Transfer Learning for Multiscale Analysis: Delamination of Carbon-Reinforced Composite Material Exploration

2026-01-01

STATISTICAL ANALYSIS OF A COMPLEX PLASMA SYSTEM FROM A SMALL NUMBER OF SIMULATIONS

International Journal for Uncertainty Quantification · 2026-01-01

This work aims to enhance the small amount of data obtained from simulations using statistical methods, in order to improve the analysis of the underlying physical properties of plasma behavior, particularly electron density and electron temperature in the boundary region of the tokamak. Electron density and electron temperature are important observables for characterizing plasma behavior in the boundary region of the tokamak, as they influence transport properties and confinement regimes. While the simulations used in this work are fully deterministic, we aim to extract statistical information by interpreting numerical simulations as samples from underlying random fields. This approach allows for the construction of marginal and joint probability density functions (PDFs) that provide physical insight beyond standard deterministic interpretation and capture key structural features of the plasma behavior in the boundary region of the tokamak, including the role of triangularity, the impact of the diffusion coefficient, and the implications for plasma behavior. Numerical simulations are performed with the Gkeyll gyrokinetic code. Despite their resolution, the computational cost limits the number of available simulation data, suggesting a role for advanced analysis techniques capable of extracting meaningful physical insights from a small dataset. To this end, we explore a statistical framework based on probabilistic learning on manifolds (PLoM), a nonparametric method designed for small-sample inference.

Effect of experimental noise on internal damage detection of sealed spent nuclear fuel canisters

Engineering With Computers · 2025-06-27 · 1 citations

Abstract Nuclear fuel assemblies (FA) become high-level radioactive waste known as spent nuclear fuel (SNF) after several years of operation in nuclear reactors. Currently, a considerable portion of SNF is temporarily stored in sealed stainless-steel dry storage canisters. Handling, storage or transportation events (normal operations or accidents) can cause potential damage to the FAs inside the canisters. Damage to FAs inside the canisters needs to be identified for safety purposes during storage or before and after transportation. Due to the difficulty of a visual inspection of the sealed canisters, non-destructive evaluation (NDE) is critical to identify the potential internal damage. In this study, a high-fidelity finite element (FE) model was used to simulate different levels of FA damage. Wasserstein generative adversarial networks (WGAN) were developed to learn and generate noise using data from previously conducted experiments, which was then added to the numerically obtained frequency response functions (FRF) to bridge the gap between experimental and numerical domains. The noisy computational data were analyzed by a multi-task extreme gradient boosting (XGBoost) model to identify the damage level and location. The XGBoost achieved macro-F1 scores of 0.998 and 0.900 for damage detection and localization tasks in the FE dataset and perfect scores of 1.0 for the same in the experimental dataset. The results demonstrate that the machine learning (ML)-aided NDE method was successful in identifying various damage modes within SNF canisters even in the presence of noise levels observed in actual large-scale experiments.

Generative Learning of Densities on Manifolds

ArXiv.org · 2025-03-05

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an Itô stochastic differential equation in the latent space. Additional realizations of the data are generated by lifting the samples back to the ambient space using Double Diffusion Maps, a recently introduced technique typically employed in studying dynamical system reduction; here the focus lies in sampling densities rather than system dynamics. The proposed approaches enable sampling high dimensional data densities restricted to low-dimensional, a priori unknown manifolds. The efficacy of the proposed framework is demonstrated through a benchmark problem and a material with multiscale structure.

Joint probabilistic modelling and sampling from small data via probabilistic learning on manifolds and decoupled multi-probability density evolution method

Probabilistic Engineering Mechanics · 2025-01-01 · 8 citations

Spectral Expansions Based Multi-Fidelity Surrogate Modelling for Flows in Thermochemical Non-Equilibrium

2025-01-03

This research presents a novel methodology for multi-fidelity modelling in coarse-graining models (CGM) to investigate thermo-chemical non-equilibrium effects in hypersonic flows. The focus is on combining abundant solutions from inexpensive yet inaccurate low-fidelity model with sparse set of accurate but expensive mid and high-fidelity model samples. Principal Component Analysis (PCA) is first used to reduce the dimensionality of quantities of interest followed by which a Polynomial Chaos Expansion (PCE) is constructed to map the random input parameters to PCA coefficients. Furthermore, to account for the error introduced by low-fidelity model and insufficient number of samples from mid and high-fidelity models, the PCE coefficients are assumed to be probabilistic whose posterior distributions are obtained by Bayesian inference. The surrogate modelling methodology developed in this work is well suited for high dimensional quantities of interest and strikes a balance between computational cost and accuracy. The multi-fidelity surrogate model is subsequently used for forward propagation of uncertainty in free-stream conditions to obtain probabilistic predictions of the quantities of interest including species mole fractions and translational temperature around a spherical reentry vehicle.

Clustered Projection Pursuit Adaptation (CPPA) for Combustion Chemistry

SSRN Electronic Journal · 2025-01-01

Reliability-Based Design and Certification of Hybrid Composites

2025-01-01

Microstructure characterization in thermal barrier coatings using Sparse Polynomial Chaos Classifiers and Global Sensitivity Analysis

Reliability Engineering & System Safety · 2025-07-30

Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks

Computer Methods in Applied Mechanics and Engineering · 2025-01-04 · 5 citations