Barnes-Hut Research Articles

Ncorpi[formula omitted]N : A [formula omitted] software for N-body integration in collisional and fragmenting systems

NcorpiON is a general purpose N-body software initially developed for the time-efficient integration of collisional and fragmenting systems of planetesimals or moonlets orbiting a central mass. It features a fragmentation model, based on crater scaling and ejecta models, able to realistically simulate a violent impact.The user of NcorpiON can choose between four different built-in modules to compute self-gravity and detect collisions. One of these makes use of a mesh-based algorithm to treat mutual interactions in O(N) time. Another module, much more efficient than the standard Barnes–Hut tree code, is a O(N) tree-based algorithm called FalcON. It relies on fast multipole expansion for gravity computation and we adapted it to collision detection as well. Computational time is reduced by building the tree structure using a three-dimensional Hilbert curve. For the same precision in mutual gravity computation, NcorpiON is found to be up to 25 times faster than the famous software REBOUND.NcorpiON is written entirely in the C language and only needs a C compiler to run. A python add-on, that requires only basic python libraries, produces animations of the simulations from the output files. NcorpiON can communicate with REBOUND’s webGL viewer via MPI for 3D visualization. The name NcorpiON, reminding of a scorpion, comes from the French N-corps, meaning N-body, and from the mathematical notation O(N), due to the running time of the software being almost linear in the total number N of bodies. NcorpiON detects collisions and computes mutual gravity faster than REBOUND, and unlike other N-body integrators, it can resolve a collision by fragmentation. The fast multipole expansions are implemented up to order eight to allow for a high precision in mutual gravity computation.

Fast Semi-Supervised t-SNE for Transfer Function Enhancement in Direct Volume Rendering-Based Medical Image Visualization

Magnetic resonance imaging and computed tomography produce three-dimensional volumetric medical images. While a scalar value represents each individual volume element, or voxel, volumetric data are characterized by features derived from groups of neighboring voxels and their inherent relationships, which may vary depending on the specific clinical application. Labeled samples are also required in most applications, which can be problematic for large datasets such as medical images. We propose a direct volume rendering (DVR) framework based on multi-scale dimensionality reduction neighbor embedding that generates two-dimensional transfer function (TF) domains. In this way, we present FSS.t-SNE, a fast semi-supervised version of the t-distributed stochastic neighbor embedding (t-SNE) method that works over hundreds of thousands of voxels without the problem of crowding and with better separation in a 2D histogram compared to traditional TF domains. Our FSS.t-SNE scatters voxels of the same sub-volume in a wider region through multi-scale neighbor embedding, better preserving both local and global data structures and allowing for its internal exploration based on the original features of the multi-dimensional space, taking advantage of the partially provided labels. Furthermore, FSS.t-SNE untangles sample paths among sub-volumes, allowing us to explore edges and transitions. In addition, our approach employs a Barnes–Hut approximation to reduce computational complexity from O(N2) (t-SNE) to O(NlogN). Although we require the additional step of generating the 2D TF domain from multiple features, our experiments show promising performance in volume segmentation and visual inspection.

Numerical simulation of 3D vorticity dynamics with the Diffused Vortex Hydrodynamics method

In this paper the three-dimensional extension of the Diffused Vortex Hydrodynamics (DVH) is discussed along with free vorticity dynamics simulations. DVH is a vortex particle method developed in-house and widely validated in a 2D framework. The DVH approach has been embedded in a new frontend to the open-source code PEPC, the Pretty Efficient Parallel Coulomb solver. Within this parallel Barnes–Hut tree code, a superposition of elementary heat equation solutions in a cubic support is performed during the diffusion step. This redistribution avoids excessive clustering or rarefaction of the vortex particles, providing robustness and high accuracy of the method. An ascending vortex dipole at various resolutions is selected as a test-case and heuristic convergence measurements are performed, taking into account the conservation of prime integrals and the energy–enstrophy balance.

