Inverse Uncertainty Quantification using the Modular Bayesian Approach based on Gaussian Process, Part 2: Application to TRACE

Inverse Uncertainty Quantification (UQ) is a process to quantify the uncertainties in random input parameters while achieving consistency between code simulations and physical observations. In this paper, we performed inverse UQ using an improved modular Bayesian approach based on Gaussian Process (GP) for TRACE physical model parameters using the BWR Full-size Fine-Mesh Bundle Tests (BFBT) benchmark steady-state void fraction data. The model discrepancy is described with a GP emulator. Numerical tests have demonstrated that such treatment of model discrepancy can avoid over-fitting. Furthermore, we constructed a fast-running and accurate GP emulator to replace TRACE full model during Markov Chain Monte Carlo (MCMC) sampling. The computational cost was demonstrated to be reduced by several orders of magnitude. A sequential approach was also developed for efficient test source allocation (TSA) for inverse UQ and validation. This sequential TSA methodology first selects experimental tests for validation that has a full coverage of the test domain to avoid extrapolation of model discrepancy term when evaluated at input setting of tests for inverse UQ. Then it selects tests that tend to reside in the unfilled zones of the test domain for inverse UQ, so that one can extract the most information for posterior probability distributions of calibration parameters using only a relatively small number of tests. This research addresses the "lack of input uncertainty information" issue for TRACE physical input parameters, which was usually ignored or described using expert opinion or user self-assessment in previous work. The resulting posterior probability distributions of TRACE parameters can be used in future uncertainty, sensitivity and validation studies of TRACE code for nuclear reactor system design and safety analysis

Time Series Synthesis via Multi-scale Patch-based Generation of Wavelet Scalogram

A framework is proposed for the unconditional generation of synthetic time series based on learning from a single sample in low-data regime case. The framework aims at capturing the distribution of patches in wavelet scalogram of time series using single image generative models and producing realistic wavelet coefficients for the generation of synthetic time series. It is demonstrated that the framework is effective with respect to fidelity and diversity for time series with insignificant to no trends. Also, the performance is more promising for generating samples with the same duration (reshuffling) rather than longer ones (retargeting).Comment: 8 pages, 3 figures, 2 table

Physics-Informed Regularization of Deep Neural Networks

This paper presents a novel physics-informed regularization method for training of deep neural networks (DNNs). In particular, we focus on the DNN representation for the response of a physical or biological system, for which a set of governing laws are known. These laws often appear in the form of differential equations, derived from first principles, empirically-validated laws, and/or domain expertise. We propose a DNN training approach that utilizes these known differential equations in addition to the measurement data, by introducing a penalty term to the training loss function to penalize divergence form the governing laws. Through three numerical examples, we will show that the proposed regularization produces surrogates that are physically interpretable with smaller generalization errors, when compared to other common regularization methods

Attention-based Spatial-Temporal Graph Neural ODE for Traffic Prediction

Traffic forecasting is an important issue in intelligent traffic systems (ITS). Graph neural networks (GNNs) are effective deep learning models to capture the complex spatio-temporal dependency of traffic data, achieving ideal prediction performance. In this paper, we propose attention-based graph neural ODE (ASTGODE) that explicitly learns the dynamics of the traffic system, which makes the prediction of our machine learning model more explainable. Our model aggregates traffic patterns of different periods and has satisfactory performance on two real-world traffic data sets. The results show that our model achieves the highest accuracy of the root mean square error metric among all the existing GNN models in our experiments