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Item type:Publication, Access status: with files , Inelastic Constitutive Kolmogorov–Arnold Networks: a generalized framework for automated discovery of interpretable inelastic material models(Elsevier, 2026-11-01); ; ; ; A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain history and stress. Machine learning has led to considerable advances in this field lately. Here we introduce inelastic Constitutive Kolmogorov–Arnold Networks (iCKANs). This novel artificial neural network architecture can discover in an automated manner symbolic constitutive laws describing both the elastic and inelastic behavior of materials. That is, it can translate data from material testing into corresponding free energy and dissipation potential functions in closed mathematical form. We demonstrate the advantages of iCKANs using both synthetic data and experimental data of the viscoelastic polymer materials VHB 4910 and VHB 4905. The results demonstrate that iCKANs accurately capture complex viscoelastic behavior while preserving physical interpretability. It is a particular strength of iCKANs that they can process not only mechanical data but also arbitrary additional information available about a material (e.g., about temperature-dependent behavior). This makes iCKANs a powerful tool to discover in the future also how specific processing or service conditions affect the properties of materials.Publicationtype: Journal Article29 11 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , LLM-driven design of physics-constrained constitutive models: Two agents are better than one(Springer, 2026-10-01); ; ; ; Developing constitutive models that capture how materials deform under load traditionally requires years of specialized expertise in continuum mechanics, machine learning, and scientific programming. Large language models (LLMs) have recently been shown to lower this barrier by generating constitutive models on demand, but existing single-agent pipelines lack systematic checks that the resulting models respect fundamental physical laws. To close this gap, we introduce the first multi-agent LLM-driven approach for constitutive model generation: a Creator agent proposes a model tailored to the data, while an Inspector agent critically audits each proposal against nine physical constraints and returns it for refinement whenever a violation is detected. We demonstrate this concept with constitutive artificial neural networks (CANNs) and benchmark it on brain tissue and rubber as isotropic materials, and on porcine skin tissue as a transversely isotropic material with a preferred fiber direction, using two different LLM backbones (Claude Opus 4.7 and Kimi K2.5). Whether a generated model satisfies the physical constraints is assessed numerically, by probing each constraint across a broad sample of deformation states, rotations, and perturbation directions. Adding the Inspector raises the share of exported models that pass all these checks from 90% to 95% for Opus and from 47% to 60% for Kimi. In addition, the generated models are on par with or even surpass expert-designed models in accuracy, extrapolate reliably beyond the training data, and generalize remarkably well to unseen loading paths. Separating generation from inspection thus turns LLM-driven constitutive modeling into a substantially more trustworthy process. The paradigm is deliberately technique-agnostic and scales automatically with advances in LLM capability, opening a promising path toward automated, physics-aware model discovery.Publicationtype: Journal Article16 34 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , LLMs as designers of physics-constrained neural networks for constitutive modeling: a demonstration on hyperelastic solids(Springer, 2026-06-12); ; ; ; Large language model (LLM)-based frameworks extend beyond agents; they also enable the on-demand creation of specialized scientific and engineering tools. We demonstrate this concept in the field of solid mechanics. There, so-called constitutive models describe the relationship between body deformation and mechanical stress. They are essential for both the scientific understanding and industrial application of materials. However, even recent data-driven methods of constitutive modeling, such as constitutive artificial neural networks (CANNs), still require substantial expert knowledge and human labor. We present a framework in which an LLM generates a CANN on demand, tailored to a given material class and dataset provided by the user. The framework covers LLM-based architecture selection, integration of physical constraints, and complete implementation. Evaluation on three benchmark problems demonstrates that LLM-generated CANNs achieve accuracy and generalization comparable to or greater than manually engineered counterparts, while substantially reducing the expertise required for constitutive modeling.Publicationtype: Journal Article33 28 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Thermodynamically consistent viscoelastic constitutive artificial neural networks: automating the pipeline from experimental data to finite element simulationsViscoelastic constitutive artificial neural networks (vCANNs) leverage neural networks for data-driven modeling of the viscoelastic behavior of materials. Here, we propose a thermodynamically consistent extension of vCANNs that captures anisotropic, nonlinear, and time-dependent material behavior. A key strength of this approach is its ability to incorporate arbitrary auxiliary features—such as temperature, microstructural descriptors, or processing parameters—directly into neural constitutive laws. We propose an automated computational pipeline for the generation and implementation of such constitutive laws within the proposed framework into finite element (FE) simulations without manual model design. The proposed framework is validated across a broad range of representative material tests, including the nonlinear, thermo-viscoelastic response of soft polymers and arterial tissue with fiber dispersion. In addition, we demonstrate the accuracy and robustness in FE simulations using benchmark problems such as Cook’s membrane. The results underscore the flexibility, physical plausibility, and numerical stability of vCANNs as a powerful class of constitutive models for modern FE simulations enhanced by machine learning.Publicationtype: Journal Article31 54 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Adversarial robustness of LLM-based multi-agent systems for engineering problems(Frontiers Media S.A., 2026-05-13); ; ; ; Large language models (LLMs) are increasingly deployed in multi-agent systems (MAS), including for solving engineering problems. Unlike purely linguistic tasks, engineering workflows demand formal rigor and numerical accuracy, meaning that adversarial perturbations can cause not just degraded performance but systematically incorrect or unsafe results. In this work, we present one of the first systematic studies of adversarial robustness of LLM-based