An important challenge in scientific machine learning is to develop methods that can exploit and maximize the amount of learning possible from scarce data [1-4]. The need for such methods arises often in science and engineering, especially in the case of computational fluid dynamics (CFD), since expensive-to-evaluate high-fidelity (HF) models make many-query problems such as uncertainty quantification, risk analysis, optimization, and optimization under uncertainty computationally prohibitive [5]. Surrogate models that approximate the solutions to HF models can facilitate the design and analysis process; however, lack of sufficient HF data in tandem with high-dimensional quantities of interest adversely affect surrogate model accuracy. We propose multifidelity (MF) linear regression methods that leverage abundant low-cost, lower-fidelity (LF) data alongside limited HF data to construct linear regression models. These models operate within a reduced-dimensional subspace, obtained through the principal component analysis (PCA), to effectively handle both training data scarcity and the high dimensionality (on the order of tens of thousands of quantities of interest) inherent in our problem setting. Linear regression has been widely utilized as a surrogate modeling approach in aerospace applications due to its simplicity and interpretability. We note that linear regression encompasses a broad class of models that are linear in their parameters but can include features that are arbitrarily nonlinear functions of the input variables [6].

The linear regression (LR) method offers the advantage that optimal parameters can be calculated relatively easily, although its representation capability is limited than that of the deep learning technique. To improve deep reinforcement learning, the Least Squares Deep Q Network (LS-DQN) method was proposed by Levine et al., which combines Deep Q Network (DQN) with LR method. However, the LS-DQN method assumes that the actions are discrete. In this study, we propose the Double Least Squares Deep Deterministic Policy Gradient (DLS-DDPG) method to address this limitation. This method combines the LR method with the Deep Deterministic Policy Gradient (DDPG) technique, one of the representative deep reinforcement learning algorithms for continuous action cases. Numerical experiments conducted in MuJoCo environments showed that the LR update improved performance at least in some tasks, although there are difficulties such as the inability to make the regularization terms small.

Vision-based tactile sensors that can measure 3D geometry of the contacting objects are crucial for robots to perform dexterous manipulation tasks. However, the existing sensors are usually complicated to fabricate and delicate to extend. In this work, we novelly take advantage of the reflection property of semitransparent elastomer to design a robust, low-cost, and easy-to-fabricate tactile sensor named DTact. DTact measures high-resolution 3D geometry accurately from the darkness shown in the captured tactile images with only a single image for calibration. In contrast to previous sensors, DTact is robust under various illumination conditions. Then, we build prototypes of DTact that have non-planar contact surfaces with minimal extra efforts and costs. Finally, we perform two intelligent robotic tasks including pose estimation and object recognition using DTact, in which DTact shows large potential in applications.

Copulas and Rank Order Correlation are two ways to model and/or explain the dependence between 2 or more variables. Historically used in biology and epidemiology, copulas have gained acceptance and prominence in the financial services sector. In this article we are going to untangle what correlation and copulas are and how they relate to each other. In order to prepare a summary overview, I had to read painfully dry material… but the results is a practical guide to understanding copulas and when you should consider them. I lay no claim to being a stats expert or mathematician… just a risk analysis professional. So my approach to this will be pragmatic.