Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Y et the optimal construction of these methods requires tedious analysis and is often available only in simplified, structured-grid settings, limiting their use for more complex problems.

Water from Air could produce enough daily water for a family of four.

Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Y et the optimal construction of these methods requires tedious analysis and is often available only in simplified, structured-grid settings, limiting their use for more complex problems.

We present the approaches and contributions of the winning team NimbRo@Home at the RoboCup@Home 2024 competition in the Open Platform League held in Eindhoven, NL. Further, we describe our hardware setup and give an overview of the results for the task stages and the final demonstration. For this year's competition, we put a special emphasis on open-vocabulary object segmentation and grasping approaches that overcome the labeling overhead of supervised vision approaches, commonly used in RoboCup@Home. We successfully demonstrated that we can segment and grasp non-labeled objects by text descriptions. Further, we extensively employed LLMs for natural language understanding and task planning. Throughout the competition, our approaches showed robustness and generalization capabilities. A video of our performance can be found online.

This paper presents and evaluates a framework for the coupling of subdomain-local projection-based reduced order models (PROMs) using the Schwarz alternating method following a domain decomposition (DD) of the spatial domain on which a given problem of interest is posed. In this approach, the solution on the full domain is obtained via an iterative process in which a sequence of subdomain-local problems are solved, with information propagating between subdomains through transmission boundary conditions (BCs). We explore several new directions involving the Schwarz alternating method aimed at maximizing the method's efficiency and flexibility, and demonstrate it on three challenging two-dimensional nonlinear hyperbolic problems: the shallow water equations, Burgers' equation, and the compressible Euler equations. We demonstrate that, for a cell-centered finite volume discretization and a non-overlapping DD, it is possible to obtain a stable and accurate coupled model utilizing Dirichlet-Dirichlet (rather than Robin-Robin or alternating Dirichlet-Neumann) transmission BCs on the subdomain boundaries. We additionally explore the impact of boundary sampling when utilizing the Schwarz alternating method to couple subdomain-local hyper-reduced PROMs. Our numerical results suggest that the proposed methodology has the potential to improve PROM accuracy by enabling the spatial localization of these models via domain decomposition, and achieve up to two orders of magnitude speedup over equivalent coupled full order model solutions and moderate speedups over analogous monolithic solutions.

This paper presents and evaluates an approach for coupling together subdomain-local reduced order models (ROMs) constructed via non-intrusive operator inference (OpInf) with each other and with subdomain-local full order models (FOMs), following a domain decomposition of the spatial geometry on which a given partial differential equation (PDE) is posed. Joining subdomain-local models is accomplished using the overlapping Schwarz alternating method, a minimally-intrusive multiscale coupling technique that works by transforming a monolithic problem into a sequence of subdomain-local problems, which communicate through transmission boundary conditions imposed on the subdomain interfaces. After formulating the overlapping Schwarz alternating method for OpInf ROMs, termed OpInf-Schwarz, we evaluate the method's accuracy and efficiency on several test cases involving the heat equation in two spatial dimensions. We demonstrate that the method is capable of coupling together arbitrary combinations of OpInf ROMs and FOMs, and that speed-ups over a monolithic FOM are possible when performing OpInf ROM coupling.

Physics-informed neural networks (PINNs) are appealing data-driven tools for solving and inferring solutions to nonlinear partial differential equations (PDEs). Unlike traditional neural networks (NNs), which train only on solution data, a PINN incorporates a PDE's residual into its loss function and trains to minimize the said residual at a set of collocation points in the solution domain. This paper explores the use of the Schwarz alternating method as a means to couple PINNs with each other and with conventional numerical models (i.e., full order models, or FOMs, obtained via the finite element, finite difference or finite volume methods) following a decomposition of the physical domain. It is well-known that training a PINN can be difficult when the PDE solution has steep gradients. We investigate herein the use of domain decomposition and the Schwarz alternating method as a means to accelerate the PINN training phase. Within this context, we explore different approaches for imposing Dirichlet boundary conditions within each subdomain PINN: weakly through the loss and/or strongly through a solution transformation. As a numerical example, we consider the one-dimensional steady state advection-diffusion equation in the advection-dominated (high Peclet) regime. Our results suggest that the convergence of the Schwarz method is strongly linked to the choice of boundary condition implementation within the PINNs being coupled. Surprisingly, strong enforcement of the Schwarz boundary conditions does not always lead to a faster convergence of the method. While it is not clear from our preliminary study that the PINN-PINN coupling via the Schwarz alternating method accelerates PINN convergence in the advection-dominated regime, it reveals that PINN training can be improved substantially for Peclet numbers as high as 1e6 by performing a PINN-FOM coupling.

This paper presents a retrospective overview of a decade of research in our department towards self-organizing personal knowledge assistants in evolving corporate memories. Our research is typically inspired by real-world problems and often conducted in interdisciplinary collaborations with research and industry partners. We summarize past experiments and results comprising topics like various ways of knowledge graph construction in corporate and personal settings, Managed Forgetting and (Self-organizing) Context Spaces as a novel approach to Personal Information Management (PIM) and knowledge work support. Past results are complemented by an overview of related work and some of our latest findings not published so far. Last, we give an overview of our related industry use cases including a detailed look into CoMem, a Corporate Memory based on our presented research already in productive use and providing challenges for further research. Many contributions are only first steps in new directions with still a lot of untapped potential, especially with regard to further increasing the automation in PIM and knowledge work support.

Scientists from China's Zhejiang University have unveiled a drone swarm capable of navigating through a dense bamboo forest without human guidance. The group of 10 palm-sized drones communicate with one another to stay in formation, sharing data collected by on-board depth-sensing cameras to map their surroundings. This method means that if the path in front of one drone is blocked, it can use information collected by its neighbors to plot a new route. The researchers note that this technique can also be used by the swarm to track a human walking through the same environment. If one drone loses sight of the target, others are able to pick up the trail.

It's the sort of thing that can almost pass for background noise these days: over the past week, a number of publications tentatively declared, based on a UN report from the Libyan civil war, that killer robots may have hunted down humans autonomously for the first time. As one headline put it: "The Age of Autonomous Killer Robots May Already Be Here." As you might guess, it's a hard question to answer. The new coverage has sparked a debate among experts that goes to the heart of our problems confronting the rise of autonomous robots in war. Some said the stories were wrongheaded and sensational, while others suggested there was a nugget of truth to the discussion.