Jorge-Humberto Urrea-Quintero

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.

Pallavi Sharma, Jorge-Humberto Urrea-Quintero, Bogdan Bogdan et al.

This work proposes variational autoencoders (VAEs) to predict a vehicle's jerk signals from torque demand in the context of limited real-world drivetrain datasets. We implement both unconditional and conditional VAEs, trained on experimental data from two variants of a fully electric SUV with differing torque and drivetrain configurations. The VAEs synthesize jerk signals that capture characteristics from multiple drivetrain scenarios by leveraging the learned latent space. A performance comparison with baseline physics-based and hybrid models confirms the effectiveness of the VAEs, without requiring detailed system parametrization. Unconditional VAEs generate realistic jerk signals without prior system knowledge, while conditional VAEs enable the generation of signals tailored to specific torque inputs. This approach reduces the dependence on costly and time-intensive real-world experiments and extensive manual modeling. The results support the integration of generative models such as VAEs into drivetrain simulation pipelines, both for data augmentation and for efficient exploration of complex operational scenarios, with the potential to streamline validation and accelerate vehicle development.