David Anton

David Anton, Henning Wessels

The identification of material parameters occurring in constitutive models has a wide range of applications in practice. One of these applications is the monitoring and assessment of the actual condition of infrastructure buildings, as the material parameters directly reflect the resistance of the structures to external impacts. Physics-informed neural networks (PINNs) have recently emerged as a suitable method for solving inverse problems. The advantages of this method are a straightforward inclusion of observation data. Unlike grid-based methods, such as the least square finite element method (LS-FEM) approach, no computational grid and no interpolation of the data is required. In the current work, we propose PINNs for the calibration of constitutive models from full-field displacement and global force data in a realistic regime on the example of linear elasticity. We show that conditioning and reformulation of the optimization problem play a crucial role in real-world applications. Therefore, among others, we identify the material parameters from initial estimates and balance the individual terms in the loss function. In order to reduce the dependency of the identified material parameters on local errors in the displacement approximation, we base the identification not on the stress boundary conditions but instead on the global balance of internal and external work. We demonstrate that the enhanced PINNs are capable of identifying material parameters from both experimental one-dimensional data and synthetic full-field displacement data in a realistic regime. Since displacement data measured by, e.g., a digital image correlation (DIC) system is noisy, we additionally investigate the robustness of the method to different levels of noise.

Jorge-Humberto Urrea-Quintero, David Anton, Laura De Lorenzis et al.

The automated discovery of constitutive models from data has recently emerged as a promising alternative to the traditional model calibration paradigm. In this work, we present a fully automated framework for constitutive model discovery that systematically pairs three sparse regression algorithms (Least Absolute Shrinkage and Selection Operator (LASSO), Least Angle Regression (LARS), and Orthogonal Matching Pursuit (OMP)) with three model selection criteria: $K$-fold cross-validation (CV), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). This pairing yields nine distinct algorithms for model discovery and enables a systematic exploration of the trade-off between sparsity, predictive performance, and computational cost. While LARS serves as an efficient path-based solver for the $\ell_1$-constrained problem, OMP is introduced as a tractable heuristic for $\ell_0$-regularized selection. The framework is applied to both isotropic and anisotropic hyperelasticity, utilizing both synthetic and experimental datasets. Results reveal that all nine algorithm-criterion combinations perform consistently well in discovering isotropic and anisotropic materials, yielding highly accurate constitutive models. These findings broaden the range of viable discovery algorithms beyond $\ell_1$-based approaches such as LASSO.

David Anton, Henning Wessels, Ulrich Römer et al.

Constitutive model discovery refers to the task of identifying an appropriate model structure, usually from a predefined model library, while simultaneously inferring its material parameters. The data used for model discovery are measured in mechanical tests and are thus inevitably affected by noise which, in turn, induces uncertainties. Previously proposed methods for uncertainty quantification in model discovery either require the selection of a prior for the material parameters, are restricted to the linear coefficients of the model library or are limited in the flexibility of the inferred parameter probability distribution. We therefore propose a four-step partially Bayesian framework for uncertainty quantification in model discovery that does not require prior selection for the material parameters and also allows for the discovery of non-linear constitutive models: First, we augment the available stress-deformation data with a Gaussian process. Second, we approximate the parameter distribution by a normalizing flow, which allows for capturing complex joint distributions. Third, we distill the parameter distribution by matching the distribution of stress-deformation functions induced by the parameters with the Gaussian process posterior. Fourth, we perform a Sobol' sensitivity analysis to obtain a sparse and interpretable model. We demonstrate the capability of our framework for both isotropic and anisotropic experimental data as well as linear and non-linear model libraries.

David Anton, Idoia Berges, Jesús Bermúdez et al.

Telerehabilitation systems that support physical therapy sessions anywhere can help save healthcare costs while also improving the quality of life of the users that need rehabilitation. The main contribution of this paper is to present, as a whole, all the features supported by the innovative Kinect-based Telerehabilitation System (KiReS). In addition to the functionalities provided by current systems, it handles two new ones that could be incorporated into them, in order to give a step forward towards a new generation of telerehabilitation systems. The knowledge extraction functionality handles knowledge about the physical therapy record of patients and treatment protocols described in an ontology, named TRHONT, to select the adequate exercises for the rehabilitation of patients. The teleimmersion functionality provides a convenient, effective and user-friendly experience when performing the telerehabilitation, through a two-way real-time multimedia communication. The ontology contains about 2300 classes and 100 properties, and the system allows a reliable transmission of Kinect video depth, audio and skeleton data, being able to adapt to various network conditions. Moreover, the system has been tested with patients who suffered from shoulder disorders or total hip replacement.