Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every forward evaluation of a NODE requires numerical integration of the neural network used to capture the system dynamics, making their training prohibitively expensive. Existing works rely on off-the-shelf adaptive step-size numerical integration schemes, which often require an excessive number of evaluations of the underlying dynamics network to obtain sufficient accuracy for training. By contrast, we accelerate the evaluation and the training of NODEs by proposing a data-driven approach to their numerical integration. The proposed Taylor-Lagrange NODEs (TL-NODEs) use a fixed-order Taylor expansion for numerical integration, while also learning to estimate the expansion's approximation error. As a result, the proposed approach achieves the same accuracy as adaptive step-size schemes while employing only low-order Taylor expansions, thus greatly reducing the computational cost necessary to integrate the NODE. A suite of numerical experiments, including modeling dynamical systems, image classification, and density estimation, demonstrate that TL-NODEs can be trained more than an order of magnitude faster than state-of-the-art approaches, without any loss in performance.

Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation laws) or from the system's design (e.g., the Jacobian matrix of a robot), even if large portions of the system dynamics remain unknown. We develop a framework to learn dynamics models from trajectory data while incorporating a-priori system knowledge as inductive bias. More specifically, the proposed framework uses physics-based side information to inform the structure of the neural network itself, and to place constraints on the values of the outputs and the internal states of the model. It represents the system's vector field as a composition of known and unknown functions, the latter of which are parametrized by neural networks. The physics-informed constraints are enforced via the augmented Lagrangian method during the model's training. We experimentally demonstrate the benefits of the proposed approach on a variety of dynamical systems -- including a benchmark suite of robotics environments featuring large state spaces, non-linear dynamics, external forces, contact forces, and control inputs. By exploiting a-priori system knowledge during training, the proposed approach learns to predict the system dynamics two orders of magnitude more accurately than a baseline approach that does not include prior knowledge, given the same training dataset.

我们详细阐述了布尔分类器$ \ sigma $的纠正概念。给定$ \ sigma $和某些背景知识$ t $，表征$ \ sigma $的方式必须更改为符合$ t $的新分类器$ \ sigma \ star t $。我们在这里重点关注单标签布尔分类器的特定情况，即有一个单个目标概念，任何实例都被分类为正（概念的元素）或负面（互补概念的元素）。在这种特定情况下，我们的主要贡献是双重的：（1）我们证明有一个独特的整流操作员$ \ star $满足假设，并且（2）当$ \ sigma $和$ t $是布尔电路时，我们会显示如何在$ \ sigma $和$ t $的大小上计算出相当于$ \ sigma \ star t $的分类电路；当$ \ sigma $和$ t $是决策树时，可以按$ \ sigma $和$ t $的大小计算出相当于$ \ sigma \ star t $的决策树。

我们的食品偏好指导我们的食物选择，反过来影响我们的个人健康和社交生活。在本文中，我们采用了一种方法，使用OWL2中表达的域本体进行支持，以支持正规主义CP-Net中的偏好的获取和表示。具体而言，我们展示了域本体论的构建和问卷设计来获取和代表偏好。偏好的收购和代表在大学食堂的领域实施。我们在这项初步工作中的主要贡献是获取偏好，并优选地通过本体中所代表的域知识来获取偏好。

从制造环境到个人房屋的最终用户任务的巨大多样性使得预编程机器人非常具有挑战性。事实上，教学机器人从划痕的新行动可以重复使用以前看不见的任务仍然是一个艰难的挑战，一般都留给了机器人专家。在这项工作中，我们展示了Iropro，这是一个交互式机器人编程框架，允许最终用户没有技术背景，以教授机器人新的可重用行动。我们通过演示和自动规划技术将编程结合起来，以允许用户通过通过动力学示范教授新的行动来构建机器人的知识库。这些行动是概括的，并重用任务计划程序来解决用户定义的先前未经调查的问题。我们将iropro作为Baxter研究机器人的端到端系统实施，同时通过演示通过示范来教授低级和高级操作，以便用户可以通过图形用户界面自定义以适应其特定用例。为了评估我们的方法的可行性，我们首先进行了预设计实验，以更好地了解用户采用所涉及的概念和所提出的机器人编程过程。我们将结果与设计后实验进行比较，在那里我们进行了用户学习，以验证我们对真实最终用户的方法的可用性。总体而言，我们展示了具有不同编程水平和教育背景的用户可以轻松学习和使用Iropro及其机器人编程过程。

在本文中，我们提出了一个被称为Rkhsmetamod的R包，其实现了估计复杂模型的元模型的过程。元模型近似于复杂模型的Hoeffding分解，并允许我们对其进行灵敏度分析。它属于一个再现内核希尔伯特空间，该空间被构造成作为希尔伯特空间的直接总和。元模型的估计是用Hilbert标准的总和和经验L ^ 2-Norm的最小化最小化的抵抗的经验性最小平方。此过程称为RKHS Ridge Group Sparse，允许选择和估算Hoeffding分解中的术语，因此选择和估计非零的Sobol指数。 RKHSMetamod包提供从R统计计算环境到C ++库EIGEN和GSL的接口。为了加快执行时间并优化存储内存，除了用R写入R的函数，可以使用RCPPeigen和RCPPGSL软件包使用高效的C ++库写入此包的所有功能。然后，这些功能在R环境中接通，以提出用户友好的包装。