arXiv subjects

Leon Herrmann

Publications and source records attributed to Leon Herrmann.

10 recordsLinked to original sources

arXiv2026

Machine Learning Inference Limits of Routine Cement Characterization for CEM I Performance: Evidence From a Multi-Producer Dataset

Routine cement performance characterization provides continuous quality control data, but its information content for performance inference and transferability across independent producers remains uncertain. This study analyzes 476 cement records from 23 European producers, collected in one laboratory over 27 years, to determine what can be inferred from routine measurements. The analysis focuses on CEM I and combines oxide chemistry, Blaine fineness, particle-size distribution descriptors, physical properties, and derived Bogue and equivalent-alkali descriptors with machine learning attribution and producer-transfer tests. For CEM I, fineness is the strongest descriptor family for strength class and water demand, but oxide chemistry contributes a comparable signal when evaluated jointly. Blaine and compact particle-size distribution representations are largely interchangeable within the descriptor space, indicating that the dominant recoverable fineness information is captured by routine measurements. Equivalent alkali shows a consistent negative association with 28-day strength, through K$_2$O in this dataset. Strength class and water demand can be recovered from routine cement characterization data. The early-strength designation is recovered only as a population-level tendency, not a physically separable class, because early-strength development can arise from combinations of fineness, sulfate--alkali chemistry, phase assemblage, and plant practice. Producer-holdout tests show that absolute prediction errors remain comparable across the held-out producers in this dataset, whereas recovery of within-producer strength variation is producer-dependent. Routine CEM I characterization therefore supports useful performance inference across producers, while exposing producer-specific variation whose recovery may require additional speciation.

cond-mat.mtrl-sci↗

arXiv2026

Lightweight return-mapping surrogates for multiscale plasticity: a practical guide

This paper presents a practical guide to building lightweight neural-network surrogates for the plastic return-mapping process in concurrent multiscale (FE2) simulations. Rather than proposing a new architecture, we show how a deliberately simple feed-forward network, structured to mirror the classical return-mapping update, can replace the prohibitively expensive nested fine-scale solves that dominate the cost of conventional FE2 schemes based on FFT homogenization at the meso-scale. We walk through the full workflow: generating training data from incremental homogenization analyses, constructing a compact yet sufficient dataset, embedding material symmetries directly into the mapping, and deploying the trained network as a user-defined material subroutine (UMAT) in a standard finite-element solver -- enabling widespread use. A sensitivity study examines the model's robustness to data density, increment size, and mesh refinement, and we characterize the regimes in which the surrogate holds and where it breaks down. For the macroscopically isotropic, two-dimensional plane-stress setting considered here, the surrogate reproduces the reference response while reducing the per-analysis cost from hours to seconds with speed-ups up to 30,000 over standard FE2. The approach extends naturally to three dimensions and to weaker symmetry assumptions, given an appropriate sampling strategy and dataset.

math.NA↗

arXiv2025

A Memory Efficient Adjoint Method to Enable Billion Parameter Optimization on a Single GPU in Dynamic Problems

Dynamic optimization is currently limited by sensitivity computations that require information from full forward and adjoint wave fields. Since the forward and adjoint solutions are computed in opposing time directions, the forward solution must be stored. This requires a substantial amount of memory for large-scale problems even when using check pointing or data compression techniques. As a result, the problem size is memory bound rather than bound by wall clock time, when working with modern GPU-based implementations that have limited memory capacity. To overcome this limitation, we introduce a new approach for approximate sensitivity computation based on the adjoint method (for self-adjoint problems) that relies on the principle of superposition. The approximation allows an iterative computation of the sensitivity, reducing the memory burden to that of the solution at a small number of time steps, i.e., to the number of degrees of freedom. This enables sensitivity computations for problems with billions of degrees of freedom on current GPUs, such as the A100 from NVIDIA (from 2020). We demonstrate the approach on full waveform inversion and transient acoustic topology optimization problems, relying on a highly efficient finite difference forward solver implemented in CUDA. Phenomena such as damping cannot be considered, as the approximation technique is limited to self-adjoint problems.

cs.CE↗

arXiv2024

Accelerating Full Waveform Inversion By Transfer Learning

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.

