Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has resulted in opening doors to solving a variety of real-world problems ranging from mathematical finance to stochastic control for industrial applications. Although feasible, these deep learning methods are still constrained by training time and memory. Tackling these shortcomings, Tensor Neural Networks (TNN) demonstrate that they can provide significant parameter savings while attaining the same accuracy as compared to the classical Dense Neural Network (DNN). In addition, we also show how TNN can be trained faster than DNN for the same accuracy. Besides TNN, we also introduce Tensor Network Initializer (TNN Init), a weight initialization scheme that leads to faster convergence with smaller variance for an equivalent parameter count as compared to a DNN. We benchmark TNN and TNN Init by applying them to solve the parabolic PDE associated with the Heston model, which is widely used in financial pricing theory.

部分微分方程（PDE）用于对科学和工程中的各种动力系统进行建模。深度学习的最新进展使我们能够以新的方式解决维度的诅咒，从而在更高的维度中解决它们。但是，深度学习方法受到训练时间和记忆的约束。为了解决这些缺点，我们实施了张量神经网络（TNN），这是一种量子启发的神经网络体系结构，利用张量网络的想法来改进深度学习方法。我们证明，与经典密集神经网络（DNN）相比，TNN提供了明显的参数节省，同时获得了与经典密集的神经网络相同的准确性。此外，我们还展示了如何以相同的精度来比DNN更快地训练TNN。我们通过将它们应用于求解抛物线PDE，特别是Black-Scholes-Barenblatt方程，该方程广泛用于金融定价理论，基于基准测试。还讨论了进一步的例子，例如汉密尔顿 - 雅各比 - 贝尔曼方程。

分布式机器人系统在很大程度上依赖于支持它的Publish-Subscriber通信范式和中间件框架，例如机器人操作系统（ROS），以有效地实现模块化计算图。 ROS 2执行程序是一个处理ROS 2消息的高级任务调度程序，是性能瓶颈。我们扩展了ROS2_Tracing，这是一个带有仪器和用于实时跟踪ROS 2的工具的框架，并在分布式ROS 2系统中分析和可视化消息流的分析和可视化。我们的方法检测输入和输出消息之间的一对多因果关系，包括通过简单的用户级注释，包括间接因果链接。我们在合成和真实机器人系统上验证了我们的方法，并证明了其低运行时开销。此外，可以进一步利用基本的中间执行表示数据库来提取其他指标和高级结果。这可以提供有价值的时机和调度信息，以进一步研究和改善ROS 2执行者，并优化任何ROS 2系统。源代码可在以下网址获得：https：//github.com/christophebedard/ros2-message-flow-analysis。

由于高系统复杂性和动态环境，测试和调试已成为机器人软件开发的主要障碍。标准，基于中间件的数据记录不提供有关内部计算和性能瓶颈的足够信息。其他现有方法还针对非常特定的问题，因此不能用于多用途分析。此外，它们不适合实时应用。在本文中，我们呈现ROS2_TRACING，一个灵活的跟踪工具和ROS 2的多功能仪器集合。它允许使用低开销LTTNG示踪器收集实时分布式系统的运行时执行信息。工具还将跟踪集成到无价的ROS 2 Orchestration系统和其他可用性工具中。消息延迟实验表明，当所有ROS 2仪器启用时，端到端消息延迟开销低于0.0055毫秒，我们认为适用于生产实时系统。使用ROS2_TRACING获得的ROS 2执行信息可以与操作系统的跟踪数据组合，从而实现更广泛的精确分析，有助于了解应用程序执行，以找到性能瓶颈和其他问题的原因。源代码可用于：https://gitlab.com/ros-tracing/ros2_tracing。

This report summarizes the work carried out by the authors during the Twelfth Montreal Industrial Problem Solving Workshop, held at Universit\'e de Montr\'eal in August 2022. The team tackled a problem submitted by CBC/Radio-Canada on the theme of Automatic Text Simplification (ATS).

