Adaptive and Localized Basis Functions for Linear Scaling, Large Systems and Complex QM Simulations
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1 Max Conference on the Materials Design Ecosystem at the Exascale: High-Performance and High-Throughput Computing TRIESTE Adaptive and Localized Basis Functions for Linear Scaling, Large Systems and Complex QM Simulations Luigi Genovese, Stephan Mohr, L. Ratcliff, D. Caliste, S. Goedecker, T. Deutsch INAC CEA Grenoble January 30, 2018
2 BigDFT: A DFT code based on Daubechies wavelets A pseudopotential Kohn-Sham code Daubechies wavelets have unique properties for DFT usage Systematic, Orthogonal Localised, Adaptive Kohn-Sham operators are analytic Efficient Poisson solver, capable of handling different boundary conditions free, wire, surface, periodic φ(x) ψ(x) Explicit treatment of charged systems x
3 Adaptivity of the mesh Atomic positions (H 2 O)
4 Adaptivity of the mesh Fine grid (high resolution)
5 Adaptivity of the mesh Coarse grid (low resolution)
6 Adaptivity of the mesh No close form: Scaling relations! All functions have compact support, centered on grid points. φ(x) = m j= m h j φ(2x j) We only use the filters h j : short convolutions (GPU-friendly) φ(x) ψ(x) x
7 DeltaTest benchmark: = 1.0 Science, 351, 6280 (2016) For the first three rows Screenshot of DeltaTest webpage as of 24/02/16, elements up to Ar, new NLCC - HGH - NC - PSP (S. Saha)
8 version A code both for solid-state and physical chemistry 3D periodic, surfaces and free BC ( Poisson Solver) Usage of analytic HGH pseudopotentials Very high precision (analytic Kohn-Sham operators) All-electron accuracy, benchs in G2-1, (DeltaTest) Present functionalities Kohn-Sham DFT (metals, van der Walls, Hybrid Functionals), Systems embedded in electrostatic environments, Library of Structural Prediction, O(N) calculations Under implementation Non orthorhombic cells, PAW, linear response TD-DFT
9 BigDFT breakdown process (1.8.x) Modularity first Each section of BigDFT is, when appropriate, defined as a module with its own build system and compilation instructions. At present: FUTILE 1.0 (low level) GaIn 1.0 (Gaussian Integral from Fiesta GW code) CheSS 1.0 (talk Stephan) PSolver 1.8 Poisson solver + exchange
10 Hybrid Functionals for large systems γ=pbe0/pbe Since 2009, BigDFT ported on GPU. Use for the exchange part (N 2 Poisson Solver evaluations).
11 Hybrid Functionals for large systems γ=pbe0/pbe UO 2 systems: Atoms Orbitals
12 Scaling of Traditional BigDFT (linear scaling) Traditional BigDFT code We can reach systems containing up to a few thousand electrons thanks to wavelet properties and efficient parallelization: (MPI + OpenMP + GPU) DFT operations scale differently: O(N log N): Poisson solver O(N 2 ): convolutions O(N 3 ): linear algebra Time / iteration (s) and have different prefactors: c O(N3 ) c O(N2 ) c O(N log N) 0 For bigger systems the O(N 3 ) will dominate Number of atoms Motivation for a new approach
13 Localized optimized minimal basis set Kohn-Sham orbitals Linear combinations of support functions φ α (r): Ψ i (r) = c α i φ α (r) α localized around atoms expanded in wavelets optimized in-situ Density Matrix (linear scaling) Defined via the kernel K αβ in the φ α (r) basis: ρ(r,r ) = f i Ψ i (r)ψ i (r ) i = φ α (r)k αβ φ β (r ) α,β Localization Sparse matrices (H αβ, K αβ ) O (N)
14 Comparison with the cubic version (linear scaling) total runtime linear total runtime cubic linear extrapolation, reference 3000 atoms time (seconds) min for atoms CPU Time and memory number of atoms number of atoms High flexibility, like the cubic code Different levels of precision via the cutoff radii: Without fine-tuning converges to absolute energy differences of the order of 10 mev/atom, and almost exact forces. System sizes: K atoms 1M basis functions
15 Features of the localized optimized minimal basis set Ideal properties to work at the many thousand atoms scale Accurate results with good localization Low No. of degrees of freedom Low condition number (quasi-orthogonal) Small Spectral Width (thanks to pseudo-potential) S H system (#atoms) sparsity κ sparsity SW (ev) DNA (15613) 99.57% % bulk pentacene (6876) 98.96% % perovskite (768) 90.34% % Si nanowire (706) 93.24% % H 2 O droplet (1800) 96.71% % 38.26
16 Our record: 250,000 atoms (Stephan Mohr) Algorithm is robust and reliable on a variety of systems Accurate and efficient linear scaling DFT calculations with universal applicability S. Mohr, L. E. Ratcliff, L. Genovese, D. Caliste, P. Boulanger, S. Goedecker and T. Deutsch Phys. Chem. Chem. Phys., 2015, 17, 47, DOI: /c5cp00437c Included in the Real-space numerical grid methods in quantum chemistry themed issue of PCCP Guest-edited by Luca Frediani (The Arctic University of Norway) and Dage Sundholm (University of Helsinki)
