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Register a new userFlowPM: Distributed TensorFlow Implementation of the FastPM Cosmological N-body Solver
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We present FlowPM, a Particle-Mesh (PM) cosmological N-body code implemented in Mesh-TensorFlow for GPU-accelerated, distributed, and differentiable simulations. We implement and validate the accuracy of a novel multi-grid scheme based on multiresolution pyramids to compute large scale forces efficiently on distributed platforms. We explore the scaling of the simulation on large-scale supercomputers and compare it with corresponding python based PM code, finding on an average 10x speed-up in terms of wallclock time. We also demonstrate how this novel tool can be used for efficiently solving large scale cosmological inference problems, in particular reconstruction of cosmological fields in a forward model Bayesian framework with hybrid PM and neural network forward model. We provide skeleton code for these examples and the entire code is publicly available at https://github.com/modichirag/flowpm.
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Cosmological large scale structure $N$-body simulations are computation-light, memory-heavy problems in supercomputing. The considerable amount of memory is usually dominated by an inefficient way of storing more than sufficient phase space information of particles. We present a new parallel, information-optimized, particle-mesh-based $N$-body code CUBE, in which information-efficiency and memory-efficiency are increased by nearly an order of magnitude. This is accomplished by storing particles relative phase space coordinates instead of global values, and in the format of fixed point as light as 1 byte. The remaining information is given by complementary density and velocity fields (negligible in memory space) and proper ordering of particles (no extra memory). Our numerical experiments show that this information-optimized $N$-body algorithm provides accurate results within the error of the particle-mesh algorithm. This significant lowering of the memory-to-computation ratio breaks the bottleneck of scaling up and speeding up large cosmological $N$-body simulations on multi-core and heterogeneous computing systems.
Gravitational softening length is one of the key parameters to properly set up a cosmological $N$-body simulation. In this paper, we perform a large suit of high-resolution $N$-body simulations to revise the optimal softening scheme proposed by Power et al. (P03). Our finding is that P03 optimal scheme works well but is over conservative. Using smaller softening lengths than that of P03 can achieve higher spatial resolution and numerically convergent results on both circular velocity and density profiles. However using an over small softening length overpredicts matter density at the inner most region of dark matter haloes. We empirically explore a better optimal softening scheme based on P03 form and find that a small modification works well. This work will be useful for setting up cosmological simulations.
Cosmology is entering an era of percent level precision due to current large observational surveys. This precision in observation is now demanding more accuracy from numerical methods and cosmological simulations. In this paper, we study the accuracy of $N$-body numerical simulations and their dependence on changes in the initial conditions and in the simulation algorithms. For this purpose, we use a series of cosmological $N$-body simulations with varying initial conditions. We test the influence of the initial conditions, namely the pre-initial configuration (preIC), the order of the Lagrangian perturbation theory (LPT), and the initial redshift, on the statistics associated with the large scale structures of the universe such as the halo mass function, the density power spectrum, and the maximal extent of the large scale structures. We find that glass or grid pre-initial conditions give similar results at $zlesssim 2$. However, the initial excess of power in the glass initial conditions yields a subtle difference in the power spectra and the mass function at high redshifts. The LPT order used to generate the ICs of the simulations is found to play a crucial role. First-order LPT (1LPT) simulations underestimate the number of massive haloes with respect to second-order (2LPT) ones, typically by 2% at $10^{14} h^{-1} M_odot$ for an initial redshift of 23, and the small-scale power with an underestimation of 6% near the Nyquist frequency for $z_mathrm{ini} = 23$. Moreover, at higher redshifts, the high-mass end of the mass function is significantly underestimated in 1LPT simulations. On the other hand, when the LPT order is fixed, the starting redshift has a systematic impact on the low-mass end of the halo mass function.
As an entry for the 2012 Gordon-Bell performance prize, we report performance results of astrophysical N-body simulations of one trillion particles performed on the full system of K computer. This is the first gravitational trillion-body simulation in the world. We describe the scientific motivation, the numerical algorithm, the parallelization strategy, and the performance analysis. Unlike many previous Gordon-Bell prize winners that used the tree algorithm for astrophysical N-body simulations, we used the hybrid TreePM method, for similar level of accuracy in which the short-range force is calculated by the tree algorithm, and the long-range force is solved by the particle-mesh algorithm. We developed a highly-tuned gravity kernel for short-range forces, and a novel communication algorithm for long-range forces. The average performance on 24576 and 82944 nodes of K computer are 1.53 and 4.45 Pflops, which correspond to 49% and 42% of the peak speed.
We introduce here our new approach to modeling particle cloud evolution off surface of small bodies (asteroids and comets), following the evolution of ejected particles requires dealing with various time and spatial scales, in an efficient, accurate and modular way. In order to improve computational efficiency and accuracy of such calculations, we created an N-body modeling package as an extension to the increasingly popular orbital dynamics N-body integrator Rebound. Our code is currently a stand-alone variant of the Rebound code and is aimed at advancing a comprehensive understanding of individual particle trajectories, external forcing, and interactions, at the scale which is otherwise overlooked by other modeling approaches. The package we developed -- Rebound Ejecta Dynamics (RED) -- is a Python-based implementation with no additional dependencies. It incorporates several major mechanisms that affect the evolution of particles in low-gravity environments and enables a more straightforward simulation of combined effects. We include variable size and velocity distributions, solar radiation pressure, ellipsoidal gravitational potential, binary or triple asteroid systems, and particle-particle interactions. In this paper, we present a sample of the RED package capabilities. These are applied to a small asteroid binary system (characterized following the Didymos/Dimorphos system, which is the target for NASAs Double Asteroid Redirection Test mission)
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