cs.LG↗

arXiv2024

Neural Networks for Generating Better Local Optima in Topology Optimization

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.

cs.LG↗

arXiv2023

The Discontinuous Strain Method: accurately representing fatigue and failure

Fatigue simulation requires accurate modeling of unloading and reloading. However, classical ductile damage models treat deformations after complete failure as irrecoverable -- which leads to unphysical behavior during unloading. This unphysical behavior stems from the continued accumulation of plastic strains after failure, resulting in an incorrect stress state at crack closure. As a remedy, we introduce a discontinuity strain in the additive elasto-plastic strain decomposition, which absorbs the excess strain after failure. This allows representing pre- and post-cracking regimes in a fully continuous setting, wherein the transition from the elasto-plastic response to cracking can be triggered at any arbitrary stage in a completely smooth manner. Moreover, the presented methodology does not exhibit the spurious energy release observed in hybrid approaches. In addition, our approach guarantees mesh-independent results by relying on a characteristic length scale -- based on the discretization's resolution. We name this new methodology the discontinuous strain method. The proposed approach requires only minor modifications of conventional plastic-damage routines. To convey the method in a didactic manner, the algorithmic modifications are first discussed for one- and subsequently for two-/three-dimensional implementations. Using a simple ductile constitutive model, the discontinuous strain method is validated against established two-dimensional benchmarks. The method is, however, independent of the employed constitutive model. Elastic, plastic, and damage models may thus be chosen arbitrarily. Furthermore, computational efforts associated with the method are minimal, rendering it advantageous for accurately representing low-cycle fatigue but potentially also for other scenarios requiring a discontinuity representation within a plastic-damage framework.

cs.CE↗

arXiv2023

Deep Learning in Deterministic Computational Mechanics

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.

cs.LG↗

arXiv2023

From ductile damage to unilateral contact via point-wise implicit discontinuity at the infinitesimal element level

Ductile damage models and cohesive laws incorporate the material plasticity entailing the growth of irrecoverable deformations even after complete failure. This unrealistic growth remains concealed until the unilateral effects arising from the crack closure emerge. We address this issue by proposing a new strategy to cope with the entire process of failure, from the very inception in the form of diffuse damage to the final stage, i.e. the emergence of sharp cracks. To this end, we introduce a new strain field, termed discontinuity strain, to the conventional additive strain decomposition to account for discontinuities in a continuous sense so that the standard principle of virtual work applies. We treat this strain field similar to a strong discontinuity, yet without introducing new kinematic variables and nonlinear boundary conditions. In this paper, we demonstrate the effectiveness of this new strategy at a simple ductile damage constitutive model. The model uses a scalar damage index to control the degradation process. The discontinuity strain field is injected into the strain decomposition if this damage index exceeds a certain threshold. The threshold corresponds to the limit at which the induced imperfections merge and form a discrete crack. With three-point bending tests under pure mode I and mixed-mode conditions, we demonstrate that this augmentation does not show the early crack closure artifact which is wrongly predicted by plastic damage formulations at load reversal. We also use the concrete damaged plasticity model provided in Abaqus commercial finite element program for our comparison. Lastly, a high-intensity low-cycle fatigue test demonstrates the unilateral effects resulting from the complete closure of the induced crack.

cs.CE↗

arXiv2023

Transfer Learning Enhanced Full Waveform Inversion

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.

cs.LG↗

arXiv2023

On the Use of Neural Networks for Full Waveform Inversion

Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform inversion is the considered inverse problem. The performance of PINNs is compared against classical adjoint optimization, focusing on three key aspects: the forward-solver, the neural network Ansatz for the inverse field, and the sensitivity computation for the gradient-based minimization. Starting from PINNs, each of these key aspects is adapted individually until the classical adjoint optimization emerges. It is shown that it is beneficial to use the neural network only for the discretization of the unknown material field, where the neural network produces reconstructions without oscillatory artifacts as typically encountered in classical full waveform inversion approaches. Due to this finding, a hybrid approach is proposed. It exploits both the efficient gradient computation with the continuous adjoint method as well as the neural network Ansatz for the unknown material field. This new hybrid approach outperforms Physics-Informed Neural Networks and the classical adjoint optimization in settings of two and three-dimensional examples.

math.NA↗