Quantum Chemistry in Dataflow: Density-Fitting MP2.

We demonstrate the use of dataflow technology in the computation of the correlation energy in molecules at the Møller-Plesset perturbation theory (MP2) level. Specifically, we benchmark density fitting (DF)-MP2 for as many as 168 atoms (in valinomycin) and show that speed-ups between 3 and 3.8 times can be achieved when compared to the MOLPRO package run on a single CPU. Acceleration is achieved by offloading the matrix multiplications steps in DF-MP2 to Dataflow Engines (DFEs). We project that the acceleration factor could be as much as 24 with the next generation of DFEs.

[1]  Wayne Luk,et al.  Leveraging FPGAs for Accelerating Short Read Alignment , 2017, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[2]  Marco D. Santambrogio,et al.  A Scalable Dataflow Implementation of Curran's Approximation Algorithm , 2017, 2017 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW).

[3]  Tyler Y Takeshita,et al.  Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller-Plesset Perturbation Theory. , 2017, Journal of chemical theory and computation.

[4]  Georgi Gaydadjiev,et al.  From exaflop to exaflow , 2017, Design, Automation & Test in Europe Conference & Exhibition (DATE), 2017.

[5]  Takahito Nakajima,et al.  Massively parallel algorithm and implementation of RI‐MP2 energy calculation for peta‐scale many‐core supercomputers , 2016, J. Comput. Chem..

[6]  So Hirata,et al.  Monte Carlo MP2 on Many Graphical Processing Units. , 2016, Journal of chemical theory and computation.

[7]  R. Baer,et al.  Stochastic self-consistent Green's function second-order perturbation theory (sGF2) , 2016, 1603.04141.

[8]  Ross C. Walker,et al.  Electronic Structure Calculations on Graphics Processing Units From Quantum Chemistry to Condensed Matter Physics , 2016 .

[9]  Wayne Luk,et al.  Ramethy: Reconfigurable Acceleration of Bisulfite Sequence Alignment , 2015, FPGA.

[10]  Chao Yang,et al.  A highly-efficient and green data flow engine for solving euler atmospheric equations , 2014, 2014 24th International Conference on Field Programmable Logic and Applications (FPL).

[11]  M. Head‐Gordon,et al.  Shared memory multiprocessing implementation of resolution-of-the-identity second-order Møller–Plesset perturbation theory with attenuated and unattenuated results for intermolecular interactions between large molecules , 2014 .

[12]  Takahito Nakajima,et al.  MPI/OpenMP Hybrid Parallel Algorithm of Resolution of Identity Second-Order Møller-Plesset Perturbation Calculation for Massively Parallel Multicore Supercomputers. , 2013, Journal of chemical theory and computation.

[13]  Michael J. Flynn,et al.  Finite-Difference Wave Propagation Modeling on Special-Purpose Dataflow Machines , 2013, IEEE Transactions on Parallel and Distributed Systems.

[14]  Jason Helge Anderson,et al.  Multi-pumping for resource reduction in FPGA high-level synthesis , 2013, 2013 Design, Automation & Test in Europe Conference & Exhibition (DATE).

[15]  R. Baer,et al.  Expeditious Stochastic Approach for MP2 Energies in Large Electronic Systems. , 2012, Journal of chemical theory and computation.

[16]  Julio Daniel Carvalho Maia,et al.  GPU Linear Algebra Libraries and GPGPU Programming for Accelerating MOPAC Semiempirical Quantum Chemistry Calculations. , 2012, Journal of chemical theory and computation.

[17]  Mark S. Gordon,et al.  Mixed-precision evaluation of two-electron integrals by Rys quadrature , 2012, Comput. Phys. Commun..

[18]  Oskar Mencer,et al.  Rapid computation of value and risk for derivatives portfolios , 2012, Concurr. Comput. Pract. Exp..

[19]  Wayne Luk,et al.  Multi-level Customisation Framework for Curve Based Monte Carlo Financial Simulations , 2012, ARC.

[20]  Martin Schütz,et al.  Molpro: a general‐purpose quantum chemistry program package , 2012 .

[21]  Dieter Cremer,et al.  Møller–Plesset perturbation theory: from small molecule methods to methods for thousands of atoms , 2011 .

[22]  Ivan S. Ufimtsev,et al.  Dynamic Precision for Electron Repulsion Integral Evaluation on Graphical Processing Units (GPUs). , 2011, Journal of chemical theory and computation.

[23]  Michael J. Flynn,et al.  Beyond Traditional Microprocessors for Geoscience High-Performance Computing Applications , 2011, IEEE Micro.

[24]  Klaus Schulten,et al.  GPU-accelerated molecular modeling coming of age. , 2010, Journal of molecular graphics & modelling.

[25]  Alán Aspuru-Guzik,et al.  Accelerating Correlated Quantum Chemistry Calculations Using Graphical Processing Units , 2010, Computing in Science & Engineering.

[26]  Ivan S Ufimtsev,et al.  Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics. , 2009, Journal of chemical theory and computation.

[27]  Ivan S Ufimtsev,et al.  Quantum Chemistry on Graphical Processing Units. 2. Direct Self-Consistent-Field Implementation. , 2009, Journal of chemical theory and computation.

[28]  Jörg Kussmann,et al.  Linear-scaling atomic orbital-based second-order Møller-Plesset perturbation theory by rigorous integral screening criteria. , 2009, The Journal of chemical physics.

[29]  Christian Ochsenfeld,et al.  Tighter multipole-based integral estimates and parallel implementation of linear-scaling AO-MP2 theory. , 2008, Physical chemistry chemical physics : PCCP.

