Carola Bibiane Schönlieb

Niccolò Grillo, James Rowbottom, Pietro Liò et al.

Adaptive mesh refinement is central to the efficient solution of partial differential equations (PDEs) via the finite element method (FEM). Classical $r$-adaptivity optimizes vertex positions but requires solving expensive auxiliary PDEs such as the Monge-Ampère equation, while classical $h$-adaptivity modifies topology through element subdivision but suffers from expensive error indicator computation and is constrained by isotropic refinement patterns that impose accuracy ceilings. Combined $hr$-adaptive techniques naturally outperform single-modality approaches, yet inherit both computational bottlenecks and the restricted cost-accuracy trade-off. Emerging machine learning methods for adaptive mesh refinement seek to overcome these limitations, but existing approaches address $h$-adaptivity or $r$-adaptivity in isolation. We present HypeR, a deep reinforcement learning framework that jointly optimizes mesh relocation and refinement. HypeR casts the joint adaptation problem using tools from hypergraph neural networks and multi-agent reinforcement learning. Refinement is formulated as a heterogeneous multi-agent Markov decision process (MDP) where element agents decide discrete refinement actions, while relocation follows an anisotropic diffusion-based policy on vertex agents with provable prevention of mesh tangling. The reward function combines local and global error reduction to promote general accuracy. Across benchmark PDEs, HypeR reduces approximation error by up to 6--10$\times$ versus state-of-art $h$-adaptive baselines at comparable element counts, breaking through the uniform refinement accuracy ceiling that constrains subdivision-only methods. The framework produces meshes with improved shape metrics and alignment to solution anisotropy, demonstrating that jointly learned $hr$-adaptivity strategies can substantially enhance the capabilities of automated mesh generation.

Ziruo Cai, Junqi Tang, Subhadip Mukherjee et al.

Bayesian methods for solving inverse problems are a powerful alternative to classical methods since the Bayesian approach offers the ability to quantify the uncertainty in the solution. In recent years, data-driven techniques for solving inverse problems have also been remarkably successful, due to their superior representation ability. In this work, we incorporate data-based models into a class of Langevin-based sampling algorithms for Bayesian inference in imaging inverse problems. In particular, we introduce NF-ULA (Normalizing Flow-based Unadjusted Langevin algorithm), which involves learning a normalizing flow (NF) as the image prior. We use NF to learn the prior because a tractable closed-form expression for the log prior enables the differentiation of it using autograd libraries. Our algorithm only requires a normalizing flow-based generative network, which can be pre-trained independently of the considered inverse problem and the forward operator. We perform theoretical analysis by investigating the well-posedness and non-asymptotic convergence of the resulting NF-ULA algorithm. The efficacy of the proposed NF-ULA algorithm is demonstrated in various image restoration problems such as image deblurring, image inpainting, and limited-angle X-ray computed tomography (CT) reconstruction. NF-ULA is found to perform better than competing methods for severely ill-posed inverse problems.

Kyriaki, Kokka, Rahul Goel et al.

Transportation influence health by shaping exposure to physical activity, air pollution and injury risk. Comparative data on cycling and motorcycling behaviours is scarce, particularly at a global scale. Street view imagery, such as Google Street View (GSV), combined with computer vision, is a valuable resource for efficiently capturing travel behaviour data. This study demonstrates a novel approach using deep learning on street view images to estimate cycling and motorcycling levels across diverse cities worldwide. We utilized data from 185 global cities. The data on mode shares of cycling and motorcycling estimated using travel surveys or censuses. We used GSV images to detect cycles and motorcycles in sampled locations, using 8000 images per city. The YOLOv4 model, fine-tuned using images from six cities, achieved a mean average precision of 89% for detecting cycles and motorcycles. A global prediction model was developed using beta regression with city-level mode shares as outcome, with log transformed explanatory variables of counts of GSV-detected images with cycles and motorcycles, while controlling for population density. We found strong correlations between GSV motorcycle counts and motorcycle mode share (0.78) and moderate correlations between GSV cycle counts and cycling mode share (0.51). Beta regression models predicted mode shares with $R^2$ values of 0.614 for cycling and 0.612 for motorcycling, achieving median absolute errors (MDAE) of 1.3% and 1.4%, respectively. Scatterplots demonstrated consistent prediction accuracy, though cities like Utrecht and Cali were outliers. The model was applied to 60 cities globally for which we didn't have recent mode share data. We provided estimates for some cities in the Middle East, Latin America and East Asia. With computer vision, GSV images capture travel modes and activity, providing insights alongside traditional data sources.

Georgios Batzolis, Marcello Carioni, Christian Etmann et al.

We introduce CAFLOW, a new diverse image-to-image translation model that simultaneously leverages the power of auto-regressive modeling and the modeling efficiency of conditional normalizing flows. We transform the conditioning image into a sequence of latent encodings using a multi-scale normalizing flow and repeat the process for the conditioned image. We model the conditional distribution of the latent encodings by modeling the auto-regressive distributions with an efficient multi-scale normalizing flow, where each conditioning factor affects image synthesis at its respective resolution scale. Our proposed framework performs well on a range of image-to-image translation tasks. It outperforms former designs of conditional flows because of its expressive auto-regressive structure.

Philip Sellars, Angelica Aviles-Rivero, Carola Bibiane Schönlieb

Given the potential difficulties in obtaining large quantities of labelled data, many works have explored the use of deep semi-supervised learning, which uses both labelled and unlabelled data to train a neural network architecture. The vast majority of SSL approaches focus on implementing the low-density separation assumption or consistency assumption, the idea that decision boundaries should lie in low density regions. However, they have implemented this assumption by making local changes to the decision boundary at each data point, ignoring the global structure of the data. In this work, we explore an alternative approach using the global information present in the clustered data to update our decision boundaries. We propose a novel framework, CycleCluster, for deep semi-supervised classification. Our core optimisation is driven by a new clustering based regularisation along with a graph based pseudo-labels and a shared deep network. Demonstrating that direct implementation of the cluster assumption is a viable alternative to the popular consistency based regularisation. We demonstrate the predictive capability of our technique through a careful set of numerical results.