Which Training Methods for GANs do actually Converge?

Recent work has shown local convergence of GAN training for absolutely continuous data and generator distributions. In this paper, we show that the requirement of absolute continuity is necessary: we describe a simple yet prototypical counterexample showing that in the more realistic case of distributions that are not absolutely continuous, unregularized GAN training is not always convergent. Furthermore, we discuss regularization strategies that were recently proposed to stabilize GAN training. Our analysis shows that GAN training with instance noise or zero-centered gradient penalties converges. On the other hand, we show that Wasserstein-GANs and WGAN-GP with a finite number of discriminator updates per generator update do not always converge to the equilibrium point. We discuss these results, leading us to a new explanation for the stability problems of GAN training. Based on our analysis, we extend our convergence results to more general GANs and prove local convergence for simplified gradient penalties even if the generator and data distribution lie on lower dimensional manifolds. We find these penalties to work well in practice and use them to learn high-resolution generative image models for a variety of datasets with little hyperparameter tuning.Comment: conferenc

Automated Driving on a Skid Road with a Forwarder in a CTL Logging Process

In a fully mechanized Cut-to-Length (CTL) logging process, a harvester fells the trees and cuts them into logs of specific length according to the log quality. In the subsequent process step, a forwarder loads the logs and moves them from the logging area to a forest road. This step shows a huge potential towards automation. Within this paper, a method is presented for driving a forwarder automated on a skid road based on environmental recognition, avoiding the disadvantages of gps-based systems and their lacking accuracy under tree canopy. The presented method exploits the process flow of a CTL process, as a Lidar is mounted on the harvester, which delivers a highly accurate point cloud of the environment and works well regardless of the lighting conditions. Applying the SLAM-algorithm ‘Google Cartographer’ on the collected point cloud data of the 3D-LIDAR from the Harvester creates a map, on which an offline path planning is performed. This map results firstly in a 2D occupancy grid map, showing which areas contains objects and which areas are free space. The data in the map is further processed by identifying trees using a clustering algorithm on the object points. After receiving such a simplified map, the subsequent path planning consists of two steps due to the articulated steering of the forestry machine. In the first step, a guiding path for the skid road is created by using gradient descent after creating an artificial potential field with a high potential for areas containing trees. In the second step, this path is recalculated with a simplified kinematics model of the vehicle, avoiding collisions of the forwarder with the trees adjacent to the skid road. Furthermore, the calculated path contains the steering and heading angles of the vehicle. Based on this information, the necessary steering angle of a vehicle on the map can be calculated online and sent to the machine control. The presented method was proven simulation-based with measurement data recorded at real logging sites during thinning and will be tested under real working conditions for an 11-ton forwarder in near future. Thereby, a stump detection based on a Convolutional Neural Network resulting in an online obstacle avoidance system will be implemented by mounting an additional depth camera on the Forwarder

Asynchronous Discrete Event Schemes for PDEs

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations are introduced, which is based on the principle of allowing quanta of mass to pass through faces of a Cartesian finite volume grid. The timescales of these events are linked to the flux on the the face, and the schemes are self-adaptive, local in time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate results where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased

Channeling: a new class of dissolution in complex porous media

The current conceptual model of mineral dissolution in porous media is comprised of three dissolution patterns (wormhole, compact, and uniform) - or regimes - that develop depending on the relative dominance of flow, diffusion, and reaction rate. Here, we examine the evolution of pore structure during acid injection using numerical simulations on two porous media structures of increasing complexity. We examine the boundaries between regimes and characterise the existence of a forth regime called channeling, where already existing fast flow pathways are preferentially widened by dissolution. Channeling occurs in cases where the distribution in pore throat size results in orders of magnitude differences in flow rate for different flow pathways. This focusing of dissolution along only dominant flow paths induces an immediate, large change in permeability with a comparatively small change in porosity, resulting in a porosity-permeability relationship unlike any that has been previously seen. This work demonstrates that our current conceptual model of dissolution regimes must be modified to include channeling for accurate predictions of dissolution in applications such as geologic carbon storage and geothermal energy production