Michael Kraus

Michael Kraus, Omar Maj

A variational integrator for ideal magnetohydrodynamics is derived by applying a discrete action principle to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their geometrical character. The resulting numerical method is free of numerical resistivity, thus the magnetic field line topology is preserved and unphysical reconnection is absent. In 2D numerical examples we find that important conservation laws like total energy, magnetic helicity and cross helicity are satisfied within machine accuracy.

Vera M. Balmer, Sophia V. Kuhn, Rafael Bischof et al.

For conceptual design, engineers rely on conventional iterative (often manual) techniques. Emerging parametric models facilitate design space exploration based on quantifiable performance metrics, yet remain time-consuming and computationally expensive. Pure optimisation methods, however, ignore qualitative aspects (e.g. aesthetics or construction methods). This paper provides a performance-driven design exploration framework to augment the human designer through a Conditional Variational Autoencoder (CVAE), which serves as forward performance predictor for given design features as well as an inverse design feature predictor conditioned on a set of performance requests. The CVAE is trained on 18'000 synthetically generated instances of a pedestrian bridge in Switzerland. Sensitivity analysis is employed for explainability and informing designers about (i) relations of the model between features and/or performances and (ii) structural improvements under user-defined objectives. A case study proved our framework's potential to serve as a future co-pilot for conceptual design studies of pedestrian bridges and beyond.

Rafael Bischof, Florian Scheidegger, Michael A. Kraus et al.

Neural Image Classifiers are effective but inherently hard to interpret and susceptible to adversarial attacks. Solutions to both problems exist, among others, in the form of counterfactual examples generation to enhance explainability or adversarially augment training datasets for improved robustness. However, existing methods exclusively address only one of the issues. We propose a unified framework leveraging image-to-image translation Generative Adversarial Networks (GANs) to produce counterfactual samples that highlight salient regions for interpretability and act as adversarial samples to augment the dataset for more robustness. This is achieved by combining the classifier and discriminator into a single model that attributes real images to their respective classes and flags generated images as "fake". We assess the method's effectiveness by evaluating (i) the produced explainability masks on a semantic segmentation task for concrete cracks and (ii) the model's resilience against the Projected Gradient Descent (PGD) attack on a fruit defects detection problem. Our produced saliency maps are highly descriptive, achieving competitive IoU values compared to classical segmentation models despite being trained exclusively on classification labels. Furthermore, the model exhibits improved robustness to adversarial attacks, and we show how the discriminator's "fakeness" value serves as an uncertainty measure of the predictions.

Rafael Bischof, Michal Piovarči, Michael A. Kraus et al.

We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parameterizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions with varying source terms, geometries, and mixed Dirichlet/Neumann boundary conditions, including interior boundaries. HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN literature, outperforming U-Nets, Poseidon, and Physics-Informed Neural Operators (PINO). Further, we introduce an iterative refinement procedure that treats the residual of the generated PINN as "delta PDE" and performs another forward pass to generate a corrective PINN. Summing their contributions and repeating this process forms an ensemble whose combined solution progressively reduces the error on six benchmarks and achieves a >100x lower $L_2$ loss in the best case, while retaining forward-only inference. Additionally, we evaluate the fine-tuning behavior of PINNs initialized by HyPINO and show that they converge faster and to lower final error than both randomly initialized and Reptile-meta-learned PINNs on five benchmarks, performing on par on the remaining two. Our results highlight the potential of this scalable approach as a foundation for extending neural operators toward solving increasingly complex, nonlinear, and high-dimensional PDE problems. The code and model weights are publicly available at https://github.com/rbischof/hypino.

Michael A. Kraus, Helen Bartsch

This research introduces a unified approach combining Automated Machine Learning (AutoML) with Explainable Artificial Intelligence (XAI) to predict fatigue strength in welded transverse stiffener details. It integrates expert-driven feature engineering with algorithmic feature creation to enhance accuracy and explainability. Based on the extensive fatigue test database regression models - gradient boosting, random forests, and neural networks - were trained using AutoML under three feature schemes: domain-informed, algorithmic, and combined. This allowed a systematic comparison of expert-based versus automated feature selection. Ensemble methods (e.g. CatBoost, LightGBM) delivered top performance. The domain-informed model $\mathcal M_2$ achieved the best balance: test RMSE $\approx$ 30.6 MPa and $R^2 \approx 0.780% over the full $Δσ_{c,50\%}$ range, and RMSE $\approx$ 13.4 MPa and $R^2 \approx 0.527% within the engineering-relevant 0 - 150 MPa domain. The denser-feature model ($\mathcal M_3$) showed minor gains during training but poorer generalization, while the simpler base-feature model ($\mathcal M_1$) performed comparably, confirming the robustness of minimalist designs. XAI methods (SHAP and feature importance) identified stress ratio $R$, stress range $Δσ_i$, yield strength $R_{eH}$, and post-weld treatment (TIG dressing vs. as-welded) as dominant predictors. Secondary geometric factors - plate width, throat thickness, stiffener height - also significantly affected fatigue life. This framework demonstrates that integrating AutoML with XAI yields accurate, interpretable, and robust fatigue strength models for welded steel structures. It bridges data-driven modeling with engineering validation, enabling AI-assisted design and assessment. Future work will explore probabilistic fatigue life modeling and integration into digital twin environments.

