arXiv subjects

Rodrigo L. S. Silva

Publications and source records attributed to Rodrigo L. S. Silva.

3 recordsLinked to original sources

arXiv2026

Discretization-optimized Bayesian model calibration for nonlinear constitutive modeling in heat conduction

We present a Bayesian model calibration framework for inferring nonlinear constitutive relationships in heat conduction problems, with a focus on temperature-dependent thermal conductivity. The proposed framework integrates gradient-based optimization and uncertainty quantification (UQ) to address the inverse problem of estimating the conductivity function from transient temperature measurements. A key contribution is an adaptive algorithm that sequentially refines both the numerical discretization for model simulation, and the model complexity used to represent the conductivity curve. The discretization is optimized through the minimization of a loss function, and Morozov's discrepancy principle is used as an uncertainty-motivated stopping criterion. The model complexity is selected using an approach that balances maximizing the likelihood of the data with penalizing excessive model complexity. As a result, the numerical and modeling biases remain of the same order as the uncertainty imposed by the measurement noise, leading to robust and computationally efficient inference. The methodology is demonstrated on both synthetic and experimental data, showing that it enables accurate calibration of nonlinear constitutive models with minimal overfitting and limited computational cost.

cs.CE↗

arXiv2026

A comparison of Markov Chain Monte Carlo algorithms for Bayesian inference of constitutive models

Employing Bayesian inference to calibrate constitutive model parameters has grown substantially in recent years. Among the available techniques, Markov Chain Monte Carlo (MCMC) sampling remains one of the most widely used approaches for estimating the posterior distribution. Nevertheless, the selection of a specific MCMC algorithm is often driven by practical considerations, such as software availability or prior user experience. To support sampler selection, we present a comparison of three prominent samplers in the context of two distinct physical systems: a thermal conduction system and a viscous flow system. Calibration data are obtained through tailor-made experimental setups. We use the Kullback-Leibler (KL) divergence, which quantifies the statistical distance between the sampled posterior and the reference ('true') posterior, as a measure of convergence to compare the performance of the following MCMC sampling methods: the Metropolis-Hastings (MH) sampler, the Affine Invariant Stretch Move (AISM) sampler, and the No-U-Turn Sampler (NUTS). We study how this metric correlates to heuristic indicators such as the Gelman-Rubin diagnostic and the effective sample size. In addition, we assess the samplers' computational effort in terms of required number of model evaluations. Based on the results, we find that the heuristic convergence and performance indicators provide a good qualitative measure for KL-divergence for both systems. Regarding computational effort, the NUTS is net beneficial for the viscous flow system, as the high effective sample size outweighs the additional effort required for gradient-based proposal generation. For the thermal conduction system, which involves more expensive model evaluations, the NUTS is not advantageous. Thus, the computational efficiency of gradient evaluations is an important argument in sampler selection.

cs.CE↗

arXiv2024

Bayesian estimation and uncertainty quantification of a temperature-dependent thermal conductivity

We consider the problem of estimating a temperature-dependent thermal conductivity model (curve) from temperature measurements. We apply a Bayesian estimation approach that takes into account measurement errors and limited prior information of system properties. The approach intertwines system simulation and Markov chain Monte Carlo (MCMC) sampling. We investigate the impact of assuming different model classes - cubic polynomials and piecewise linear functions - their parametrization, and different types of prior information - ranging from uninformative to informative. Piecewise linear functions require more parameters (conductivity values) to be estimated than the four parameters (coefficients or conductivity values) needed for cubic polynomials. The former model class is more flexible, but the latter requires less MCMC samples. While parametrizing polynomials with coefficients may feel more natural, it turns out that parametrizing them using conductivity values is far more natural for the specification of prior information. Robust estimation is possible for all model classes and parametrizations, as long as the prior information is accurate or not too informative. Gaussian Markov random field priors are especially well-suited for piecewise linear functions.

cs.CE↗