Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes for this task, overtaking classical methods based on fixed molecular kernels. However, they still appear very limited from a theoretical perspective, since regular GNNs cannot distinguish certain types of graphs. In this work we close this gap between theory and practice. We show that GNNs with directed edge embeddings and two-hop message passing are indeed universal approximators for predictions that are invariant to translation, and equivariant to permutation and rotation. We then leverage these insights and multiple structural improvements to propose the geometric message passing neural network (GemNet). We demonstrate the benefits of the proposed changes in multiple ablation studies. GemNet outperforms previous models on the COLL, MD17, and OC20 datasets by 34%, 41%, and 20%, respectively, and performs especially well on the most challenging molecules. Our implementation is available online.

We consider a class of quasi-variational inequalities (QVIs) for adaptive image restoration, where the adaptivity is described via solution-dependent constraint sets. In previous work we studied both theoretical and numerical issues. While we were able to show the existence of solutions for a relatively broad class of problems, we encountered difficulties concerning uniqueness of the solution as well as convergence of existing algorithms for solving QVIs. In particular, it seemed that with increasing image size the growing condition number of the involved differential operator posed severe problems. In the present paper we prove uniqueness for a larger class of problems, particularly independent of the image size. Moreover, we provide a numerical algorithm with proved convergence. Experimental results support our theoretical findings.

A variational approach is presented to the estimation of turbulent fluid flow from particle image sequences in experimental fluid mechanics. The approach comprises two coupled optimizations for adapting size and shape of a Gaussian correlation window at each location and for estimating the flow, respectively. The method copes with a wide range of particle densities and image noise levels without any data-specific parameter tuning. Based on a careful implementation of a multiscale nonlinear optimization technique, we demonstrate robustness of the solution over typical experimental scenarios and highest estimation accuracy for an international benchmark data set (PIV Challenge).

In the above paper (ibid., vol. 21, no. 6, pp. 3053-3065, Jun. 2012), several corrections requested by the authors were omitted. The IEEE regrets the error. On pp. 3058 and 3059, the algorithms were not indented corrected. They are corrected here.

We present an approach to jointly estimating camera motion and dense scene structure in terms of depth maps from monocular image sequences in driver-assistance scenarios. For two consecutive frames of a sequence taken with a single fast moving camera, the approach combines numerical estimation of egomotion on the Euclidean manifold of motion parameters with variational regularization of dense depth map estimation. Embedding this online joint estimator into a recursive framework achieves a pronounced spatio-temporal filtering effect and robustness. We report the evaluation of thousands of images taken from a car moving at speed up to 100 km/h. The results compare favorably with two alternative settings that require more input data: stereo based scene reconstruction and camera motion estimation in batch mode using multiple frames. The employed benchmark dataset is publicly available.

Intelligent Environments are currently implemented with standard WSN technologies using conventional connection-based communications. However, connection-based communications may impede progress towards IE scenarios involving high mobility or massive amounts of sensor nodes. We present a novel approach based on collective transmission for item level tagging using printed organic electronics, which implements robust, collective, approximate read-out of large numbers of simple tags. Our approach uses mechanisms for calculation by simultaneous transmission. We detail the collective transmission approach, discuss its implementation in the organic printed label scenario, and show first results of experiments conducted with our smart label test bed. We conclude with an outlook on the potential of collective transmission, and argue that collective transmission is a fundamental building block for realizing distributed intelligence.

We introduce a linearly weighted variant of the total variation for vector fields in order to formulate regularizers for multi-class labeling problems with non-trivial interclass distances. We characterize the possible distances, show that Euclidean distances can be exactly represented, and review some methods to approximate non-Euclidean distances in order to define novel total variation based regularizers. We show that the convex relaxed problem can be efficiently optimized to a prescribed accuracy with optimality certificates using Nesterov's method, and evaluate and compare our approach on several synthetical and real-world examples.