Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomena are lacking. In this work, we develop AirfRANS, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged Navier-Stokes equations over airfoils at a subsonic regime and for different angles of attacks. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem. Finally, we propose deep learning baselines on four machine learning tasks to study AirfRANS under different constraints for generalization considerations: big and scarce data regime, Reynolds number, and angle of attack extrapolation.

\ emph {几何深度学习}（GDL）的最新进展显示了其提供强大数据驱动模型的潜力。这提供了探索从图形数据中\ emph {部分微分方程}（PDES）控制的物理系统的新方法的动力。然而，尽管做出了努力和最近的成就，但几个研究方向仍未开发，进步仍然远非满足现实现象的身体要求。主要障碍之一是缺乏基准数据集和常见的物理评估协议。在本文中，我们提出了一个2-D Graph-Mesh数据集，以研究High Reynolds制度的机翼上的气流（从$ 10^6 $及以后）。我们还对翼型上的应力力引入指标，以评估重要的物理量的GDL模型。此外，我们提供广泛的GDL基准。

在不同尺度上代表物理信号是工程中最具挑战性的问题之一。已经开发了几种多尺度建模工具来描述由\ emph {部分微分方程}（PDES）控制的物理系统。这些工具处于原则性物理模型和数值模式的十字路口。最近，与数值求解器相比，已经引入了数据驱动的模型来加快PDE溶液的近似值。在这些最新数据驱动的方法中，神经积分运算符是一个学习函数空间之间映射的类。这些功能在图形（网格）上离散化，适用于在物理现象中建模相互作用。在这项工作中，我们使用\ emph {消息传递图神经网络}（mpgnns）近似的积分内核操作员研究了三个多分辨率架构。为了验证我们的研究，我们通过考虑稳定且不稳定的PDE进行了精心选择的指标进行广泛的MPGNN实验。

建模物理系统的数据驱动方法无法推广到与学习域共享相同一般动态的看不见的系统，但与不同的物理环境相对应。我们为此关键问题提出了一个新的框架，即上下文知识的动态适应（CODA），该框架考虑了整个系统之间的分布转移，以快速有效地适应新的动力学。 CODA利用多个环境，每个环境都与不同的动态相关联，并学会将动态模型定为上下文参数（特定于每个环境）。调节是通过超网络进行的，并从观察到的数据与上下文向量共同学习。提出的公式限制了搜索假设空间，以促进跨环境的快速适应和更好的概括。我们从理论上激励我们的方法，并在一组非线性动力学上显示出最新的概括结果，这是多种应用领域的代​​表。我们还在这些系统上还显示，可以从上下文向量中推断出新的系统参数，并以最小的监督为准。

诸如医学诊断的关键背景下的关键问题是决策系统采用的深度学习模型的可解释性。解释的人工智能（XAI）在试图解决这个问题。然而，通常XAI方法仅在通用分类器上进行测试，并且不代表诸如医学诊断等现实问题。在本文中，我们分析了对皮肤病变图像的案例研究，我们定制了一种现有的XAI方法，以解释能够识别不同类型的皮肤病变的深度学习模型。通过综合示例和皮肤病变的相反示例图像形成的解释，并为从业者提供一种突出负责分类决策的关键性状的方法。通过域专家，初学者和非熟练的人进行了一项调查，证明了解释的使用增加了自动决策系统的信任和信心。此外，解释器采用的潜在空间的分析推出了一些最常见的皮肤病变类是明显分开的。这种现象可以得出每个班级的内在特征，希望能够在解决人类专家的最常见的错误分类中提供支持。

我们为生成对抗网络（GAN）提出了一个新颖的理论框架。我们揭示了先前分析的基本缺陷，通过错误地对GANS的训练计划进行了错误的建模，该缺陷受到定义不定的鉴别梯度的约束。我们克服了这个问题，该问题阻碍了对GAN培训的原则研究，并考虑了歧视者的体系结构在我们的框架内解决它。为此，我们通过其神经切线核为歧视者提供了无限宽度神经网络的理论。我们表征了训练有素的判别器，以实现广泛的损失，并建立网络的一般可怜性属性。由此，我们获得了有关生成分布的融合的新见解，从而促进了我们对GANS训练动态的理解。我们通过基于我们的框架的分析工具包来证实这些结果，并揭示了与GAN实践一致的直觉。