Sophia V. Kuhn, Rafael Bischof, Marius Weber et al.

Aging infrastructure portfolios pose a critical resource allocation challenge: deciding which structures require intervention and which can safely remain in service. Structural assessments must balance the trade-off between cheaper, conservative analysis methods and accurate but costly simulations that do not scale portfolio-wide. We propose Bayesian neural network (BNN) surrogates for rapid structural pre-assessment of worldwide common bridge types, such as reinforced concrete frame bridges. Trained on a large-scale database of non-linear finite element analyses generated via a parametric pipeline and developed based on the Swiss Federal Railway's bridge portfolio, the models accurately and efficiently estimate high-fidelity structural analysis results by predicting code compliance factors with calibrated epistemic uncertainty. Our BNN surrogate enables fast, uncertainty-aware triage: flagging likely critical structures and providing guidance where refined analysis is pertinent. We demonstrate the framework's effectiveness in a real-world case study of a railway underpass, showing its potential to significantly reduce costs and emissions by avoiding unnecessary analyses and physical interventions across entire infrastructure portfolios.

Rafael Bischof, Michael Kraus

Physics-Informed Neural Networks (PINN) are algorithms from deep learning leveraging physical laws by including partial differential equations together with a respective set of boundary and initial conditions as penalty terms into their loss function. In this work, we observe the significant role of correctly weighting the combination of multiple competitive loss functions for training PINNs effectively. To this end, we implement and evaluate different methods aiming at balancing the contributions of multiple terms of the PINNs loss function and their gradients. After reviewing of three existing loss scaling approaches (Learning Rate Annealing, GradNorm and SoftAdapt), we propose a novel self-adaptive loss balancing scheme for PINNs named \emph{ReLoBRaLo} (Relative Loss Balancing with Random Lookback). We extensively evaluate the performance of the aforementioned balancing schemes by solving both forward as well as inverse problems on three benchmark PDEs for PINNs: Burgers' equation, Kirchhoff's plate bending equation and Helmholtz's equation. The results show that ReLoBRaLo is able to consistently outperform the baseline of existing scaling methods in terms of accuracy, while also inducing significantly less computational overhead.

Henrik Riedel, Sleheddine Mokdad, Isabell Schulz et al.

Vacuum Insulated Glazing (VIG) is a highly thermally insulating window technology, which boasts an extremely thin profile and lower weight as compared to gas-filled insulated glazing units of equivalent performance. The VIG is a double-pane configuration with a submillimeter vacuum gap between the panes and therefore under constant atmospheric pressure over their service life. Small pillars are positioned between the panes to maintain the gap, which can damage the glass reducing the lifetime of the VIG unit. To efficiently assess any surface damage on the glass, an automated damage detection system is highly desirable. For the purpose of classifying the damage, we have developed, trained, and tested a deep learning computer vision system using convolutional neural networks. The classification model flawlessly classified the test dataset with an area under the curve (AUC) for the receiver operating characteristic (ROC) of 100%. We have automatically cropped the images down to their relevant information by using Faster-RCNN to locate the position of the pillars. We employ the state-of-the-art methods Grad-CAM and Score-CAM of explainable Artificial Intelligence (XAI) to provide an understanding of the internal mechanisms and were able to show that our classifier outperforms ResNet50V2 for identification of crack locations and geometry. The proposed methods can therefore be used to detect systematic defects even without large amounts of training data. Further analyses of our model's predictive capabilities demonstrates its superiority over state-of-the-art models (ResNet50V2, ResNet101V2 and ResNet152V2) in terms of convergence speed, accuracy, precision at 100% recall and AUC for ROC.

Michael Kraus, Irfan Custovic, Walter Kaufmann

Our goal is to transform traditional paper-based instruction into an immersive lesson. This paper presents the conception, workflow and deployment of two MR applications for verification of typical yet geometrically complex structural members: a reinforced concrete corbel and a steel frame. The aim of this research is threefold: (i) to develop and implement the technological feasibility of such applications, (ii) to demonstrate possible use cases in the context of structural engineering lectures and (iii) to evaluate the presented MR examples and the future potential of such MR applications in structural engineering lectures through a survey. The workflow and MR teaching applications were developed with Apple's ARKit. The verification process was reproduced in the MR applications based on conventional exercises taught on paper. Users can navigate independently through the applications and review every single step, including a true-to-scale, spatial representation of the specific component as well as associated verification formulas in the respective step. The applications were used to assess the demand and expectations for immersive teaching techniques among students and instructors through a survey. The participants were asked to test the MR applications on their devices or watch pre-recorded video demonstrations, afterwards perception was elicited through a questionnaire. The results of subsequent data analysis show generally positive judgement of the MR application over the six questioned categories (style, usefulness, ease of use, enjoyment, attitude as well as intention towards using). The statistical analysis revealed (positivity) biases for users with prior XR experience w.r.t. to usage and navigation, while inexperienced users underlined increased enjoyment or excitement with this learning format. The outlook covers identified shortcomings and future developments in this field.