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Many real-world applications require artificial agents to compete and coordinate with other agents in complex environments. As a stepping stone to this goal, the domain of StarCraft has emerged as an important challenge for artificial intelligence research, owing to its iconic and enduring status among the most difficult professional esports and its relevance to the real world in terms of its raw complexity and multi-agent challenges. Over the course of a decade and numerous competitions 1 – 3 , the strongest agents have simplified important aspects of the game, utilized superhuman capabilities, or employed hand-crafted sub-systems 4 . Despite these advantages, no previous agent has come close to matching the overall skill of top StarCraft players. We chose to address the challenge of StarCraft using general-purpose learning methods that are in principle applicable to other complex domains: a multi-agent reinforcement learning algorithm that uses data from both human and agent games within a diverse league of continually adapting strategies and counter-strategies, each represented by deep neural networks 5 , 6 . We evaluated our agent, AlphaStar, in the full game of StarCraft II, through a series of online games against human players. AlphaStar was rated at Grandmaster level for all three StarCraft races and above 99.8% of officially ranked human players. AlphaStar uses a multi-agent reinforcement learning algorithm and has reached Grandmaster level, ranking among the top 0.2% of human players for the real-time strategy game StarCraft II.

Mechanics-related tasks often present unique challenges in achieving accurate geometric and physical representations, particularly for non-uniform structures. Graph neural networks (GNNs) have emerged as a promising tool to tackle these challenges by adeptly learning from graph data with irregular underlying structures. Consequently, recent years have witnessed a surge in complex mechanics-related applications inspired by the advancements of GNNs. Despite this process, there is a notable absence of a systematic review addressing the recent advancement of GNNs in solving mechanics-related tasks. To bridge this gap, this review article aims to provide an in-depth overview of the GNN applications in mechanics-related domains while identifying key challenges and outlining potential future research directions. In this review article, we begin by introducing the fundamental algorithms of GNNs that are widely employed in mechanics-related applications. We provide a concise explanation of their underlying principles to establish a solid understanding that will serve as a basis for exploring the applications of GNNs in mechanics-related domains. The scope of this paper is intended to cover the categorisation of literature into solid mechanics, fluid mechanics, and interdisciplinary mechanics-related domains, providing a comprehensive summary of graph representation methodologies, GNN architectures, and further discussions in their respective subdomains. Additionally, open data and source codes relevant to these applications are summarised for the convenience of future researchers. This article promotes an interdisciplinary integration of GNNs and mechanics and provides a guide for researchers interested in applying GNNs to solve complex mechanics-related tasks.

The development of lightweight robust structures for battery box is critical for enhancing the performance and energy efficiency of electric vehicles. Hot stamping technology is widely used to form these geometries from high strength-to-weight materials. Recent efforts have leveraged surrogate models to predict material deformation behaviours, offering critical insights into the design of component geometries. However, most surrogate models rely on image-based data representations, which faces challenges in feature representation and permutation invariance. To address these challenges, this study introduces a Recurrent U Net-based Graph Neural Network (RUGNN) surrogate model. The RUGNN model is designed to make spatial-temporal prediction of material deformation under varying contact conditions imposed by different forming tool geometries. This model enables rapid and accurate predictions of spatial-temporal deformation fields under hot stamping conditions. It allows designers to quickly evaluate the effects of forming tools geometry on blank material deformation behaviour and optimise designs during early-stage exploration. Training is conducted on a diverse dataset of deep-drawn corner geometries, which serve as a typical demonstrator in battery box design. The network predictions closely match the ground truth from FE simulations. The RUGNN framework supports early-stage tool design explorations and enables efficient evaluation of complex geometries.

Wheat is of high importance for a healthy and sustainable diet for the growing world population, partly due to its high mineral content. However, several minerals are bound in a phytate complex in the grain and unavailable to humans. We performed a series of trials to compare the contents of minerals and phytic acid as well as phytase activity in several varieties from alternative wheat species spelt, emmer and einkorn with common wheat. Additionally, we investigated the potential of recent popular bread making recipes in German bakeries to reduce phytic acid content, and thus increase mineral bioavailability in bread. For all studied ingredients, we found considerable variance both between varieties within a species and across wheat species. For example, whole grain flours, particularly from emmer and einkorn, appear to have higher mineral content than common wheat, but also a higher phytic acid content with similar phytase activity. Bread making recipes had a greater effect on phytic acid content in the final bread than the choice of species for whole grain flour production. Recipes with long yeast proofing or sourdough and the use of whole grain rye flour in a mixed wheat bread minimized the phytic acid content in the bread. Consequently, optimizing food to better nourish a growing world requires close collaboration between research organizations and practical stakeholders ensuring a streamlined sustainable process from farm to fork.

Due to the large heterogeneity in the hydraulic properties of natural soils, estimation of field-scale hydraulic parameters is difficult. Past research revealed that data from accurate but small-scale laboratory measurements could hardly ever be transferred to the field scale. In this study, we explore an alternative approach where apparent hydraulic properties of a layered soil profile are directly estimated from hydraulic inverse modelling of a time series of in situ measured soil water contents obtained from time domain reflectometry. The data covered a one-year period with both wet and dry soil conditions. For the time period used for inversion, the model is able to reproduce the general evolution of water content in the different soil layers reasonably well. However, distinct drying and wetting events could not be reproduced in detail which we explain by the complicated natural processes that are not fully represented in the rather simple model. The study emphasises the importance of a correct average representation of the soil-atmosphere interaction.