预测在环境中只有部分了解其动态的综合动态现象是各种科学领域的普遍存在问题。虽然纯粹的数据驱动方法在这种情况下可以说是不充分的，但是基于标准的物理建模的方法往往是过于简单的，诱导不可忽略的错误。在这项工作中，我们介绍了适当性框架，是一种具有深度数据驱动模型的微分方程所描述的不完整物理动态的原则方法。它包括将动态分解为两个组件：对我们有一些先验知识的动态的物理组件，以及物理模型错误的数据驱动组件核对。仔细制定学习问题，使得物理模型尽可能多地解释数据，而数据驱动组件仅描述了物理模型不能捕获的信息，不再少。这不仅为这种分解提供了存在和唯一性，而且还确保了可解释性和益处泛化。在三个重要用例中进行的实验，每个代表不同的现象，即反应 - 扩散方程，波动方程和非线性阻尼摆锤，表明，空间程度可以有效地利用近似物理模型来准确地预测系统的演变并正确识别相关的物理参数。

We consider the contextual bandit problem on general action and context spaces, where the learner's rewards depend on their selected actions and an observable context. This generalizes the standard multi-armed bandit to the case where side information is available, e.g., patients' records or customers' history, which allows for personalized treatment. We focus on consistency -- vanishing regret compared to the optimal policy -- and show that for large classes of non-i.i.d. contexts, consistency can be achieved regardless of the time-invariant reward mechanism, a property known as universal consistency. Precisely, we first give necessary and sufficient conditions on the context-generating process for universal consistency to be possible. Second, we show that there always exists an algorithm that guarantees universal consistency whenever this is achievable, called an optimistically universal learning rule. Interestingly, for finite action spaces, learnable processes for universal learning are exactly the same as in the full-feedback setting of supervised learning, previously studied in the literature. In other words, learning can be performed with partial feedback without any generalization cost. The algorithms balance a trade-off between generalization (similar to structural risk minimization) and personalization (tailoring actions to specific contexts). Lastly, we consider the case of added continuity assumptions on rewards and show that these lead to universal consistency for significantly larger classes of data-generating processes.

In this paper, we present a novel visual SLAM and long-term localization benchmark for autonomous driving in challenging conditions based on the large-scale 4Seasons dataset. The proposed benchmark provides drastic appearance variations caused by seasonal changes and diverse weather and illumination conditions. While significant progress has been made in advancing visual SLAM on small-scale datasets with similar conditions, there is still a lack of unified benchmarks representative of real-world scenarios for autonomous driving. We introduce a new unified benchmark for jointly evaluating visual odometry, global place recognition, and map-based visual localization performance which is crucial to successfully enable autonomous driving in any condition. The data has been collected for more than one year, resulting in more than 300 km of recordings in nine different environments ranging from a multi-level parking garage to urban (including tunnels) to countryside and highway. We provide globally consistent reference poses with up to centimeter-level accuracy obtained from the fusion of direct stereo-inertial odometry with RTK GNSS. We evaluate the performance of several state-of-the-art visual odometry and visual localization baseline approaches on the benchmark and analyze their properties. The experimental results provide new insights into current approaches and show promising potential for future research. Our benchmark and evaluation protocols will be available at https://www.4seasons-dataset.com/.

Implicit Neural Representations (INR) have recently shown to be powerful tool for high-quality video compression. However, existing works are limiting as they do not explicitly exploit the temporal redundancy in videos, leading to a long encoding time. Additionally, these methods have fixed architectures which do not scale to longer videos or higher resolutions. To address these issues, we propose NIRVANA, which treats videos as groups of frames and fits separate networks to each group performing patch-wise prediction. This design shares computation within each group, in the spatial and temporal dimensions, resulting in reduced encoding time of the video. The video representation is modeled autoregressively, with networks fit on a current group initialized using weights from the previous group's model. To further enhance efficiency, we perform quantization of the network parameters during training, requiring no post-hoc pruning or quantization. When compared with previous works on the benchmark UVG dataset, NIRVANA improves encoding quality from 37.36 to 37.70 (in terms of PSNR) and the encoding speed by 12X, while maintaining the same compression rate. In contrast to prior video INR works which struggle with larger resolution and longer videos, we show that our algorithm is highly flexible and scales naturally due to its patch-wise and autoregressive designs. Moreover, our method achieves variable bitrate compression by adapting to videos with varying inter-frame motion. NIRVANA achieves 6X decoding speed and scales well with more GPUs, making it practical for various deployment scenarios.