Multi-Grid Graph Neural Networks with Self-Attention for Computational Mechanics

Advancement in finite element methods have become essential in various disciplines, and in particular for Computational Fluid Dynamics (CFD), driving research efforts for improved precision and efficiency. While Convolutional Neural Networks (CNNs) have found success in CFD by mapping meshes into images, recent attention has turned to leveraging Graph Neural Networks (GNNs) for direct mesh processing. This paper introduces a novel model merging Self-Attention with Message Passing in GNNs, achieving a 15\% reduction in RMSE on the well known flow past a cylinder benchmark. Furthermore, a dynamic mesh pruning technique based on Self-Attention is proposed, that leads to a robust GNN-based multigrid approach, also reducing RMSE by 15\%. Additionally, a new self-supervised training method based on BERT is presented, resulting in a 25\% RMSE reduction. The paper includes an ablation study and outperforms state-of-the-art models on several challenging datasets, promising advancements similar to those recently achieved in natural language and image processing. Finally, the paper introduces a dataset with meshes larger than existing ones by at least an order of magnitude. Code and Datasets will be released at https://github.com/DonsetPG/multigrid-gnn.

Semi-Supervised Learning for Bilingual Lexicon Induction

We consider the problem of aligning two sets of continuous word representations, corresponding to languages, to a common space in order to infer a bilingual lexicon. It was recently shown that it is possible to infer such lexicon, without using any parallel data, by aligning word embeddings trained on monolingual data. Such line of work is called unsupervised bilingual induction. By wondering whether it was possible to gain experience in the progressive learning of several languages, we asked ourselves to what extent we could integrate the knowledge of a given set of languages when learning a new one, without having parallel data for the latter. In other words, while keeping the core problem of unsupervised learning in the latest step, we allowed the access to other corpora of idioms, hence the name semi-supervised. This led us to propose a novel formulation, considering the lexicon induction as a ranking problem for which we used recent tools of this machine learning field. Our experiments on standard benchmarks, inferring dictionary from English to more than 20 languages, show that our approach consistently outperforms existing state of the art benchmark. In addition, we deduce from this new scenario several relevant conclusions allowing a better understanding of the alignment phenomenon.

Evaluating Soccer Player: from Live Camera to Deep Reinforcement Learning

Scientifically evaluating soccer players represents a challenging Machine Learning problem. Unfortunately, most existing answers have very opaque algorithm training procedures; relevant data are scarcely accessible and almost impossible to generate. In this paper, we will introduce a two-part solution: an open-source Player Tracking model and a new approach to evaluate these players based solely on Deep Reinforcement Learning, without human data training nor guidance. Our tracking model was trained in a supervised fashion on datasets we will also release, and our Evaluation Model relies only on simulations of virtual soccer games. Combining those two architectures allows one to evaluate Soccer Players directly from a live camera without large datasets constraints. We term our new approach Expected Discounted Goal (EDG), as it represents the number of goals a team can score or concede from a particular state. This approach leads to more meaningful results than the existing ones that are based on real-world data, and could easily be extended to other sports.

A review on Deep Reinforcement Learning for Fluid Mechanics

Deep reinforcement learning (DRL) has recently been adopted in a wide range of physics and engineering domains for its ability to solve decision-making problems that were previously out of reach due to a combination of non-linearity and high dimensionality. In the last few years, it has spread in the field of computational mechanics, and particularly in fluid dynamics, with recent applications in flow control and shape optimization. In this work, we conduct a detailed review of existing DRL applications to fluid mechanics problems. In addition, we present recent results that further illustrate the potential of DRL in Fluid Mechanics. The coupling methods used in each case are covered, detailing their advantages and limitations. Our review also focuses on the comparison with classical methods for optimal control and optimization. Finally, several test cases are described that illustrate recent progress made in this field. The goal of this publication is to provide an understanding of DRL capabilities along with state-of-the-art applications in fluid dynamics to researchers wishing to address new problems with these methods.