Constraint Enforcement on Decision Trees: a Survey

Decision trees have the particularity of being machine learning models that are visually easy to interpret and understand. Therefore, they are primarily suited for sensitive domains like medical diagnosis, where decisions need to be explainable. However, if used on complex problems, decision trees can become large, making them hard to grasp. In addition to this aspect, when learning decision trees, it may be necessary to consider a broader class of constraints, such as the fact that two variables should not be used in a single branch of the tree. This motivates the need to enforce constraints in learning algorithms of decision trees. We propose a survey of works that attempted to solve the problem of learning decision trees under constraints. Our contributions are fourfold. First, to the best of our knowledge, this is the first survey that deals with constraints on decision trees. Second, we define a flexible taxonomy of constraints applied to decision trees and methods for their treatment in the literature. Third, we benchmark state-of-the art depth-constrained decision tree learners with respect to predictive accuracy and computational time. Fourth, we discuss potential future research directions that would be of interest for researchers who wish to conduct research in this field.

Real-Time Cloth Simulation Using Compute Shader in Unity3D for AR/VR Contents

While the cloth component in Unity engine has been used to represent the 3D cloth object for augmented reality (AR) and virtual reality (VR), it has several limitations in term of resolution and performance. The purpose of our research is to develop a stable cloth simulation based on a parallel algorithm. The method of a mass–spring system is applied to real-time cloth simulation with three types of springs. However, cloth simulation using the mass–spring system requires a small integration time-step to use a large stiffness coefficient. Furthermore, constraint enforcement is applied to obtain the stable behavior of the cloth model. To reduce the computational burden of constraint enforcement, the adaptive constraint activation and deactivation (ACAD) technique that includes the mass–spring system and constraint enforcement method is applied to prevent excessive elongation of the cloth. The proposed algorithm utilizes the graphics processing unit (GPU) parallel processing, and implements it in Compute Shader that executes in different pipelines to the rendering pipeline. In this paper, we investigate the performance and compare the behavior of the mass–spring system, constraint enforcement, and ACAD techniques using a GPU-based parallel method.

Comparing double-step and penalty-based semirecursive formulations for hydraulically actuated multibody systems in a monolithic approach

The simulation of mechanical systems often requires modeling of systems of other physical nature, such as hydraulics. In such systems, the numerical stiffness introduced by the hydraulics can become a significant aspect to consider in the modeling, as it can negatively effect to the computational efficiency. The hydraulic system can be described by using the lumped fluid theory. In this approach, a pressure can be integrated from a differential equation in which effective bulk modulus is divided by a volume size. This representation can lead to numerical stiffness as a consequence of which time integration of a hydraulically driven system becomes cumbersome. In this regard, the used multibody formulation plays an important role, as there are many different procedures for the constraint enforcement and different sets of coordinates to choose from. This paper introduces the double-step semirecursive approach and compares it with a penalty-based semirecursive approach in case of coupled multibody and hydraulic dynamics within the monolithic framework. To this end, hydraulically actuated four-bar and quick-return mechanisms are analyzed as case studies. The two approaches are compared in terms of the work cycle, energy balance, constraint violation, and numerical efficiency of the mechanisms. It is concluded that the penalty-based semirecursive approach has a number of advantages compared with the double-step semirecursive approach, which is in accordance with the literature.

Section Translational Movement Imposition for Macroelements

Boundary conditions play a very important role in any mathematical model. They heavily influence the response near the region they are, but the farther the interest region is, the less important the boundary condition influence becomes. Also, the response depends of which movements are constrained or imposed and which are not. This influence can be seen in all type of problems, ranging from simple beams to complicated structures. For tubular structures, such as flexible pipes and umbilical cables, the boundary conditions are usually given in terms of imposed movements in sections, which are commonly assumed, by hypothesis, as rigid bodies. To deal with this type of structures, the authors presented in previous works the macroelements. They are finite elements that incorporate geometrical characteristics in the formulation, leading to well behaved contact models with a smaller number of degrees of freedom. One major feature of the model is the orthotropic cylindrical layer that uses Fourier series for the displacements. This led to specific contact models and bring the difficulty in the representation of boundary conditions in terminal sections, since different nature displacements (one the aforementioned Fourier and other one standard description) must be dealt with. This paper address how to impose translational movement for sections using macroelements. All the description of how the coupling is made and the constraint enforcement done by using a penalty-based formulation. This work also highlights the implementation, finalizing with comparison with a conventional finite element program.