Stefan Kollmannsberger

John N. Jomo, Nils Zander, Mohamed Elhaddad et al.

The multi-level hp-refinement scheme is a powerful extension of the finite element method that allows local mesh adaptation without the trouble of constraining hanging nodes. This is achieved through hierarchical high-order overlay meshes, a hp-scheme based on spatial refinement by superposition. An efficient parallelization of this method using standard domain decomposition approaches in combination with ghost elements faces the challenge of a large basis function support resulting from the overlay structure and is in many cases not feasible. In this contribution, a parallelization strategy for the multi-level hp-scheme is presented that is adapted to the scheme's simple hierarchical structure. By distributing the computational domain among processes on the granularity of the active leaf elements and utilizing shared mesh data structures, good parallel performance is achieved, as redundant computations on ghost elements are avoided. We show the scheme's parallel scalability for problems with a few hundred elements per process. Furthermore, the scheme is used in conjunction with the finite cell method to perform numerical simulations on domains of complex shape.

Stefan Kollmannsberger, Divya Singh, Leon Herrmann

We propose a way to favorably employ neural networks in the field of non-destructive testing using Full Waveform Inversion (FWI). The presented methodology discretizes the unknown material distribution in the domain with a neural network within an adjoint optimization. To further increase efficiency of the FWI, pretrained neural networks are used to provide a good starting point for the inversion. This reduces the number of iterations in the Full Waveform Inversion for specific, yet generalizable settings.

Tim Bürchner, Simon Schmid, Ernst Rank et al.

Accurate modeling of ultrasound wave propagation is essential for high-fidelity simulation and imaging in ultrasonic testing. A primary challenge lies in characterizing the excitation source, particularly for transducers with large apertures relative to the acoustic wavelengths. In such cases, non-uniform excitation and spatial interference significantly affect the resulting radiation patterns. This paper proposes a distributed source inversion strategy to reconstruct an effective spatio-temporal transducer model that reproduces experimentally measured wavefields. The reconstructed source model captures aperture-dependent phase and amplitude variations without the need for detailed knowledge of the transducer structure. The approach is validated using directivity measurements on an aluminum half-cylinder, where simulations incorporating the reconstructed source model show close agreement with experimental directivity patterns and waveform shapes. Finally, synthetic studies on reverse time migration and full-waveform inversion demonstrate that accurate transducer modeling is critical for the success of simulation-based imaging and inversion workflows and significantly improves reconstruction quality.

Divya Shyam Singh, Leon Herrmann, Qing Sun et al.

Full waveform inversion (FWI) is a powerful tool for reconstructing material fields based on sparsely measured data obtained by wave propagation. For specific problems, discretizing the material field with a neural network (NN) improves the robustness and reconstruction quality of the corresponding optimization problem. We call this method NN-based FWI. Starting from an initial guess, the weights of the NN are iteratively updated to fit the simulated wave signals to the sparsely measured data set. For gradient-based optimization, a suitable choice of the initial guess, i.e., a suitable NN weight initialization, is crucial for fast and robust convergence. In this paper, we introduce a novel transfer learning approach to further improve NN-based FWI. This approach leverages supervised pretraining to provide a better NN weight initialization, leading to faster convergence of the subsequent optimization problem. Moreover, the inversions yield physically more meaningful local minima. The network is pretrained to predict the unknown material field using the gradient information from the first iteration of conventional FWI. In our computational experiments on two-dimensional domains, the training data set consists of reference simulations with arbitrarily positioned elliptical voids of different shapes and orientations. We compare the performance of the proposed transfer learning NN-based FWI with three other methods: conventional FWI, NN-based FWI without pretraining and conventional FWI with an initial guess predicted from the pretrained NN. Our results show that transfer learning NN-based FWI outperforms the other methods in terms of convergence speed and reconstruction quality.

Leon Herrmann, Ole Sigmund, Viola Muning Li et al.

Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for some inverse problems, the benefit for topology optimization has been limited -- where the focus of investigations has been the compliance problem. We demonstrate how neural network material discretizations can, under certain conditions, find better local optima in more challenging optimization problems, where we here specifically consider acoustic topology optimization. The chances of identifying a better optimum can significantly be improved by running multiple partial optimizations with different neural network initializations. Furthermore, we show that the neural network material discretization's advantage comes from the interplay with the Adam optimizer and emphasize its current limitations when competing with constrained and higher-order optimization techniques. At the moment, this discretization has only been shown to be beneficial for unconstrained first-order optimization.

Leon Herrmann, Stefan Kollmannsberger

The rapid growth of deep learning research, including within the field of computational mechanics, has resulted in an extensive and diverse body of literature. To help researchers identify key concepts and promising methodologies within this field, we provide an overview of deep learning in deterministic computational mechanics. Five main categories are identified and explored: simulation substitution, simulation enhancement, discretizations as neural networks, generative approaches, and deep reinforcement learning. This review focuses on deep learning methods rather than applications for computational mechanics, thereby enabling researchers to explore this field more effectively. As such, the review is not necessarily aimed at researchers with extensive knowledge of deep learning -- instead, the primary audience is researchers at the verge of entering this field or those who attempt to gain an overview of deep learning in computational mechanics. The discussed concepts are, therefore, explained as simple as possible.

Jing Rao, Fangshu Yang, Huadong Mo et al.

Ultrasonic methods have great potential applications to detect and characterize defects in multi-layered bonded composites. However, it remains challenging to quantitatively reconstruct defects, such as disbonds and kissing bonds, that influence the integrity of adhesive bonds and seriously reduce the strength of assemblies. In this work, an ultrasonic method based on the supervised fully convolutional network (FCN) is proposed to quantitatively reconstruct defects hidden in multi-layered bonded composites. In the training process of this method, an FCN establishes a non-linear mapping from measured ultrasonic data to the corresponding velocity models of multi-layered bonded composites. In the predicting process, the trained network obtained from the training process is used to directly reconstruct the velocity models from the new measured ultrasonic data of adhesively bonded composites. The presented FCN-based inversion method can automatically extract useful features in multi-layered composites. Although this method is computationally expensive in the training process, the prediction itself in the online phase takes only seconds. The numerical results show that the FCN-based ultrasonic inversion method is capable to accurately reconstruct ultrasonic velocity models of the high contrast defects, which has great potential for online detection of adhesively bonded composites.

Ali Özcan, Stefan Kollmannsberger, John N. Jomo et al.

This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This application demands for the solution of a coupled thermo-elasto-plastic problem on transient meshes within which history variables need to be managed dynamically on non-boundary conforming discretizations. To this end, we propose to combine the multi-level hp-method and the finite cell method. The former was specifically designed to treat high-order finite element discretizations on transient meshes, while the latter offers a remedy to retain high-order convergence rates also in cases where the physical boundary does not coincide with the boundary of the discretization. We investigate the performance of the method at two analytical and one experimental benchmark.