Mechanics-related problems often present unique challenges in achieving accurate geometric and physical representations, particularly for non-uniform structures. Graph neural networks (GNNs) have emerged as a promising tool to tackle these challenges by adeptly learning from graph data with irregular underlying structures. Consequently, recent years have witnessed a surge in complex mechanics-related applications inspired by the advancements of GNNs. Despite this process, there is a notable absence of a systematic review addressing the recent advancement of GNNs in solving mechanics-related problems. To bridge this gap, this review article aims to provide an in-depth overview of the GNN applications in mechanics-related domains while identifying key challenges and outlining potential future research directions. In this review article, we begin by introducing the fundamental algorithms of GNNs that are widely employed in mechanics-related applications. We provide a concise explanation of their underlying principles to establish a solid understanding that will serve as a basis for exploring the applications of GNNs in mechanics-related domains. The scope of this paper is intended to cover the categorisation of literature into solid mechanics, fluid mechanics, and interdisciplinary mechanics-related domains, providing a comprehensive summary of graph representation methodologies, GNN architectures, and further discussions in their respective subdomains. Additionally, open data and source codes relevant to these applications are summarised for the convenience of future researchers. This article promotes an interdisciplinary integration of GNNs and mechanics and provides a guide for researchers interested in applying GNNs to solve complex mechanics-related problems.

In recent years, there has been a growing interest in using machine learning to overcome the high cost of numerical simulation, with some learned models achieving impressive speed-ups over classical solvers whilst maintaining accuracy. However, these methods are usually tested at low-resolution settings, and it remains to be seen whether they can scale to the costly high-resolution simulations that we ultimately want to tackle. In this work, we propose two complementary approaches to improve the framework from MeshGraphNets, which demonstrated accurate predictions in a broad range of physical systems. MeshGraphNets relies on a message passing graph neural network to propagate information, and this structure becomes a limiting factor for high-resolution simulations, as equally distant points in space become further apart in graph space. First, we demonstrate that it is possible to learn accurate surrogate dynamics of a high-resolution system on a much coarser mesh, both removing the message passing bottleneck and improving performance; and second, we introduce a hierarchical approach (MultiScale MeshGraphNets) which passes messages on two different resolutions (fine and coarse), significantly improving the accuracy of MeshGraphNets while requiring less computational resources.

Simulating large scenes with many rigid objects is crucial for a variety of applications, such as robotics, engineering, film and video games. Rigid interactions are notoriously hard to model: small changes to the initial state or the simulation parameters can lead to large changes in the final state. Recently, learned simulators based on graph networks (GNNs) were developed as an alternative to hand-designed simulators like MuJoCo and PyBullet. They are able to accurately capture dynamics of real objects directly from real-world observations. However, current state-of-the-art learned simulators operate on meshes and scale poorly to scenes with many objects or detailed shapes. Here we present SDF-Sim, the first learned rigid-body simulator designed for scale. We use learned signed-distance functions (SDFs) to represent the object shapes and to speed up distance computation. We design the simulator to leverage SDFs and avoid the fundamental bottleneck of the previous simulators associated with collision detection. For the first time in literature, we demonstrate that we can scale the GNN-based simulators to scenes with hundreds of objects and up to 1.1 million nodes, where mesh-based approaches run out of memory. Finally, we show that SDF-Sim can be applied to real world scenes by extracting SDFs from multi-view images.

Accurately simulating real world object dynamics is essential for various applications such as robotics, engineering, graphics, and design. To better capture complex real dynamics such as contact and friction, learned simulators based on graph networks have recently shown great promise. However, applying these learned simulators to real scenes comes with two major challenges: first, scaling learned simulators to handle the complexity of real world scenes which can involve hundreds of objects each with complicated 3D shapes, and second, handling inputs from perception rather than 3D state information. Here we introduce a method which substantially reduces the memory required to run graph-based learned simulators. Based on this memory-efficient simulation model, we then present a perceptual interface in the form of editable NeRFs which can convert real-world scenes into a structured representation that can be processed by graph network simulator. We show that our method uses substantially less memory than previous graph-based simulators while retaining their accuracy, and that the simulators learned in synthetic environments can be applied to real world scenes captured from multiple camera angles. This paves the way for expanding the application of learned simulators to settings where only perceptual information is available at inference time.

Theory suggests that subjective well-being is affected by income comparisons and adaptation to income. Empirical tests of the effects often rely on self-constructed measures from survey data. This paper shows that results can be highly sensitive to simple parameter changes. Using large-scale panel data from Germany and the UK, I report cases where plausible variations in the underlying income type substantially affect tests of the relationship between life satisfaction, income rank, reference income, and income adaptation. Models simultaneously controlling for income and income rank as well as models with a number of income lags are prone to imperfect multicollinearity with consequences for the precision and robustness of estimates. When testing relative-income effects, researchers should be aware that reference income constructed as average of a rather arbitrarily defined reference group and reference income predicted from Mincer-type earnings equations are two approaches that can produce inconsistent results, and that are probably not as reliable and valid as previously assumed. The analysis underlines the importance of robustness checks and regression diagnostics, two routines that are often not carried out diligently in empirical research.