Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Statistics for Spatial Data.

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Part I. Foundations: 1. Random variables 2. Probability measures 3. Stochastic processes 4. The stochastic integral Part II. Existence and Uniqueness: 5. Linear equations with additive noise 6. Linear equations with multiplicative noise 7. Existence and uniqueness for nonlinear equations 8. Martingale solutions Part III. Properties of Solutions: 9. Markov properties and Kolmogorov equations 10. Absolute continuity and Girsanov's theorem 11. Large time behaviour of solutions 12. Small noise asymptotic.

Stochastic Equations in Infinite Dimensions

Genetics and analysis of quantitative traits

The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the process state is infinite dimensional. In this paper we show how such approximations can be avoided for a variety of infinite dimensional models driven by some form of Brownian noise. The approach is based on a variational representation for functionals of Brownian motion. Proofs of large deviations properties are reduced to demonstrating basic qualitative properties (existence, uniqueness and tightness) of certain perturbations of the original process.

Large deviations for infinite dimensional stochastic dynamical systems

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Une formule variationnelle pour des fonctionnelles positives d’une mesure de Poisson aleatoire et d’un mouvement brownien est demontree. Cette formule provient de la representation des integrales exponentielles par l’entropie relative, et peut etre utilisee pour obtenir des estimees de grandes deviations. Un resultat de grandes deviations general est demontre.

Variational representations for continuous time processes

Machine learning and high-throughput computational screening have been valuable tools in accelerated first-principles screening for the discovery of the next generation of functionalized molecules and materials The application of machine learning for chemical applications requires the conversion of molecular structures to a machine-readable format known as a molecular representation The choice of such representations impacts the performance and outcomes of chemical machine learning methods Herein, we present a new concise molecular representation derived from persistent homology, an applied branch of mathematics We have demonstrated its applicability in a high-throughput computational screening of a large molecular database (GDB-9) with more than 133,000 organic molecules Our target is to identify novel molecules that selectively interact with CO2 The methodology and performance of the novel molecular fingerprinting method is presented and the new chemically-driven persistence image representation is used to screen the GDB-9 database to suggest molecules and/or functional groups with enhanced properties The choice of molecular representations can severely impact the performances of machine-learning methods Here the authors demonstrate a persistence homology based molecular representation through an active-learning approach for predicting CO2/N2 interaction energies at the density functional theory (DFT) level

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Vasileios Maroulas

Papers

Large deviations for infinite dimensional stochastic dynamical systems

Large deviations for infinite dimensional stochastic dynamical systems

Variational representations for continuous time processes

Representation of molecular structures with persistent homology for machine learning applications in chemistry

Improved particle filters for multi-target tracking