Regularizing the fast multipole method for use in molecular simulation

Energy stable scheme for random batch molecular dynamics

The computational bottleneck of molecular dynamics is pairwise additive long-range interactions between particles. The random batch Ewald (RBE) method provides a highly efficient and superscalable solver for long-range interactions, but the stochastic nature of this algorithm leads to unphysical self-heating effect during the simulation. We propose an energy stable scheme (ESS) for particle systems by employing a Berendsen-type energy bath. The scheme removes the notorious energy drift, which exists due to the force error even when a symplectic integrator is employed. Combining the RBE with the ESS, the new method provides a perfect solution to the computational bottleneck of molecular dynamics at the microcanonical ensemble. Numerical results for a primitive electrolyte and all-atom pure water systems demonstrate the attractive performance of the algorithm, including its dramatically high accuracy, linear complexity, and overcoming the energy drift for long-time simulations.

Pre-exascale HPC approaches for molecular dynamics simulations. Covid-19 research: A use case

Exascale computing has been a dream for ages and is close to becoming a reality that will impact how molecular simulations are being performed, as well as the quantity and quality of the information derived for them. We review how the biomolecular simulations field is anticipating these new architectures, making emphasis on recent work from groups in the BioExcel Center of Excellence for High Performance Computing. We exemplified the power of these simulation strategies with the work done by the HPC simulation community to fight Covid-19 pandemics. This article is categorized under:Data Science > Computer Algorithms and ProgrammingData Science > Databases and Expert SystemsMolecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods.

A fast spectral method for electrostatics in doubly periodic slit channels

We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly periodic slabs with jumps in the dielectric permittivity at the slab boundaries. Our method achieves spectral accuracy by using Ewald splitting to replace the original Poisson equation for nearly singular sources with a smooth far-field Poisson equation, combined with a localized near-field correction. Unlike existing spectral Ewald methods, which make use of the Fourier transform in the aperiodic direction, we recast the problem as a two-point boundary value problem in the aperiodic direction for each transverse Fourier mode for which exact analytic boundary conditions are available. We solve each of these boundary value problems using a fast, well-conditioned Chebyshev method. In the presence of dielectric jumps, combining Ewald splitting with the classical method of images results in smoothed charge distributions, which overlap the dielectric boundaries themselves. We show how to preserve the spectral accuracy in this case through the use of a harmonic correction, which involves solving a simple Laplace equation with smooth boundary data. We implement our method on graphical processing units and combine our doubly periodic Poisson solver with Brownian dynamics to study the equilibrium structure of double layers in binary electrolytes confined by dielectric boundaries. Consistent with prior studies, we find strong charge depletion near the interfaces due to repulsive interactions with image charges, which points to the need for incorporating polarization effects in understanding confined electrolytes, both theoretically and computationally.

Fast Ewald summation for electrostatic potentials with arbitrary periodicity

A unified treatment for the fast and spectrally accurate evaluation of electrostatic potentials with periodic boundary conditions in any or none of the three spatial dimensions is presented. Ewald decomposition is used to split the problem into real-space and Fourier-space parts, and the Fast Fourier Transform (FFT)-based Spectral Ewald (SE) method is used to accelerate computation of the latter, yielding the total runtime O(N⁡log(N)) for N sources. A key component is a new FFT-based solution technique for the free-space Poisson problem. The computational cost is further reduced by a new adaptive FFT for the doubly and singly periodic cases, allowing for different local upsampling factors. The SE method is most efficient in the triply periodic case where the cost of computing FFTs is the lowest, whereas the rest of the algorithm is essentially independent of periodicity. We show that removing periodic boundary conditions from one or two directions out of three will only moderately increase the total runtime, and in the free-space case, the runtime is around four times that of the triply periodic case. The Gaussian window function previously used in the SE method is compared with a new piecewise polynomial approximation of the Kaiser-Bessel window, which further reduces the runtime. We present error estimates and a parameter selection scheme for all parameters of the method, including a new estimate for the shape parameter of the Kaiser-Bessel window. Finally, we consider methods for force computation and compare the runtime of the SE method with that of the fast multipole method.

A GPU-Accelerated Fast Multipole Method for GROMACS: Performance and Accuracy

An important and computationally demanding part of molecular dynamics simulations is the calculation of long-range electrostatic interactions. Today, the prevalent method to compute these interactions is particle mesh Ewald (PME). The PME implementation in the GROMACS molecular dynamics package is extremely fast on individual GPU nodes. However, for large scale multinode parallel simulations, PME becomes the main scaling bottleneck as it requires all-to-all communication between the nodes; as a consequence, the number of exchanged messages scales quadratically with the number of involved nodes in that communication step. To enable efficient and scalable biomolecular simulations on future exascale supercomputers, clearly a method with a better scaling property is required. The fast multipole method (FMM) is such a method. As a first step on the path to exascale, we have implemented a performance-optimized, highly efficient GPU FMM and integrated it into GROMACS as an alternative to PME. For a fair performance comparison between FMM and PME, we first assessed the accuracies of the methods for various sets of input parameters. With parameters yielding similar accuracies for both methods, we determined the performance of GROMACS with FMM and compared it to PME for exemplary benchmark systems. We found that FMM with a multipole order of 8 yields electrostatic forces that are as accurate as PME with standard parameters. Further, for typical mixed-precision simulation settings, FMM does not lead to an increased energy drift with multipole orders of 8 or larger. Whereas an ≈50 000 atom simulation system with our FMM reaches only about a third of the performance with PME, for systems with large dimensions and inhomogeneous particle distribution, e.g., aerosol systems with water droplets floating in a vacuum, FMM substantially outperforms PME already on a single node.

Heterogeneous parallelization and acceleration of molecular dynamics simulations in GROMACS

The introduction of accelerator devices such as graphics processing units (GPUs) has had profound impact on molecular dynamics simulations and has enabled order-of-magnitude performance advances using commodity hardware. To fully reap these benefits, it has been necessary to reformulate some of the most fundamental algorithms, including the Verlet list, pair searching, and cutoffs. Here, we present the heterogeneous parallelization and acceleration design of molecular dynamics implemented in the GROMACS codebase over the last decade. The setup involves a general cluster-based approach to pair lists and non-bonded pair interactions that utilizes both GPU and central processing unit (CPU) single instruction, multiple data acceleration efficiently, including the ability to load-balance tasks between CPUs and GPUs. The algorithm work efficiency is tuned for each type of hardware, and to use accelerators more efficiently, we introduce dual pair lists with rolling pruning updates. Combined with new direct GPU-GPU communication and GPU integration, this enables excellent performance from single GPU simulations through strong scaling across multiple GPUs and efficient multi-node parallelization.