Ensemble Meta-Learning-Based Robust Chipping Prediction for Wafer Dicing

Our previous study utilized importance analysis, random forest, and Barnes–Hut t-SNE dimensionality reduction to analyze critical dicing parameters and used bidirectional long short-term memory (BLSTM) to predict wafer chipping occurrence successfully in a single dicing machine. However, each dicing machine of the same type may produce unevenly distributed non-IID dicing signals, which may lead to the undesirable result that a pre-trained model trained by dicing machine #1 could not effectively predict chipping occurrence in dicing machine #2. Therefore, regarding the model robustness, this study introduces an ensemble meta-learning-based model that can evaluate many dicing machines for chipping prediction with high stability and accuracy. This approach constructs several base learners, such as the hidden Markov model (HMM), the variational autoencoder (VAE), and BLSTM, to form an ensemble learning. We use model-agnostic meta-learning (MAML) to train and test the ensemble learning model by several prediction tasks from machine #1. After MAML learning, we call the trained model a meta learner. Then, we successfully apply a retrieved data set from machine #2 to the meta learner for training and testing wafer chipping occurrence in this machine. As a result, our contribution to the robust chipping prediction on cross-machines can improve the yield of wafer dicing with a prediction accuracy of 93.21%, preserve the practical wearing of dicing kerfs, and significantly cut wafer manufacturing costs.

Fast Barnes–Hut-based algorithm in 2D vortex method of computational hydrodynamics

In the present paper, the efficient modification of the Barnes–Hut algorithm is proposed based on ideas of multipole and local expansions. Such an approach allows for forming a hierarchy of fast method schemes with different accuracy and computational complexity depending on the number of expansion terms. All the necessary formulae for computational are derived. The parallel implementation is developed using OpenMP and CUDA technologies, which allows performing computations on multicore processors and graphics accelerators.

The Right Way to Avoid Contamination by COVID-19 Virus Based on Barnes-Hut Algorithm

The spread of COVID-19 virus (known as Corona) has an exponential growth all around the world. China, the epicenter of the epidemic, is the most infected country. Tell 07/04/2020, she count 81 740 infected, 3331 death and dramatic socio-economic consequences. At start we have believed that stay at home is possible solution, but next we have thought that this is not the right way as new mutated virus appears. So, as there are no medicines, the best solution is to coexist with the virus. Our approach is in this direction. Keep safe distance (1m or 3 feet) is the most relevant consign in order to surround the spread of the epidemic. Our approach is used to detect possible proximity of persons and to protect them in advance before contamination. We propose an algorithm, Barnes-Hut algorithm, based on Quad, a data structure which detects some proximity relative to persons and groups of persons. Alert is raised when the proximity between parsons is not respected. The algorithm can be used in decision making (e.g close frontiers). Experiments on real world dataset show the efficiency of the algorithm.

Barnes–Hut approximation based accelerating t-SNE for seizure detection

Background:Automatic detection of epileptic seizures is critical in the paradigm of epilepsy diagnosis and in relieving the cumbersome visual inspection of electroencephalogram (EEG) recordings. A speedy algorithm could help in more reliable monitoring and detection of seizures. Methods and materials:In this study, we aim to provide an EEG-based seizure detection system with computational efficiency and improved performance. In the proposed work, many features including temporal, spectral, and non-linear features from each intrinsic mode function (IMF) of empirical mode decomposition (EMD) have been used. Barnes–Hut approximation-based t-stochastic neighborhood embedding (bh t-SNE) was explored for the first time to observe the reduction in computational time (CT) period in the automatic seizure detection system. Three classes of widely-used EEG Bonn datasets were used to assess the performance of the proposed method. Results:The proposed Barnes–Hut-based accelerating t-SNE along with SVM and KNN reduced more than half of the classification time with the same accuracy. The classifier takes 2.147±0.1 s for SVM and 1.216±0.1 s for KNN without the proposed t-SNE and 1.31±0.1 s for SVM and 0.736±0.1 s for KNN (at the trade-off parameter θ=0.5) with the proposed Barnes–hut based t-SNE (bh t-SNE) at an accuracy of 100%. Conclusions: The findings of the experimental work indicate that the proposed method is effective in reducing the computational time while maintaining the required efficacy. As a result, the inclusion of these algorithms in hardware might prove to be effective in assisting neurologists in detecting seizures.

Use of Barnes-Hut Algorithm to Attack COVID-19 Virus

The epidemy COVID-19 (khnown as Corona) is very dangerous. China, the epicenter of the epidemy, is the most infected country tell 07/04/2020 with 81 740 infected, and 3 331 death. To limit the exponential propagation of the virus we have to respect some consigns. Keep safe distance (1m or 3feet) is the most relevant consign in order to surround the spread of the epidemy. Our approach is used to detect possible contamination of persons. Barnes-Hut algorithm is based on quad, a data structure which detects certain proximity relative to persons and groups of persons. Alert is raised when the proximity between parsons is not respected. The algorithm can be used in decision making (e.g close frontiers). Experiments on real world dataset shows the efficiency of the algorithm.