Physics-Informed Neural Networks (PINNs) have gained much attention in various fields of engineering thanks to their capability of incorporating physical laws into the models. PINNs integrate the physical constraints by minimizing the partial differential equations (PDEs) residuals on a set of collocation points. The distribution of these collocation points appears to have a huge impact on the performance of PINNs and the assessment of the sampling methods for these points is still an active topic. In this paper, we propose a Fixed-Budget Online Adaptive Mesh Learning (FBOAML) method, which decomposes the domain into sub-domains, for training collocation points based on local maxima and local minima of the PDEs residuals. The stopping criterion is based on a data set of reference, which leads to an adaptive number of iterations for each specific problem. The effectiveness of FBOAML is demonstrated in the context of non-parameterized and parameterized problems. The impact of the hyper-parameters in FBOAML is investigated in this work. The comparison with other adaptive sampling methods is also illustrated. The numerical results demonstrate important gains in terms of accuracy of PINNs with FBOAML over the classical PINNs with non-adaptive collocation points. We also apply FBOAML in a complex industrial application involving coupling between mechanical and thermal fields. We show that FBOAML is able to identify the high-gradient location and even give better prediction for some physical fields than the classical PINNs with collocation points taken on a pre-adapted finite element mesh.

To face the dependency on fossil fuels and limit carbon emissions, fuel cells are a very promising technology and appear to be a key candidate to tackle the increase of the energy demand and promote the energy transition. To meet future needs for both transport and stationary applications, the time to market of fuel cell stacks must be drastically reduced. Here, a new concept to shorten their development time by introducing a disruptive and highefficiency data augmentation approach based on artificial intelligence is presented. Our results allow reducing the testing time before introducing a product on the market from a thousand to a few hours. The innovative concept proposed here can support engineering and research tasks during the fuel cell development process to achieve decreased development costs alongside a reduced time to market.

Objective: Accurate visual classification of bladder tissue during Trans-Urethral Resection of Bladder Tumor (TURBT) procedures is essential to improve early cancer diagnosis and treatment. During TURBT interventions, White Light Imaging (WLI) and Narrow Band Imaging (NBI) techniques are used for lesion detection. Each imaging technique provides diverse visual information that allows clinicians to identify and classify cancerous lesions. Computer vision methods that use both imaging techniques could improve endoscopic diagnosis. We address the challenge of tissue classification when annotations are available only in one domain, in our case WLI, and the endoscopic images correspond to an unpaired dataset, i.e. there is no exact equivalent for every image in both NBI and WLI domains. Method: We propose a semi-surprised Generative Adversarial Network (GAN)-based method composed of three main components: a teacher network trained on the labeled WLI data; a cycle-consistency GAN to perform unpaired image-to-image translation, and a multi-input student network. To ensure the quality of the synthetic images generated by the proposed GAN we perform a detailed quantitative, and qualitative analysis with the help of specialists. Conclusion: The overall average classification accuracy, precision, and recall obtained with the proposed method for tissue classification are 0.90, 0.88, and 0.89 respectively, while the same metrics obtained in the unlabeled domain (NBI) are 0.92, 0.64, and 0.94 respectively. The quality of the generated images is reliable enough to deceive specialists. Significance: This study shows the potential of using semi-supervised GAN-based classification to improve bladder tissue classification when annotations are limited in multi-domain data.

We study the multiclass classification problem where the features come from the mixture of time-homogeneous diffusions. Specifically, the classes are discriminated by their drift functions while the diffusion coefficient is common to all classes and unknown. In this framework, we build a plug-in classifier which relies on nonparametric estimators of the drift and diffusion functions. We first establish the consistency of our classification procedure under mild assumptions and then provide rates of cnvergence under different set of assumptions. Finally, a numerical study supports our theoretical findings.

Dialogue summarization has recently garnered significant attention due to its wide range of applications. However, existing methods for summarizing dialogues are suboptimal because they do not take into account the inherent structure of dialogue and rely heavily on labeled data, which can lead to poor performance in new domains. In this work, we propose DIONYSUS (dynamic input optimization in pre-training for dialogue summarization), a pre-trained encoder-decoder model for summarizing dialogues in any new domain. To pre-train DIONYSUS, we create two pseudo summaries for each dialogue example: one is produced by a fine-tuned summarization model, and the other is a collection of dialogue turns that convey important information. We then choose one of these pseudo summaries based on the difference in information distribution across different types of dialogues. This selected pseudo summary serves as the objective for pre-training DIONYSUS using a self-supervised approach on a large dialogue corpus. Our experiments show that DIONYSUS outperforms existing methods on six datasets, as demonstrated by its ROUGE scores in zero-shot and few-shot settings.