Enhancing cryogenic electron microscopy (cryo-EM) 3D density maps at intermediate resolution (4-8 {\AA}) is crucial in protein structure determination. Recent advances in deep learning have led to the development of automated approaches for enhancing experimental cryo-EM density maps. Yet, these methods are not optimized for intermediate-resolution maps and rely on map density features alone. To address this, we propose CryoSAMU, a novel method designed to enhance 3D cryo-EM density maps of protein structures using structure-aware multimodal U-Nets and trained on curated intermediate-resolution density maps. We comprehensively evaluate CryoSAMU across various metrics and demonstrate its competitive performance compared to state-of-the-art methods. Notably, CryoSAMU achieves significantly faster processing speed, showing promise for future practical applications. Our code is available at https://github.com/chenwei-zhang/CryoSAMU.

In this manuscript, we consider the problem of learning a flow or diffusion-based generative model parametrized by a two-layer auto-encoder, trained with online stochastic gradient descent, on a high-dimensional target density with an underlying low-dimensional manifold structure. We derive a tight asymptotic characterization of low-dimensional projections of the distribution of samples generated by the learned model, ascertaining in particular its dependence on the number of training samples. Building on this analysis, we discuss how mode collapse can arise, and lead to model collapse when the generative model is re-trained on generated synthetic data.

A convolutional autoencoder is trained using a database of airfoil aerodynamic simulations and assessed in terms of overall accuracy and interpretability. The goal is to predict the stall and to investigate the ability of the autoencoder to distinguish between the linear and non-linear response of the airfoil pressure distribution to changes in the angle of attack. After a sensitivity analysis on the learning infrastructure, we investigate the latent space identified by the autoencoder targeting extreme compression rates, i.e. very low-dimensional reconstructions. We also propose a strategy to use the decoder to generate new synthetic airfoil geometries and aerodynamic solutions by interpolation and extrapolation in the latent representation learned by the autoencoder.

This tutorial explains how to build confidence regions (the 2D version of a confidence interval) using as little statistical theory as possible. I also avoid the traditional terminology and notation such as α, Z1-α, critical value, confidence level, significance level and so on. These can be confusing to beginners and professionals alike. Instead, I use simulations and two keywords only: confidence region, and confidence level. The purpose is to explain the concept using a framework that will appeal to machine learning professionals, software engineers and non-statisticians.

Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known as experimental design, that is, how to select the input settings where the computer simulator is run and the corresponding response is collected. Extra care should be taken in the selection process because computer simulators can be computationally expensive to run. The selection shall acknowledge and achieve the goal of the analysis. This article focuses on the goal of producing more accurate prediction which is important for risk assessment and decision making. We propose two new methods of design approaches that sequentially select input settings to achieve this goal. The approaches make novel applications of simultaneous and sequential contour estimations. Numerical examples are employed to demonstrate the effectiveness of the proposed approaches.