Simulating structural plasticity of the brain more scalable than expected

Structural plasticity of the brain describes the creation of new and the deletion of old synapses over time. Rinke et al. (JPDC 2018) introduced a scalable algorithm that simulates structural plasticity for up to one billion neurons on current hardware using a variant of the Barnes–Hut algorithm. They demonstrate good scalability and prove a runtime complexity of O(nlog2⁡n). In this comment paper, we show that with careful consideration of the algorithm and a rigorous proof, the theoretical runtime can even be classified as O(nlog⁡n).

Optimizing graph layout by t-SNE perplexity estimation

Perplexity is one of the key parameters of dimensionality reduction algorithm of t-distributed stochastic neighbor embedding (t-SNE). In this paper, we investigated the relationship of t-SNE perplexity and graph layout evaluation metrics including graph stress, preserved neighborhood information and visual inspection. As we found that a small perplexity is correlated with a relative higher normalized stress while preserving neighborhood information with a higher precision but less global structure information, we proposed our method to estimate appropriate perplexity either based on a modified standard t-SNE or the sklearn Barnes–Hut TSNE. Experimental results demonstrate effectiveness and ease of use of our approach when tested on a set of benchmark datasets.

Projection-tree reduced-order modeling for fast N-body computations

This work presents a data-driven reduced-order modeling framework to accelerate the computations of nonlocal and N-body methods that model dynamical systems. The proposed framework differs from traditional acceleration methods, like the Barnes–Hut method, which requires online tree building of the state space, or the fast-multipole method, which requires rigorous a priori analysis of governing kernels and online tree building. Our approach combines Barnes–Hut hierarchical decomposition, projection-based reduced-order modeling via the least-squares Petrov–Galerkin (LSPG) projection, and hyper-reduction by way of the Gauss–Newton with approximated tensor (GNAT) approach. The resulting projection-tree reduced-order model (PTROM) enables a drastic reduction in operational count complexity by constructing sparse hyper-reduced pairwise interactions of the non-compact N-body dynamical system. As a result, the presented framework is capable of achieving an operational count complexity that is independent of N, the number of bodies in the numerical domain. Capabilities of the PTROM method are demonstrated on the two-dimensional fluid-dynamic Biot–Savart kernel within a parametric and reproductive setting. Results show the PTROM is capable of achieving over 2000× wall-time speed-up with respect to the full-order model, where the speed-up increases with N. The resulting solution delivers quantities of interest with errors that are less than 0.1% with respect to full-order model.

Accelerating NBODY6 with a graphics processing unit-enabled Particle-Particle Particle-Tree scheme

ABSTRACTWe describe a modified version of the nbody6 code for simulating star clusters which greatly improves computational efficiency while sacrificing little in the way of accuracy. The distant force calculator is replaced by a graphics processing unit-enabled Barnes–Hut code, and integration is done with a standard leap frog scheme. Short-range forces continue to use the CPU-based fourth-order Hermite predictor-corrector scheme of nbody6. Our code outperforms nbody6 for systems with more than 3 × 105 particles and runs more than a factor 2 faster for systems of 106 particles with similar energy conservation. Our code should be useful for simulating realistic dense stellar clusters, such as globular clusters or galactic nuclei.

Simulation of Cluster Dynamics of Proton-Bound Water Clusters in a High Kinetic Energy Ion-Mobility Spectrometer.

Ions are separated in ion mobility spectrometry (IMS) by their characteristic motion through a gas-filled drift tube with a static electric field present. Chemical dynamics, such as clustering and declustering of chemically reactive systems, and physical parameters, as, for example, the electric field strength or background gas temperature, impact on the observed ion mobility. In high kinetic energy IMS (HiKE-IMS), the reduced electric field strength is up to 120 Td in both the reaction region and drift region of the instrument. The ion generation in a corona discharge driven chemical ionization source leads generally to formation of proton-bound water clusters. However, the reduced electric field strength and therefore the effective ion temperature has a significant influence on the chemical equilibria of this reaction system. In order to characterize the effects occurring in IMS systems in general, numerical simulations can support and potentially explain experimental observations. The comparison of the simulation of a well characterized chemical reaction system (i.e., the proton-bound water cluster system) with experimental results allows us to validate the numerical model applied in this work. Numerical simulations of the proton-bound water cluster system were performed with the custom particle-based ion dynamics simulation framework (IDSimF). The ion-transport calculation in the model is based on a Verlet integration of the equations of motion and uses a customized Barnes-Hut method to calculate space charge interactions. The chemical kinetics is modeled stochastically with a Monte Carlo method. The experimental and simulated drift spectra are in good qualitative and quantitative agreement, and experimentally observed individual transitions of cluster ions are clearly reproduced and identified by the numerical model.

