Efficient high order semi-implicit time discretization and local discontinuous Galerkin methods for highly nonlinear PDEs

International audienceIn this paper, we develop a high order semi-implicit time discretization method for highly nonlinear PDEs, which consist of the surface diffusion and Willmore flow of graphs, the Cahn-Hilliard equation and the Allen-Cahn/Cahn-Hilliard system. These PDEs are high order in spatial derivatives, which motivates us to develop implicit or semi-implicit time marching methods to relax the severe time step restriction for stability of explicit methods. In addition, these PDEs are also highly nonlinear, fully implicit method will incredibly increase the difficulty of implementation. In particular, we can not well separate the stiff and non-stiff components for these problems, which leads to the traditional implicit-explicit methods nearly meaningless. In this paper, a high order semi-implicit time marching method and the local discontinuous Galerkin spatial method are coupled together to achieve high order accuracy in both space and time, and to enhance the efficiency of the proposed approaches, the resulting linear or nonlinear algebraic systems are solved by multigrid solver. Numerical simulation results in one and two dimensions are presented to illustrate that the combination of the local discontinuous Galerkin method for spatial approximation, semi-implicit temporal integration with the multigrid solver provides a practical and efficient approach when solving this family of problems

Activated Carbons and Chitosan Adsorbents in Removing Contaminants from Water

Being more and more widely used for a variety of water treatments, chitosan and activated carbons are playing an increasingly significant part nowadays. Activated carbons purify water through the pore structure and adsorb ions or other particles. Chitosan also adsorb a large amount of metallic ions and purifies water through the reactions by the functional groups. This paper discusses the different features of the two substances and then gives a comparison between the two types of adsorbents by comparing their characteristics, conditions and applications. Specifically, the suitable temperatures, the specific modifications and solubility are discussed, together with other factors. The difference in their physical and chemical properties plays an important role in the comparison. For physical properties, the activated carbons have strong mechanical strength and are soluble in many types of solvents. By contrast, chitosan is generally soluble in an acidic solution. There are also some differences in the adsorption abilities and ways to purify solutions. Next, chitosan is more easily dissolved in solution with low PH and at room temperature. However, the activated carbons require lower PH and lower temperature to be dissolved. Then, activated carbons are more likely to cause secondary pollution due to the impurities in the activated carbons. The two substances require different modifications to increase the rate of adsorption. As a result, the firms should consider the features of the two types of adsorbents and choose the better one. They should also understand the suitable conditions for each adsorbent

Boosted ab initio Cryo-EM 3D Reconstruction with ACE-EM

The central problem in cryo-electron microscopy (cryo-EM) is to recover the 3D structure from noisy 2D projection images which requires estimating the missing projection angles (poses). Recent methods attempted to solve the 3D reconstruction problem with the autoencoder architecture, which suffers from the latent vector space sampling problem and frequently produces suboptimal pose inferences and inferior 3D reconstructions. Here we present an improved autoencoder architecture called ACE (Asymmetric Complementary autoEncoder), based on which we designed the ACE-EM method for cryo-EM 3D reconstructions. Compared to previous methods, ACE-EM reached higher pose space coverage within the same training time and boosted the reconstruction performance regardless of the choice of decoders. With this method, the Nyquist resolution (highest possible resolution) was reached for 3D reconstructions of both simulated and experimental cryo-EM datasets. Furthermore, ACE-EM is the only amortized inference method that reached the Nyquist resolution

Learning Vision-Guided Quadrupedal Locomotion End-to-End with Cross-Modal Transformers

We propose to address quadrupedal locomotion tasks using Reinforcement Learning (RL) with a Transformer-based model that learns to combine proprioceptive information and high-dimensional depth sensor inputs. While learning-based locomotion has made great advances using RL, most methods still rely on domain randomization for training blind agents that generalize to challenging terrains. Our key insight is that proprioceptive states only offer contact measurements for immediate reaction, whereas an agent equipped with visual sensory observations can learn to proactively maneuver environments with obstacles and uneven terrain by anticipating changes in the environment many steps ahead. In this paper, we introduce LocoTransformer, an end-to-end RL method for quadrupedal locomotion that leverages a Transformer-based model for fusing proprioceptive states and visual observations. We evaluate our method in challenging simulated environments with different obstacles and uneven terrain. We show that our method obtains significant improvements over policies with only proprioceptive state inputs, and that Transformer-based models further improve generalization across environments. Our project page with videos is at https://RchalYang.github.io/LocoTransformer .Comment: Our project page with videos is at https://RchalYang.github.io/LocoTransforme

