The quality of mesh generation has long been considered a vital aspect in providing engineers with reliable simulation results throughout the history of the Finite Element Method (FEM). The element extraction method, which is currently the most robust method, is used in business software. However, in order to speed up extraction, the approach is done by finding the next element that optimizes a target function, which can result in local mesh of bad quality after many time steps. We provide TreeMesh, a method that uses this method in conjunction with reinforcement learning (also possible with supervised learning) and a novel Monte-Carlo tree search (MCTS) (Coulom(2006), Kocsis and Szepesv\'ari(2006), Browne et~al.(2012)). The algorithm is based on a previously proposed approach (Pan et~al.(2021)). After making many improvements on DRL (algorithm, state-action-reward setting) and adding a MCTS, it outperforms the former work on the same boundary. Furthermore, using tree search, our program reveals much preponderance on seed-density-changing boundaries, which is common on thin-film materials.

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A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves connection tensors by a Galerkin method in the augmented subspace spanned by the new and old bases. This is followed by rank truncation within a specified error tolerance. The memory requirements are linear in the order of the tensor and linear in the maximal mode dimension. The integrator is robust to small singular values of matricizations of the connection tensors. Up to the rank truncation error, which is controlled by the given error tolerance, the integrator preserves norm and energy for Schrodinger equations, and it dissipates the energy in gradient systems. Numerical experiments with a basic quantum spin system illustrate the behavior of the proposed algorithm.

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The enumeration of finite models is very important to the working discrete mathematician (algebra, graph theory, etc) and hence the search for effective methods to do this task is a critical goal in discrete computational mathematics. However, it is hindered by the possible existence of many isomorphic models, which usually only add noise. Typically, they are filtered out {\em a posteriori}, a step that might take a long time just to discard redundant models. This paper proposes a novel approach to split the generated models into mutually non-isomorphic blocks. To do that we use well-designed hand-crafted invariants as well as randomly generated invariants. The blocks are then tackled separately and possibly in parallel. This approach is integrated into Mace4 (the most popular tool among mathematicians) where it shows tremendous speed-ups for a large variety of algebraic structures.

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Controllable generation is one of the key requirements for successful adoption of deep generative models in real-world applications, but it still remains as a great challenge. In particular, the compositional ability to generate novel concept combinations is out of reach for most current models. In this work, we use energy-based models (EBMs) to handle compositional generation over a set of attributes. To make them scalable to high-resolution image generation, we introduce an EBM in the latent space of a pre-trained generative model such as StyleGAN. We propose a novel EBM formulation representing the joint distribution of data and attributes together, and we show how sampling from it is formulated as solving an ordinary differential equation (ODE). Given a pre-trained generator, all we need for controllable generation is to train an attribute classifier. Sampling with ODEs is done efficiently in the latent space and is robust to hyperparameters. Thus, our method is simple, fast to train, and efficient to sample. Experimental results show that our method outperforms the state-of-the-art in both conditional sampling and sequential editing. In compositional generation, our method excels at zero-shot generation of unseen attribute combinations. Also, by composing energy functions with logical operators, this work is the first to achieve such compositionality in generating photo-realistic images of resolution 1024x1024.

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In real world settings, numerous constraints are present which are hard to specify mathematically. However, for the real world deployment of reinforcement learning (RL), it is critical that RL agents are aware of these constraints, so that they can act safely. In this work, we consider the problem of learning constraints from demonstrations of a constraint-abiding agent's behavior. We experimentally validate our approach and show that our framework can successfully learn the most likely constraints that the agent respects. We further show that these learned constraints are \textit{transferable} to new agents that may have different morphologies and/or reward functions. Previous works in this regard have either mainly been restricted to tabular (discrete) settings, specific types of constraints or assume the environment's transition dynamics. In contrast, our framework is able to learn arbitrary \textit{Markovian} constraints in high-dimensions in a completely model-free setting. The code can be found it: \url{https://github.com/shehryar-malik/icrl}.

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One of the key steps in Neural Architecture Search (NAS) is to estimate the performance of candidate architectures. Existing methods either directly use the validation performance or learn a predictor to estimate the performance. However, these methods can be either computationally expensive or very inaccurate, which may severely affect the search efficiency and performance. Moreover, as it is very difficult to annotate architectures with accurate performance on specific tasks, learning a promising performance predictor is often non-trivial due to the lack of labeled data. In this paper, we argue that it may not be necessary to estimate the absolute performance for NAS. On the contrary, we may need only to understand whether an architecture is better than a baseline one. However, how to exploit this comparison information as the reward and how to well use the limited labeled data remains two great challenges. In this paper, we propose a novel Contrastive Neural Architecture Search (CTNAS) method which performs architecture search by taking the comparison results between architectures as the reward. Specifically, we design and learn a Neural Architecture Comparator (NAC) to compute the probability of candidate architectures being better than a baseline one. Moreover, we present a baseline updating scheme to improve the baseline iteratively in a curriculum learning manner. More critically, we theoretically show that learning NAC is equivalent to optimizing the ranking over architectures. Extensive experiments in three search spaces demonstrate the superiority of our CTNAS over existing methods.