Improving Barnes-Hut t-SNE Algorithm in Modern GPU Architectures with Random Forest KNN and Simulated Wide-Warp

The t-Distributed Stochastic Neighbor Embedding (t-SNE) is a widely used technique for dimensionality reduction but is limited by its scalability when applied to large datasets. Recently, BH-tSNE was proposed; this is a successful approximation that transforms a step of the original algorithm into an N-Body simulation problem that can be solved by a modified Barnes-Hut algorithm. However, this improvement still has limitations to process large data volumes (millions of records). Late studies, such as t-SNE-CUDA, have used GPUs to implement highly parallel BH-tSNE. In this research we have developed a new GPU BH-tSNE implementation that produces the embedding of multidimensional data points into three-dimensional space. We examine scalability issues in two of the most expensive steps of GPU BH-tSNE by using efficient memory access strategies , recent acceleration techniques , and a new approach to compute the KNN graph structure used in BH-tSNE with GPU. Our design allows up to 460% faster execution when compared to the t-SNE-CUDA implementation. Although our SIMD acceleration techniques were used in a modern GPU setup, we have also verified a potential for applications in the context of multi-core processors.

Particle–particle particle–tree code for planetary system formation with individual cut-off method: GPLUM

Abstract In a standard theory of the formation of the planets in our Solar System, terrestrial planets and cores of gas giants are formed through accretion of kilometer-sized objects (planetesimals) in a protoplanetary disk. Gravitational N-body simulations of a disk system made up of numerous planetesimals are the most direct way to study the accretion process. However, the use of N-body simulations has been limited to idealized models (e.g., perfect accretion) and/or narrow spatial ranges in the radial direction, due to the limited number of simulation runs and particles available. We have developed new N-body simulation code equipped with a particle–particle particle–tree (P3T) scheme for studying the planetary system formation process: GPLUM. For each particle, GPLUM uses the fourth-order Hermite scheme to calculate gravitational interactions with particles within cut-off radii and the Barnes–Hut tree scheme for particles outside the cut-off radii. In existing implementations, P3T schemes use the same cut-off radius for all particles, making a simulation become slower when the mass range of the planetesimal population becomes wider. We have solved this problem by allowing each particle to have an appropriate cut-off radius depending on its mass, its distance from the central star, and the local velocity dispersion of planetesimals. In addition to achieving a significant speed-up, we have also improved the scalability of the code to reach a good strong-scaling performance up to 1024 cores in the case of N = 106.

Added resistance, heave and pitch for the KVLCC2 tanker using a fully nonlinear unsteady potential flow boundary element method

In this paper, a fully nonlinear unsteady potential flow method is used to predict added resistance, heave and pitch for the KVLCC2 hull in regular head waves at design speed. The method presents a nonlinear decomposition of the velocity potential and the wave field and an adaptive grid refinement. A formulation for the acceleration potential is used to obtain the pressure. To improve computational efficiency, a Barnes-Hut algorithm is introduced. A grid dependency study and a study on the impact of different time steps on the solution are performed. Numerical results have been compared with experimental data for the design speed. A general good agreement is found for added resistance, especially for longer waves. Heave and pitch are properly computed for all wave lengths in the range λ/Lpp=0.4 to 1.4.