MAS in engineering contexts. Using representative problems—including pipe pressure loss (Darcy-Weisbach), beam deflection, mathematical modeling, and graph traversal—we investigate how misleading agents affect collaborative reasoning and quantify error propagation under controlled adversarial influence. Our results show that adversarial vulnerabilities in engineering differ from those observed in generic MAS evaluations in important aspects: system robustness is sensitive to task type, the subtlety of injected errors, and communication order among agents. In particular, engineering tasks with higher structural complexity or easily confusable numerical variations are especially prone to adversarial influence. We further identify design choices, such as prompt framing, agent role assignment, and discussion order, that significantly improve resilience. These findings highlight the need for domain-specific evaluation of adversarial robustness and provide actionable insights for designing MAS that are trustworthy and safe in engineering applications.Publicationtype: Journal Article46 62 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A generalized dual potential for inelastic Constitutive Artificial Neural Networks: a JAX implementation at finite strainsWe present a methodology for designing a generalized dual potential, or pseudo potential, for inelastic Constitutive Artificial Neural Networks (iCANNs). This potential, expressed in terms of stress invariants, inherently satisfies thermodynamic consistency for large deformations. In comparison to our previous work, the new potential captures a broader spectrum of material behaviors, including pressure-sensitive inelasticity. To this end, we revisit the underlying thermodynamic framework of iCANNs for finite strain inelasticity and derive conditions for constructing a convex, zero-valued, and non-negative dual potential. To embed these principles in a neural network, we detail the architecture's design, ensuring a priori compliance with thermodynamics. To evaluate the proposed architecture, we study its performance and limitations discovering visco-elastic material behavior, though the method is not limited to visco-elasticity. In this context, we investigate different aspects in the strategy of discovering inelastic materials. Our results indicate that the novel architecture robustly discovers interpretable models and parameters, while autonomously revealing the degree of inelasticity. The iCANN framework, implemented in JAX, is publicly accessible at https://doi.org/10.5281/zenodo.14894687.Publicationtype: Journal Article26 22 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A computational model of coronary arteries with in-stent restenosis coupling hemodynamics and pharmacokinetics with growth mechanics(Springer, 2025-11-10); ; 24 23 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Functional partitioning through competitive learning(Frontiers Media S.A., 2025-11-05); ; ; ; Datasets often incorporate various functional patterns related to different aspects or regimes, which are typically not equally present throughout the dataset. We propose a novel partitioning algorithm that utilizes competition between models to detect and separate these functional patterns. This competition is induced by multiple models iteratively submitting their predictions for the dataset, with the best prediction for each data point being rewarded with training on that data point. This reward mechanism amplifies each model's strengths and encourages specialization in different patterns. The specializations can then be translated into a partitioning scheme. We validate our concept with datasets with clearly distinct functional patterns, such as mechanical stress and strain data in a porous structure. Our partitioning algorithm produces valuable insights into the datasets' structure, which can serve various further applications. As a demonstration of one exemplary usage, we set up modular models consisting of multiple expert models, each learning a single partition, and compare their performance on more than twenty popular regression problems with single models learning all partitions simultaneously. Our results show significant improvements, with up to 56% loss reduction, confirming our algorithm's utility.Publicationtype: Journal Article19 14 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Constitutive Kolmogorov–Arnold Networks (CKANs): Combining accuracy and interpretability in data-driven material modelingHybrid constitutive modeling integrates two complementary approaches for describing and predicting a material's mechanical behavior: purely data-driven black-box methods and physically constrained, theory-based models. While black-box methods offer high accuracy, they often lack interpretability and extrapolability. Conversely, physics-based models provide theoretical insight and generalizability but may not capture complex behaviors with the same accuracy. Traditionally, hybrid modeling has required a trade-off between these aspects. In this paper, we show how recent advances in symbolic machine learning — specifically Kolmogorov–Arnold Networks (KANs) — help to overcome this limitation. We introduce Constitutive Kolmogorov–Arnold Networks (CKANs) as a new class of hybrid constitutive models. By incorporating a post-processing symbolification step, CKANs combine the predictive accuracy of data-driven models with the interpretability and extrapolation capabilities of symbolic expressions, bridging the gap between machine learning and physical modeling.Publicationtype: Journal Article31 38 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Large language models predicting the corrosion inhibition efficiency of magnesium dissolution modulators(Elsevier, 2025-06-20); ; ; ; Large language models (LLMs), such as GPT-4o, have shown promise in solving everyday tasks and addressing fundamental scientific challenges by leveraging extensive pre-trained knowledge. In this study, we investigate their potential to predict the efficiency of various organic compounds in inhibiting the corrosion of the magnesium alloy ZE41. Traditional approaches, such as Multilayer Perceptrons (MLPs), rely on non-contextual data, often necessitating large datasets and substantial effort per sample to achieve accurate predictions. These methods particularly struggle with small datasets as their training data and domain of applicability is limited to a small area of the available chemical space. LLMs can contextualize and interpret limited data points by drawing on their vast knowledge, including the chemical properties of molecules and their influence on corrosion processes in other materials (e.g. iron and aluminium). By prompting the model with a small dataset, LLMs can provide meaningful predictions without the need for extensive training. Our study demonstrates that LLMs can predict corrosion inhibition outcomes and outperform classical approaches, such as MLPs, having access to the identical number of training samples.Publicationtype: Journal Article37 29