices, such as wave gauges, typically yields spatially sparse data. This sparsity arises from the deployment of a limited number of gauges due to their installation effort and high operational costs. The reconstruction of the spatio-temporal extent of surface elevation poses an ill-posed data assimilation problem, challenging to solve with conventional numerical techniques. To address this issue, we propose the application of a physics-informed neural network (PINN), aiming to reconstruct physically consistent wave fields between two designated measurement locations several meters apart. Our method ensures this physical consistency by integrating residuals of the hydrodynamic nonlinear Schr\"{o}dinger equation (NLSE) into the PINN's loss function. Using synthetic wave elevation time series from distinct locations within a wave tank, we initially achieve successful reconstruction quality by employing constant, predetermined NLSE coefficients. However, the reconstruction quality is further improved by introducing NLSE coefficients as additional identifiable variables during PINN training. The results not only showcase a technically relevant application of the PINN method but also represent a pioneering step towards improving the initialization of deterministic wave prediction methods.

physics.flu-dyn↗
arXiv2023

Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data

Accurate short-term predictions of phase-resolved water wave conditions are crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wave prediction models first requires a reconstruction of wave surfaces from sparse measurements like radar. Existing reconstruction methods either rely on computationally intensive optimization procedures or simplistic modelling assumptions that compromise the real-time capability or accuracy of the subsequent prediction process. We therefore address these issues by proposing a novel approach for phase-resolved wave surface reconstruction using neural networks based on the U-Net and Fourier neural operator (FNO) architectures. Our approach utilizes synthetic yet highly realistic training data on uniform one-dimensional grids, that is generated by the high-order spectral method for wave simulation and a geometric radar modelling approach. The investigation reveals that both models deliver accurate wave reconstruction results and show good generalization for different sea states when trained with spatio-temporal radar data containing multiple historic radar snapshots in each input. Notably, the FNO demonstrates superior performance in handling the data structure imposed by wave physics due to its global approach to learn the mapping between input and output in Fourier space.

physics.ao-ph↗
arXiv2022

Surface Similarity Parameter: A New Machine Learning Loss Metric for Oscillatory Spatio-Temporal Data

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 dynamics 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.

cs.LG↗
arXiv2020

Deep learning for brake squeal: vibration detection, characterization and prediction

Despite significant advances in modeling of friction-induced vibrations and brake squeal, the majority of industrial research and design is still conducted experimentally, since many aspects of squeal and its mechanisms involved remain unknown. We report here for the first time on novel strategies for handling data-intensive vibration testings to gain better insights into friction brake system vibrations and noise generation mechanisms. Machine learning-based methods to detect and characterize vibrations, to understand sensitivities and to predict brake squeal are applied with the aim to illustrate how interdisciplinary approaches can leverage the potential of data science techniques for classical mechanical engineering challenges. In the first part, a deep learning brake squeal detector is developed to identify several classes of typical friction noise recordings. The detection method is rooted in recent computer vision techniques for object detection based on convolutional neural networks. It allows to overcome limitations of classical approaches that solely rely on instantaneous spectral properties of the recorded noise. Results indicate superior detection and characterization quality when compared to a state-of-the-art brake squeal detector. In the second part, a recurrent neural network is employed to learn the parametric patterns that determine the dynamic stability of an operating brake system. Given a set of multivariate loading conditions, the RNN learns to predict the noise generation of the structure. The validated RNN represents a virtual twin model for the squeal behavior of a specific brake system. It is found that this model can predict the occurrence and the onset of brake squeal with high accuracy and that it can identify the complicated patterns and temporal dependencies in the loading conditions that drive the dynamical structure into regimes of instability.

eess.SP↗
arXiv2019

Energy harvesting below the onset of flutter

This work demonstrates preliminary results on energy harvesting from a linearly stable flutter-type system with circulatory friction forces. Harmonic external forcing is applied to study the energy flow in the steady sliding configuration. In certain parameter ranges negative excitation work is observed where the external forcing allows to pull part of the friction energy out of the system and thus makes energy harvesting possible. Studies reveal that this behavior is largely independent of the flutter point and thus that it is primarily controlled by the excitation. Contrary to existing energy harvesting approaches for such systems, this approach uses external forcing in the linearly stable regime of the oscillator which allows to control vibrations and harvest energy on demand.

physics.app-ph↗
arXiv2019

The non-linear behavior of aqueous model ice in downward flexure

As aqueous model ice is used extensively in ice tanks tests on the performance of ship hulls in sheet ice, it is imperative that such model ice replicate the main flexural strength behavior of sheets of sea ice and freshwater ice. Ice tanks use various types of aqueous model ice types, each of which contain brine dopants to scale-reduce ice-sheet strength. Dopants, though, introduce non-linear trends in the scaled flexural behavior of model ice sheets, and can affect ice loads and ice-rubble at ship-hulls and structures. This paper analyzes the non-linear behavior of model ices, and shows that all types behave non-linearly in flexure independent from crystal structure or chemical dopant. Such behavior is attributable to plasticity and vertical variations in stiffness and strength through sheets of model ice. Additionally, the problematic formation of a top layer in model ice sheets is shown to have a greater impact of sheet behavior than the literature reports heretofore. There remains a significant knowledge gap regarding the freezing and movement of brine dopants within ice sheets and their impact on the non-linear behavior. Additionally, it is found that the Hertz method for estimating the Cauchy number of model ice does not reflect the actual deformation behavior of model ice and should be revised.

physics.geo-ph↗