Hybrid Smoothed-Particle Hydrodynamics/Finite Element Method simulation of water droplet erosion on ductile metallic targets

Erosion of metallic surfaces due to the permanent impact of high-speed water droplets is a significant concern in diverse industrial applications like turbine blades, among others. In the initial stage of water droplet erosion, there is an incubation regime with negligible mass loss whose duration is strongly dependent on water droplet sizes and velocities, the initial state of the surface, and the material properties of the target. The prediction of the incubation period duration is one of the main topics of research in the field. In this work, the interaction of the water droplets with a metallic surface is simulated using a hybrid Smoothed-Particle Hydrodynamics/Finite Element Method modeling scheme. The effect of multiple random impacts on representative target areas for certain ranges of impact angles and velocities was studied using a combination of simple material and damage models for the target surface of Ti-6Al-4V titanium alloy. The simulation is able to reproduce the main dependencies of the incubation regime and the first stages of water droplet erosion on the impact angle and velocity as reported in the literature. This framework can be considered a foundation for more advanced models with the goal of a better understanding of the physical mechanisms behind the incubation regime in order to devise strategies to extend it in real applications.Deutsche Forschungsgemeinschaft (DFG, German Research Foundation

Incorporating Pre-trained Model Prompting in Multimodal Stock Volume Movement Prediction

Multimodal stock trading volume movement prediction with stock-related news is one of the fundamental problems in the financial area. Existing multimodal works that train models from scratch face the problem of lacking universal knowledge when modeling financial news. In addition, the models ability may be limited by the lack of domain-related knowledge due to insufficient data in the datasets. To handle this issue, we propose the Prompt-based MUltimodal Stock volumE prediction model (ProMUSE) to process text and time series modalities. We use pre-trained language models for better comprehension of financial news and adopt prompt learning methods to leverage their capability in universal knowledge to model textual information. Besides, simply fusing two modalities can cause harm to the unimodal representations. Thus, we propose a novel cross-modality contrastive alignment while reserving the unimodal heads beside the fusion head to mitigate this problem. Extensive experiments demonstrate that our proposed ProMUSE outperforms existing baselines. Comprehensive analyses further validate the effectiveness of our architecture compared to potential variants and learning mechanisms.Comment: 9 pages, 3 figures, 7 tables. Accepted by 2023 KDD Workshop on Machine Learning in Financ

Incorporating Fine-grained Events in Stock Movement Prediction

Considering event structure information has proven helpful in text-based stock movement prediction. However, existing works mainly adopt the coarse-grained events, which loses the specific semantic information of diverse event types. In this work, we propose to incorporate the fine-grained events in stock movement prediction. Firstly, we propose a professional finance event dictionary built by domain experts and use it to extract fine-grained events automatically from finance news. Then we design a neural model to combine finance news with fine-grained event structure and stock trade data to predict the stock movement. Besides, in order to improve the generalizability of the proposed method, we design an advanced model that uses the extracted fine-grained events as the distant supervised label to train a multi-task framework of event extraction and stock prediction. The experimental results show that our method outperforms all the baselines and has good generalizability.Comment: Accepted by 2th ECONLP workshop in EMNLP201

Stein Variational Belief Propagation for Multi-Robot Coordination

Decentralized coordination for multi-robot systems involves planning in challenging, high-dimensional spaces. The planning problem is particularly challenging in the presence of obstacles and different sources of uncertainty such as inaccurate dynamic models and sensor noise. In this paper, we introduce Stein Variational Belief Propagation (SVBP), a novel algorithm for performing inference over nonparametric marginal distributions of nodes in a graph. We apply SVBP to multi-robot coordination by modelling a robot swarm as a graphical model and performing inference for each robot. We demonstrate our algorithm on a simulated multi-robot perception task, and on a multi-robot planning task within a Model-Predictive Control (MPC) framework, on both simulated and real-world mobile robots. Our experiments show that SVBP represents multi-modal distributions better than sampling-based or Gaussian baselines, resulting in improved performance on perception and planning tasks. Furthermore, we show that SVBP's ability to represent diverse trajectories for decentralized multi-robot planning makes it less prone to deadlock scenarios than leading baselines.Comment: 8 pages, accepted for publication in Robotics and Automation Letters (RA-L); experiment updated, background methodology adde