Stick-Breaking Mixture Normalizing Flows with Component-Wise Tail Adaptation for Variational Inference

Normalizing flows with a Gaussian base provide a computationally efficient way to approximate posterior distributions in Bayesian inference, but they often struggle to capture complex posteriors with multimodality and heavy tails. We propose a stick-breaking mixture base with component-wise tail adaptation (StiCTAF) for posterior approximation. The method first learns a flexible mixture base to mitigate the mode-seeking bias of reverse KL divergence through a weighted average of component-wise ELBOs. It then estimates local tail indices of unnormalized densities and finally refines each mixture component using a shared backbone combined with component-specific tail transforms calibrated by the estimated indices. This design enables accurate mode coverage and anisotropic tail modeling while retaining exact density evaluation and stable optimization. Experiments on synthetic posteriors demonstrate improved tail recovery and better coverage of multiple modes compared to benchmark models. We also present a real-data analysis illustrating the practical benefits of our approach for posterior inference.

Fast and accurate learned multiresolution dynamical downscaling for precipitation

This study develops a neural network-based approach for emulating high-resolution modeled precipitation data with comparable statistical properties but at greatly reduced computational cost. The key idea is to use combination of low- and high- resolution simulations to train a neural network to map from the former to the latter. Specifically, we define two types of CNNs, one that stacks variables directly and one that encodes each variable before stacking, and we train each CNN type both with a conventional loss function, such as mean square error (MSE), and with a conditional generative adversarial network (CGAN), for a total of four CNN variants. We compare the four new CNN-derived high-resolution precipitation results with precipitation generated from original high resolution simulations, a bilinear interpolater and the state-of-the-art CNN-based super-resolution (SR) technique. Results show that the SR technique produces results similar to those of the bilinear interpolator with smoother spatial and temporal distributions and smaller data variabilities and extremes than the original high resolution simulations. While the new CNNs trained by MSE generate better results over some regions than the interpolator and SR technique do, their predictions are still not as close as the original high resolution simulations. The CNNs trained by CGAN generate more realistic and physically reasonable results, better capturing not only data variability in time and space but also extremes such as intense and long-lasting storms. The new proposed CNN-based downscaling approach can downscale precipitation from 50~km to 12~km in 14~min for 30~years once the network is trained (training takes 4~hours using 1~GPU), while the conventional dynamical downscaling would take 1~month using 600 CPU cores to generate simulations at the resolution of 12~km over contiguous United States.

Computer Model Calibration with Time Series Data using Deep Learning and Quantile Regression

Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiment is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer input parameters by combining information from model runs and observational data. The existing standard calibration framework suffers from inferential issues when the model output and observational data are high-dimensional dependent data such as large time series due to the difficulty in building an emulator and the non-identifiability between effects from input parameters and data-model discrepancy. To overcome these challenges we propose a new calibration framework based on a deep neural network (DNN) with long-short term memory layers that directly emulates the inverse relationship between the model output and input parameters. Adopting the 'learning with noise' idea we train our DNN model to filter out the effects from data model discrepancy on input parameter inference. We also formulate a new way to construct interval predictions for DNN using quantile regression to quantify the uncertainty in input parameter estimates. Through a simulation study and real data application with WRF-hydro model we show that our approach can yield accurate point estimates and well calibrated interval estimates for input parameters.