Adaptive tiling for parallel N-body simulations on many core

The N-body simulations consist of computing mutual gravitational forces exerted on each body in O ( N ) . The Barnes–Hut approximation allows processing a group of bodies in O ( 1 ) if they are far enough from a given body, which drops the complexity of the whole simulation to O ( N L o g N ) . The octree is used to ease the pruning process but at the cost of some irregularity in the access pattern. In a parallel N-body implementation the bodies are partitioned among threads that are executed on multiple cores. The depth-first traversal of the octree is used for processing each body, which causes repeated cache misses during traversal. This paper proposes different types of tiling methods to improve the performance of N-body simulations. It presents an experimental analysis of octree traversal by using these tiling methods to identify the potential of cache data reuse. It then evaluates these tiling methods for varying tile sizes with different galaxy sizes and a varying number of threads on several machine architectures. The efficiency of tiling approaches depends on the chosen tile size. It is shown that a speedup of 8 times can be achieved by choosing the appropriate tile size on a 60-core Intel accelerator. In order to determine appropriate tile size, the paper proposes an adaptive tiling approach to implicitly adapt the tile size to the distribution of threads, the cache capacity, cache latency, problem size and dynamic changes in the access pattern over the iterations. The proposed adaptive tiling approach can be used as an optimization option in parallel compilers. • Proposes tiling methods to improve cache data reuse for Barnes-Hut simulation. • Provides experimental analysis of octree traversal with proposed tiling approaches. • Evaluates different galaxy sizes and number of threads on several architectures. • A hybrid tiling approach with a suitable tile size provides better performance. • Proposes an adaptive tiling approach to identify an optimal tile size.

High-performance computing simulations of self-gravity in astronomical agglomerates

This article describes the advances in the design, implementation, and evaluation of efficient algorithms for self-gravity simulations in astronomical agglomerates. Three algorithms are presented and evaluated: the occupied cells method, and two variations of the Barnes–Hut method using an octal and a binary tree. Two scenarios are considered in the evaluation: two agglomerates orbiting each other and a collapsing cube. The results show that the proposed octal tree Barnes–Hut method allows improving the performance of the self-gravity calculation up to 100 times with respect to the occupied cells method, while having good numerical accuracy. The proposed algorithms are efficient and accurate methods for self-gravity simulations in astronomical agglomerates.

Fast Multiscale Neighbor Embedding.

Dimension reduction (DR) computes faithful low-dimensional (LD) representations of high-dimensional (HD) data. Outstanding performances are achieved by recent neighbor embedding (NE) algorithms such as t -SNE, which mitigate the curse of dimensionality. The single-scale or multiscale nature of NE schemes drives the HD neighborhood preservation in the LD space (LDS). While single-scale methods focus on single-sized neighborhoods through the concept of perplexity, multiscale ones preserve neighborhoods in a broader range of sizes and account for the global HD organization to define the LDS. For both single-scale and multiscale methods, however, their time complexity in the number of samples is unaffordable for big data sets. Single-scale methods can be accelerated by relying on the inherent sparsity of the HD similarities they involve. On the other hand, the dense structure of the multiscale HD similarities prevents developing fast multiscale schemes in a similar way. This article addresses this difficulty by designing randomized accelerations of the multiscale methods. To account for all levels of interactions, the HD data are first subsampled at different scales, enabling to identify small and relevant neighbor sets for each data point thanks to vantage-point trees. Afterward, these sets are employed with a Barnes-Hut algorithm to cheaply evaluate the considered cost function and its gradient, enabling large-scale use of multiscale NE schemes. Extensive experiments demonstrate that the proposed accelerations are, statistically significantly, both faster than the original multiscale methods by orders of magnitude, and better preserving the HD neighborhoods than state-of-the-art single-scale schemes, leading to high-quality LD embeddings. Public codes are freely available at https://github.com/cdebodt.

Photoemission from the gas phase using soft x-ray fs pulses: an investigation of the space-charge effects

An experimental and computational investigation of the space-charge effects occurring in ultrafast photoelectron spectroscopy from the gas phase is presented. The target sample CF3I is excited by ultrashort (100 fs) far-ultraviolet radiation pulses produced by a free-electron laser. The modification of the energy distribution of the photoelectrons, i.e. the shift and broadening of the spectral structures, is monitored as a function of the pulse intensity. The experimental results are compared with computational simulations which employ a Barnes–Hut algorithm to calculate the effect of individual Coulomb forces acting among the particles. In the presented model, a survey spectrum acquired at low radiation fluence is used to determine the initial energy distribution of the electrons after the photoemission event. The spectrum modified by the space-charge effects is then reproduced by N-body calculations that simulate the dynamics of the photoelectrons subject to the individual mutual Coulomb repulsion and to the attractive force of the positive ions. The employed numerical method accounts for the space-charge effects on the energy distribution and allows to reproduce the complete photoelectron spectrum and not just a specific photoemission structure. The simulations also provide information on the time evolution of the space-charge effects on the picosecond scale. Differences with the case of photoemission from solid samples are highlighted and discussed. The presented simulation procedure, although it omits the analysis of angular distribution, constitutes an effective simplified model that allows to predict and account for space-charge effects on the photoelectron energy spectrum in time-resolved photoemission experiments with high-intensity pulsed sources.