[30]  Yihan Shao,et al.  Accelerating resolution-of-the-identity second-order Møller-Plesset quantum chemistry calculations with graphical processing units. , 2008, The journal of physical chemistry. A.

[31]  Ivan S Ufimtsev,et al.  Quantum Chemistry on Graphical Processing Units. 1. Strategies for Two-Electron Integral Evaluation. , 2008, Journal of chemical theory and computation.

[32]  Yihan Shao,et al.  Fast evaluation of scaled opposite spin second‐order Møller–Plesset correlation energies using auxiliary basis expansions and exploiting sparsity , 2007, J. Comput. Chem..

[33]  Yihan Shao,et al.  An improved algorithm for analytical gradient evaluation in resolution‐of‐the‐identity second‐order Møller‐Plesset perturbation theory: Application to alanine tetrapeptide conformational analysis , 2007, J. Comput. Chem..

[34]  Yihan Shao,et al.  Quartic-Scaling Analytical Energy Gradient of Scaled Opposite-Spin Second-Order Møller-Plesset Perturbation Theory. , 2007, Journal of chemical theory and computation.

[35]  Martin Head-Gordon,et al.  Analytical gradient of restricted second-order Møller-Plesset correlation energy with the resolution of the identity approximation, applied to the TCNE dimer anion complex , 2006 .

[36]  Masato Kobayashi,et al.  Implementation of Surjan's density matrix formulae for calculating second-order Møller-Plesset energy , 2006 .

[37]  Christof Hättig,et al.  Optimization of auxiliary basis sets for RI-MP2 and RI-CC2 calculations: Core–valence and quintuple-ζ basis sets for H to Ar and QZVPP basis sets for Li to Kr , 2005 .

[38]  Christian Ochsenfeld,et al.  Rigorous integral screening for electron correlation methods. , 2005, The Journal of chemical physics.

[39]  Péter R. Surján,et al.  The MP2 energy as a functional of the Hartree–Fock density matrix , 2005 .

[40]  Yong Dou,et al.  64-bit floating-point FPGA matrix multiplication , 2005, FPGA '05.

[41]  T Daniel Crawford,et al.  Potential energy surface discontinuities in local correlation methods. , 2004, The Journal of chemical physics.

[42]  Thomas Bondo Pedersen,et al.  Reduced scaling in electronic structure calculations using Cholesky decompositions , 2003 .

[43]  Frederick R. Manby,et al.  Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations , 2003 .

[44]  F. Weigend,et al.  Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations , 2002 .

[45]  Georg Hetzer,et al.  Low-order scaling local correlation methods II: Splitting the Coulomb operator in linear scaling local second-order Møller–Plesset perturbation theory , 2000 .

[46]  David E. Bernholdt,et al.  Scalability of correlated electronic structure calculations on parallel computers: A case study of the RI-MP2 method , 2000, Parallel Comput..

[47]  Martin Head-Gordon,et al.  Closely approximating second-order Mo/ller–Plesset perturbation theory with a local triatomics in molecules model , 2000 .

[48]  Georg Hetzer,et al.  Low-order scaling local electron correlation methods. I. Linear scaling local MP2 , 1999 .

[49]  Philippe Y. Ayala,et al.  Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems , 1999 .

[50]  Martin Head-Gordon,et al.  Noniterative local second order Mo/ller–Plesset theory: Convergence with local correlation space , 1998 .

[51]  Holger Patzelt,et al.  RI-MP2: optimized auxiliary basis sets and demonstration of efficiency , 1998 .

[52]  D. Bernholdt,et al.  Large-scale correlated electronic structure calculations: the RI-MP2 method on parallel computers , 1996 .

[53]  Martin W. Feyereisen,et al.  Use of approximate integrals in ab initio theory. An application in MP2 energy calculations , 1993 .

[54]  Jan Almlöf,et al.  Elimination of energy denominators in Møller—Plesset perturbation theory by a Laplace transform approach , 1991 .

[55]  K. A. Gallivan,et al.  Parallel Algorithms for Dense Linear Algebra Computations , 1990, SIAM Rev..

[56]  Martin H. Schultz,et al.  Numerical Algorithms for Modern Parallel Computer Architectures , 1988 .

[57]  Jack Dongarra,et al.  Linear algebra on high performance computers , 1986 .

[58]  Peter Pulay,et al.  Orbital-invariant formulation and second-order gradient evaluation in Møller-Plesset perturbation theory , 1986 .

[59]  Peter Pulay,et al.  Localizability of dynamic electron correlation , 1983 .

[60]  Jack B. Dennis,et al.  Data Flow Supercomputers , 1980, Computer.

[61]  J. Connolly,et al.  On first‐row diatomic molecules and local density models , 1979 .

[62]  J. L. Whitten,et al.  Coulombic potential energy integrals and approximations , 1973 .

[63]  Guangwen Yang,et al.  Chapter Four - Data Flow Computing in Geoscience Applications , 2017, Adv. Comput..

[64]  Alán Aspuru-Guzik,et al.  Accelerating Resolution-ofthe-Identity Second Order Møller-Plesset Quantum Chemistry Calculations with Graphical Processing Units , 2007 .

[65]  Brett I. Dunlap,et al.  Robust and variational fitting , 2000 .

[66]  Emily A. Carter,et al.  Pseudospectral Møller-Plesset perturbation theory through third order , 1994 .

[67]  Jan Almlöf,et al.  Laplace transform techniques in Mo/ller–Plesset perturbation theory , 1992 .

[68]  Robert Schreiber,et al.  Block Algorithms for Parallel Machines , 1988 .

[69]  H. T. Kung Why systolic architectures? , 1982, Computer.