Reduced order modeling methods are often used as a mean to reduce simulation costs in industrial applications. Despite their computational advantages, reduced order models (ROMs) often fail to accurately reproduce complex dynamics encountered in real life applications. To address this challenge, we leverage NeuralODEs to propose a novel ROM correction approach based on a time-continuous memory formulation. Finally, experimental results show that our proposed method provides a high level of accuracy while retaining the low computational costs inherent to reduced models.

流体（VOF）方法的体积被广泛用于多相流仿真中，以跟踪和定位两个不混溶的流体之间的界面。VOF方法的主要瓶颈是界面重建步骤，由于其高计算成本和非结构化网格的精度较低。我们建议基于图神经网络（GNN）的机器学习增强的VOF方法，以加速通用非结构化网格上的接口重建。我们首先开发一种方法来基于在非结构化网格上离散的抛物面表面生成合成数据集。然后，我们训练基于GNN的模型并执行概括测试。我们的结果表明，在工业背景下，基于GNN的界面重建方法的效率。

本文提出了一种新颖的域翻译方法。利用生成模型和动态系统之间建立的相似之处，我们提出了对循环构造的重新制定。通过将模型嵌入哈密顿结构，我们获得了一个连续，表现力且最重要的是域翻译的可逆生成模型。

许多科学领域需要对复杂系统的时间行为的可靠预测。然而，这种强烈的兴趣是通过建模问题阻碍：通常，描述所考虑的系统物理学的控制方程是不可访问的，或者在已知时，它们的解决方案可能需要与预测时间约束不兼容的计算时间。如今，以通用功能格式近似复杂的系统，并从可用观察中通知IT Nihilo已成为一个常见的做法，如过去几年出现的巨大科学工作所示。许多基于深神经网络的成功示例已经可用，尽管易于忽视了模型和保证边缘的概括性。在这里，我们考虑长期内存神经网络，并彻底调查训练集的影响及其结构对长期预测的质量。利用ergodic理论，我们分析了保证物理系统忠实模型的先验的数据量。我们展示了根据系统不变的培训集的知情设计如何以及潜在的吸引子的结构，显着提高了所产生的模型，在积极学习的背景下开放研究。此外，将说明依赖于存储器能够的模型时内存初始化的非琐碎效果。我们的调查结果为有效数据驱动建模的任何复杂动态系统所需的数量和选择提供了基于证据的良好实践。

Computational units in artificial neural networks follow a simplified model of biological neurons. In the biological model, the output signal of a neuron runs down the axon, splits following the many branches at its end, and passes identically to all the downward neurons of the network. Each of the downward neurons will use their copy of this signal as one of many inputs dendrites, integrate them all and fire an output, if above some threshold. In the artificial neural network, this translates to the fact that the nonlinear filtering of the signal is performed in the upward neuron, meaning that in practice the same activation is shared between all the downward neurons that use that signal as their input. Dendrites thus play a passive role. We propose a slightly more complex model for the biological neuron, where dendrites play an active role: the activation in the output of the upward neuron becomes optional, and instead the signals going through each dendrite undergo independent nonlinear filterings, before the linear combination. We implement this new model into a ReLU computational unit and discuss its biological plausibility. We compare this new computational unit with the standard one and describe it from a geometrical point of view. We provide a Keras implementation of this unit into fully connected and convolutional layers and estimate their FLOPs and weights change. We then use these layers in ResNet architectures on CIFAR-10, CIFAR-100, Imagenette, and Imagewoof, obtaining performance improvements over standard ResNets up to 1.73%. Finally, we prove a universal representation theorem for continuous functions on compact sets and show that this new unit has more representational power than its standard counterpart.

Fruit is a key crop in worldwide agriculture feeding millions of people. The standard supply chain of fruit products involves quality checks to guarantee freshness, taste, and, most of all, safety. An important factor that determines fruit quality is its stage of ripening. This is usually manually classified by experts in the field, which makes it a labor-intensive and error-prone process. Thus, there is an arising need for automation in the process of fruit ripeness classification. Many automatic methods have been proposed that employ a variety of feature descriptors for the food item to be graded. Machine learning and deep learning techniques dominate the top-performing methods. Furthermore, deep learning can operate on raw data and thus relieve the users from having to compute complex engineered features, which are often crop-specific. In this survey, we review the latest methods proposed in the literature to automatize fruit ripeness classification, highlighting the most common feature descriptors they operate on.

Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware of data constraints and symmetries. We introduce a class of persistence-based neural network layers. Persistence-based layers allow the users to easily inject knowledge about symmetries (equivariance) respected by the data, are equipped with learnable weights, and can be composed with state-of-the-art neural architectures.

In this work we introduce reinforcement learning techniques for solving lexicographic multi-objective problems. These are problems that involve multiple reward signals, and where the goal is to learn a policy that maximises the first reward signal, and subject to this constraint also maximises the second reward signal, and so on. We present a family of both action-value and policy gradient algorithms that can be used to solve such problems, and prove that they converge to policies that are lexicographically optimal. We evaluate the scalability and performance of these algorithms empirically, demonstrating their practical applicability. As a more specific application, we show how our algorithms can be used to impose safety constraints on the behaviour of an agent, and compare their performance in this context with that of other constrained reinforcement learning algorithms.

In contextual linear bandits, the reward function is assumed to be a linear combination of an unknown reward vector and a given embedding of context-arm pairs. In practice, the embedding is often learned at the same time as the reward vector, thus leading to an online representation learning problem. Existing approaches to representation learning in contextual bandits are either very generic (e.g., model-selection techniques or algorithms for learning with arbitrary function classes) or specialized to particular structures (e.g., nested features or representations with certain spectral properties). As a result, the understanding of the cost of representation learning in contextual linear bandit is still limited. In this paper, we take a systematic approach to the problem and provide a comprehensive study through an instance-dependent perspective. We show that representation learning is fundamentally more complex than linear bandits (i.e., learning with a given representation). In particular, learning with a given set of representations is never simpler than learning with the worst realizable representation in the set, while we show cases where it can be arbitrarily harder. We complement this result with an extensive discussion of how it relates to existing literature and we illustrate positive instances where representation learning is as complex as learning with a fixed representation and where sub-logarithmic regret is achievable.

Relation extraction (RE) is a sub-discipline of information extraction (IE) which focuses on the prediction of a relational predicate from a natural-language input unit (such as a sentence, a clause, or even a short paragraph consisting of multiple sentences and/or clauses). Together with named-entity recognition (NER) and disambiguation (NED), RE forms the basis for many advanced IE tasks such as knowledge-base (KB) population and verification. In this work, we explore how recent approaches for open information extraction (OpenIE) may help to improve the task of RE by encoding structured information about the sentences' principal units, such as subjects, objects, verbal phrases, and adverbials, into various forms of vectorized (and hence unstructured) representations of the sentences. Our main conjecture is that the decomposition of long and possibly convoluted sentences into multiple smaller clauses via OpenIE even helps to fine-tune context-sensitive language models such as BERT (and its plethora of variants) for RE. Our experiments over two annotated corpora, KnowledgeNet and FewRel, demonstrate the improved accuracy of our enriched models compared to existing RE approaches. Our best results reach 92% and 71% of F1 score for KnowledgeNet and FewRel, respectively, proving the effectiveness of our approach on competitive benchmarks.