Nonnegative-constrained networks have a "+" in the name of the

Critical heat flux is a key quantity in boiling system modeling due to its impact on heat transfer and component temperature and performance. This study investigates the development and validation of an uncertainty-aware hybrid modeling approach that combines machine learning with physics-based models in the prediction of critical heat flux in nuclear reactors for cases of dryout. Two empirical correlations, Biasi and Bowring, were employed with three machine learning uncertainty quantification techniques: deep neural network ensembles, Bayesian neural networks, and deep Gaussian processes. A pure machine learning model without a base model served as a baseline for comparison. This study examines the performance and uncertainty of the models under both plentiful and limited training data scenarios using parity plots, uncertainty distributions, and calibration curves. The results indicate that the Biasi hybrid deep neural network ensemble achieved the most favorable performance (with a mean absolute relative error of 1.846% and stable uncertainty estimates), particularly in the plentiful data scenario. The Bayesian neural network models showed slightly higher error and uncertainty but superior calibration. By contrast, deep Gaussian process models underperformed by most metrics. All hybrid models outperformed pure machine learning configurations, demonstrating resistance against data scarcity.

Generative Adversarial Networks (GANs) are powerful tools for creating new content, but they face challenges such as sensitivity to starting conditions and mode collapse. To address these issues, we propose a deep generative model that utilizes the Gromov-Monge embedding (GME). It helps identify the low-dimensional structure of the underlying measure of the data and then maps it, while preserving its geometry, into a measure in a low-dimensional latent space, which is then optimally transported to the reference measure. We guarantee the preservation of the underlying geometry by the GME and $c$-cyclical monotonicity of the generative map, where $c$ is an intrinsic embedding cost employed by the GME. The latter property is a first step in guaranteeing better robustness to initialization of parameters and mode collapse. Numerical experiments demonstrate the effectiveness of our approach in generating high-quality images, avoiding mode collapse, and exhibiting robustness to different starting conditions.