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We present Neural A*, a novel data-driven search method for path planning problems. Despite the recent increasing attention to data-driven path planning, a machine learning approach to search-based planning is still challenging due to the discrete nature of search algorithms. In this work, we reformulate a canonical A* search algorithm to be differentiable and couple it with a convolutional encoder to form an end-to-end trainable neural network planner. Neural A* solves a path planning problem by encoding a problem instance to a guidance map and then performing the differentiable A* search with the guidance map. By learning to match the search results with ground-truth paths provided by experts, Neural A* can produce a path consistent with the ground truth accurately and efficiently. Our extensive experiments confirmed that Neural A* outperformed state-of-the-art data-driven planners in terms of the search optimality and efficiency trade-off, and furthermore, successfully predicted realistic human trajectories by directly performing search-based planning on natural image inputs.

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Neural Architecture Search (NAS) was first proposed to achieve state-of-the-art performance through the discovery of new architecture patterns, without human intervention. An over-reliance on expert knowledge in the search space design has however led to increased performance (local optima) without significant architectural breakthroughs, thus preventing truly novel solutions from being reached. In this work we 1) are the first to investigate casting NAS as a problem of finding the optimal network generator and 2) we propose a new, hierarchical and graph-based search space capable of representing an extremely large variety of network types, yet only requiring few continuous hyper-parameters. This greatly reduces the dimensionality of the problem, enabling the effective use of Bayesian Optimisation as a search strategy. At the same time, we expand the range of valid architectures, motivating a multi-objective learning approach. We demonstrate the effectiveness of this strategy on six benchmark datasets and show that our search space generates extremely lightweight yet highly competitive models.

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To improve the search efficiency for Neural Architecture Search (NAS), One-shot NAS proposes to train a single super-net to approximate the performance of proposal architectures during search via weight-sharing. While this greatly reduces the computation cost, due to approximation error, the performance prediction by a single super-net is less accurate than training each proposal architecture from scratch, leading to search inefficiency. In this work, we propose few-shot NAS that explores the choice of using multiple super-nets: each super-net is pre-trained to be in charge of a sub-region of the search space. This reduces the prediction error of each super-net. Moreover, training these super-nets can be done jointly via sequential fine-tuning. A natural choice of sub-region is to follow the splitting of search space in NAS. We empirically evaluate our approach on three different tasks in NAS-Bench-201. Extensive results have demonstrated that few-shot NAS, using only 5 super-nets, significantly improves performance of many search methods with slight increase of search time. The architectures found by DARTs and ENAS with few-shot models achieved 88.53% and 86.50% test accuracy on CIFAR-10 in NAS-Bench-201, significantly outperformed their one-shot counterparts (with 54.30% and 54.30% test accuracy). Moreover, on AUTOGAN and DARTS, few-shot NAS also outperforms previously state-of-the-art models.

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Generative Adversarial networks (GANs) have obtained remarkable success in many unsupervised learning tasks and unarguably, clustering is an important unsupervised learning problem. While one can potentially exploit the latent-space back-projection in GANs to cluster, we demonstrate that the cluster structure is not retained in the GAN latent space. In this paper, we propose ClusterGAN as a new mechanism for clustering using GANs. By sampling latent variables from a mixture of one-hot encoded variables and continuous latent variables, coupled with an inverse network (which projects the data to the latent space) trained jointly with a clustering specific loss, we are able to achieve clustering in the latent space. Our results show a remarkable phenomenon that GANs can preserve latent space interpolation across categories, even though the discriminator is never exposed to such vectors. We compare our results with various clustering baselines and demonstrate superior performance on both synthetic and real datasets.

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TraQuad is an autonomous tracking quadcopter capable of tracking any moving (or static) object like cars, humans, other drones or any other object on-the-go. This article describes the applications and advantages of TraQuad and the reduction in cost (to about 250$) that has been achieved so far using the hardware and software capabilities and our custom algorithms wherever needed. This description is backed by strong data and the research analyses which have been drawn out of extant information or conducted on own when necessary. This also describes the development of completely autonomous (even GPS is optional) low-cost drone which can act as a major platform for further developments in automation, transportation, reconnaissance and more. We describe our ROS Gazebo simulator and our STATUS algorithms which form the core of our development of our object tracking drone for generic purposes.

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