arXiv subjects

Leon Riccius

Publications and source records attributed to Leon Riccius.

3 recordsLinked to original sources

arXiv2026

Piecewise Deterministic Markov Processes for Bayesian Inference of PDE Coefficients

We develop a general framework for piecewise deterministic Markov process (PDMP) samplers that enables efficient Bayesian inference in non-linear inverse problems with expensive likelihoods. The key ingredient is a surrogate-assisted thinning scheme in which a surrogate model provides a proposal event rate and a robust correction mechanism enforces an upper bound on the true rate by dynamically adjusting an additive offset whenever violations are detected. This construction is agnostic to the choice of surrogate and PDMP, and we demonstrate it for the Zig-Zag sampler and the Bouncy particle sampler with constant, Laplace, and Gaussian process (GP) surrogates, including gradient-informed and adaptively refined GP variants. As a representative application, we consider Bayesian inference of a spatially varying Young's modulus in a one-dimensional linear elasticity problem. Across dimensions, PDMP samplers equipped with GP-based surrogates achieve substantially higher accuracy and effective sample size per forward model evaluation than Random Walk Metropolis algorithm and the No-U-Turn sampler. The Bouncy particle sampler exhibits the most favorable overall efficiency and scaling, illustrating the potential of the proposed PDMP framework beyond this particular setting.

stat.CO↗

arXiv2024

Integration of Active Learning and MCMC Sampling for Efficient Bayesian Calibration of Mechanical Properties

Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models and cutting-edge MCMC algorithms, often depend on ad-hoc decisions. A systematic assessment of their combined influence on analytical accuracy and efficiency is notably lacking. The present work offers a comprehensive comparative study, employing a scalable case study in computational mechanics focused on the inference of spatially varying material parameters, that sheds light on the impact of methodological choices for surrogate modelling and sampling. We show that a priori training of the surrogate model introduces large errors in the posterior estimation even in low to moderate dimensions. We introduce a simple active learning strategy based on the path of the MCMC algorithm that is superior to all a priori trained models, and determine its training data requirements. We demonstrate that the choice of the MCMC algorithm has only a small influence on the amount of training data but no significant influence on the accuracy of the resulting surrogate model. Further, we show that the accuracy of the posterior estimation largely depends on the surrogate model, but not even a tailored surrogate guarantees convergence of the MCMC.Finally, we identify the forward model as the bottleneck in the inference process, not the MCMC algorithm. While related works focus on employing advanced MCMC algorithms, we demonstrate that the training data requirements render the surrogate modelling approach infeasible before the benefits of these gradient-based MCMC algorithms on cheap models can be reaped.

physics.comp-ph↗

arXiv2023

Physics-Informed Tensor Basis Neural Network for Turbulence Closure Modeling

Despite the increasing availability of high-performance computational resources, Reynolds-Averaged Navier-Stokes (RANS) simulations remain the workhorse for the analysis of turbulent flows in real-world applications. Linear eddy viscosity models (LEVM), the most commonly employed model type, cannot accurately predict complex states of turbulence. This work combines a deep-neural-network-based, nonlinear eddy viscosity model with turbulence realizability constraints as an inductive bias in order to yield improved predictions of the anisotropy tensor. Using visualizations based on the barycentric map, we show that the proposed machine learning method's anisotropy tensor predictions offer a significant improvement over all LEVMs in traditionally challenging cases with surface curvature and flow separation. However, this improved anisotropy tensor does not, in general, yield improved mean-velocity and pressure field predictions in comparison with the best-performing LEVM.

physics.flu-dyn↗