arXiv subjects

Sanjan C. Muchandimath

Publications and source records attributed to Sanjan C. Muchandimath.

3 recordsLinked to original sources

arXiv2026

Synchronized step multilevel Markov chain Monte Carlo

We propose SYNCE (synchronized step correlation enhancement), a new algorithm for coupling Markov chains within multilevel Markov chain Monte Carlo (ML-MCMC) estimators. We apply this algorithm to solve Bayesian inverse problems using multiple model fidelities. SYNCE is inspired by the concept of common random number coupling in Markov chain Monte Carlo sampling. Unlike state-of-the-art methods that rely on the overlap of level-wise posteriors, our approach enables effective coupling even when posteriors differ substantially. This overlap-independence generates significantly higher correlation between samples at different fidelity levels, improving variance reduction and computational efficiency in the ML-MCMC estimator. We prove that SYNCE admits a unique invariant probability measure and demonstrate that the coupled chains converge to this measure faster than existing overlap-dependent methods, particularly when models are dissimilar. Numerical experiments validate that SYNCE consistently outperforms current coupling strategies in terms of computational efficiency and scalability across varying model fidelities and problem dimensions.

stat.AP↗

arXiv2025

Accelerating Bayesian Inference via Multi-Fidelity Transport Map Coupling

Mathematical models in computational physics contain uncertain parameters that impact prediction accuracy. In turbulence modeling, this challenge is especially significant: Reynolds averaged Navier-Stokes (RANS) models, such as the Spalart-Allmaras (SA) model, are widely used for their speed and robustness but often suffer from inaccuracies and associated uncertainties due to imperfect model parameters. Reliable quantification of these uncertainties is becoming increasingly important in aircraft certification by analysis, where predictive credibility is critical. Bayesian inference provides a framework to estimate these parameters and quantify output uncertainty, but traditional methods are prohibitively expensive, especially when relying on high-fidelity simulations. We address the challenge of expensive Bayesian parameter estimation by developing a multi-fidelity framework that combines Markov chain Monte Carlo (MCMC) methods with multilevel Monte Carlo (MLMC) estimators to efficiently solve inverse problems. The MLMC approach requires correlated samples across different fidelity levels, achieved through a novel transport map-based coupling algorithm. We demonstrate a 50% reduction in inference cost compared to traditional single-fidelity methods on the challenging NACA0012 airfoil at high angles of attack near stall, while delivering realistic uncertainty bounds for model predictions in complex separated flow regimes. These results demonstrate that multi-fidelity approaches significantly improve turbulence parameter calibration, paving the way for more accurate and efficient aircraft certification by analysis.

stat.ME↗

arXiv2020

Hydrodynamic Bulge Testing: Materials Characterization without Measuring Deformation

Characterizing the elastic properties of soft materials through bulge testing relies on accurate measurement of deformation, which is experimentally challenging. To avoid measuring deformation, we propose a hydrodynamic bulge test for characterizing the material properties of thick, pre-stressed elastic sheets via their fluid--structure interaction with a steady viscous fluid flow. Specifically, the hydrodynamic bulge test relies on a pressure drop measurement across a rectangular microchannel with a deformable top wall. We develop a mathematical model using first-order shear-deformation theory of plates with stretching, and the lubrication approximation for Newtonian fluid flow. Specifically, a relationship is derived between the imposed flow rate and the total pressure drop. Then, this relationship is inverted numerically to yield estimates of the Young's modulus (given the Poisson ratio), if the pressure drop is measured (given the steady flow rate). Direct numerical simulations of two-way-coupled fluid--structure interaction are carried out in ANSYS to determine the cross-sectional membrane deformation and the hydrodynamic pressure distribution. Taking the simulations as ``ground truth,'' a hydrodynamic bulge test is performed using the simulation data to ascertain the accuracy and validity of the proposed methodology for estimating material properties. An error propagation analysis is performed via Monte Carlo simulation to characterize the susceptibility of the hydrodynamic bulge test estimates to noise. We find that, while a hydrodynamic bulge test is less accurate in characterizing material properties, it is less susceptible to noise, in the input (measured) variable, than a hydrostatic bulge test.

cond-mat.soft↗