17 Why do we need so Large scale DFT? O (N ) vers. Laboratoire de Simulation Atomistique T. Deutsch, L. Genovese
18 Review of O(N) DFT calculations New calculation paradigms are emerging!
19 between different methods! O (N ) vers. Laboratoire de Simulation Atomistique T. Deutsch, L. Genovese
20 Testing different approaches and models I Fragments : Constrained DFT, Charge transfer, Excitations I Atomic charge analysis I Statistics of atomic configurations (snapshots from MD with force fields) I Impact of the (electrostatic) environment I Comparison between Full QM, QM/QM, and MM calculations O (N ) vers. Laboratoire de Simulation Atomistique T. Deutsch, L. Genovese
21 Dividing a system into fragments JCP 142, (2015) support function optimization We can duplicate the localized adapted orbitals for similar portions of large systems considerably reduces the cost support function reformatting O (N ) vers. * Enables manipulation of optimized basis sets (need an efficient reformatting) 4 Efficient and precise roto-translation of localized orbitals Reformatting the minimal basis set in the same grid Laboratoire de Simulation Atomistique T. Deutsch, L. Genovese
22 Fragment: Charge transport in OLEDs (statistics) Impact of environment in a realistic host-guest morphology: 6192 at., 100 molecules L. Ratcliff et al. JCP 142, (2015) Host molecule O (N ) vers. 4,4 -N,N -dicarbazole-biphenyl Guest molecule tris(2-phenylpyridine)iridium Laboratoire de Simulation Atomistique T. Deutsch, L. Genovese
23 Complex Input files: What we need? Need to build complex files and process output files Use of a Human readable markup language (YAML) An output file can be an input file to rerun a simulation Easy to parse and process as Python dictionaries Develop the Fortran FUTILE library Towards workflows (Jupyter notebooks)
24 Which structure for the data? Disclaimer: Personal experience Block structured YAML A clean and very human readable format. Very good choice for configuration files that are human readable and editable while at the same time interpretable and modifiable by a program. YAML parsers are available for scripting languages (Python, Ruby) FUTILE approach to input variables and options Options defined like an input file (key value) Logfiles come structured similarly Usage of structured I/O at FORTRAN level Allows for legacy code and enhanced modularity
25 Example of the input dictionary (YAML format) Use for Input and Output files! setup: taskgroup_size : 0 # Size of the taskgroups accel : none # Acceleration global_data : No verbose : Yes #Verbosity switch output : none #Quantities to be plotted kernel: screening : 0 #Mu screening parameter isf_order : 16 #Order of the ISF family stress_tensor : Yes #Extract stress tensor environment: cavity : none #Type of the cavity cavitation : No # Extra cavitation terms input_guess : Yes #Input guess procedure fd_order : 16 #Order of FD derivatives itermax : 50 #Max. No.of GPS iterations minres : 1.e-6 #Convergence threshold pb_method : none #Poisson Boltzmann Equation
26 How can we benefit from this? Understanding code behaviour on a new architecture Identify optimization strategies for the end-user (modification of the input file) Small demo, notebooks based on jupyter
27 Perspectives Linear-Scaling DFT: Opens up new possibilities Robust convergence, high accuracy and flexibility (BC) Reduction in degrees of freedom large systems via moderate sized machines ( TFlop/s) Lab-scale Different level of descriptions (controlling the precision) QM Fragments Atomic charges Challenges and future directions Explore interplay environment electronic excitations (CDFT, QM/MM, statistics,... ) Provide high quality back end for extraction of atomic multipoles from QM calculations Explore Linear Response Time-Dependent DFT,...
28 Acknowledgments Main maintainer Luigi Genovese Group of Stefan Goedecker Basel University B. Schaefer, A. Ghazemi, S. Saha, G. Fisicaros Order N methods (fragments, constrained DFT) Stephan Mohr (BSC), L. Ratcliff (Imperial College), Paul Boulanger (U. Montreal) Link with ABINIT and python bindings Damien Caliste (CEA) Hybrid Functionals, GPU A. Degomme (CEA) Optimized convolutions B. Videau, J.-F. Méhaut (LIG, computer scientists, Grenoble)
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