The End of Simulation? Mike Payne

If we are honest about the usefulness of simulations they should be: Genuinely predictive Free of adjustable parameters Computationally tractable and affordable..... and if you want lots of people to use them then running the simulations should be as simple as possible – ideally nothing beyond specifying the system.

ONETEP Linear scaling quantum mechanical calculations Peter Haynes Arash Mostofi Imperial College, London Chris Kriton Skylaris University of Southampton

Total energy calculations with ONETEP on pieces of DNA. The total time taken by each DNA piece is plotted as a function of the number of atoms. Also shown are times for calculations of equivalent quality with CASTEP. Application to DNA £20

Hierarchies of atomistic modelling Atoms ,000,000 Time 0 0 ps ns  s eV qualitative topological 0.01 eV Tight binding empirical DFT QMC CI Accuracy

DFT Empirical atomistic Continuum Multiscale Modelling Schemes Correlated QM

Scheme to couple continuum simulations to empirical simulations developed by Peter Gumbsch and co-workers in Many similar examples: electrostatics, solvation,... What about coupling DFT (or cheap QM) atomistic and empirical atomistic simulations.? Many so-called QM/MM schemes - few of them suitable for dynamicalyl evolving systems – let alone being parameter-free, predictive and usable.

“Learn on the fly” - Hybrid classical/ quantum molecular dynamics simulation Gábor Csányi Engineering, Cambridge Alessandro De Vita King’s College, London

Learn on the Fly Scheme (LOTF) Empirical Atomistic Continuum Atoms represented by empirical potentials with parameters fit to a quantum mechanical calculation

“Learn on the fly” Gábor Csányi 10 Learning the environment

Crack Propagation in Silicon J.R. Kermode 1, T. Albaret 2, D. Sherman 3, N. Bernstein 4, P. Gumbsch 5,6, MCP, G. Csányi 7 & A. De Vita 8,9 1. TCM Group, Cavendish Laboratory 2. Université de Lyon 1, 3. Department of Materials Engineering, Technion–Israel Institute of Technology, 4. Center for Computational Materials Science, NRL, 5. Institut für Zuverlässigkeit von Bauteilen und Systemen, Universitat Karlsruhe 6. Fraunhofer–Institut für Werkstoffmechanik Freiburg 7. Engineering Laboratory, University of Cambridge. 8. Dept. of Physics, King’s College London, 9. INFM–DEMOCRITOS CENMAT, University of Trieste

Propagation of [1-10] (111) crack in silicon Kermode et al., Nature 455, 1224 (2008) This gives detailed description of stress fields around the crack tip

Propagation of [1-10] (111) crack in silicon

Multiscale modelling

BUT

Albert Bartok-Partay & Gabor Csanyi, Engineering, Cambridge Imre Risi Kondor, Caltech

‘An art rather than a science’

Surface energies MEAM error ≈ 20-30%

Considerable recent progress by empirically correcting the limitations of DFT – DFT-D, LDA+U,.... What about when you do need properly correlated QM methods coupled to DFT simpler QM? Simple in the case of, say CI, region within Hartree-Fock calculation. Alternative approach – DMFT (Cedric Weber).

DFT Empirical atomistic Continuum Hybrid Modelling Schemes (QM/MM) Correlated QM

BUT

Hierarchies of atomistic modelling Atoms ,000,000 Time 0 0 ps ns  s eV qualitative topological 0.01 eV Tight binding empirical DFT QMC CI Accuracy But larger systems have longer timescales

Mark Buchanan, New Scientist, p42 Vol magazine, 24 October 1998 The timescale problem Some sampling based approaches: Simulated annealing Random sampling – Needs and Pickard Generic algorithms – Nested sampling – Csanyi and Bartok-Partay

Mark Buchanan, New Scientist, p42 Vol magazine, 24 October 1998 The ‘known unknowns’ The long timescales are usually associated with getting over energy barriers between minima. IF the end points are known then many techniques exist for finding the transition state and its energy or free energy: Nudged elastic band, LST, QST, Blue Moon, OPTIM - Wales

Mark Buchanan, New Scientist, p42 Vol magazine, 24 October 1998 So the problem is the ‘unknown unknowns’ Speeding up dynamics: Parallelise time ie do multiple uncorrelated dynamical simulations (perfect for Exaflops computers) Hyperdynamics – Voter Metadynamics – Parrinello

Mark Buchanan, New Scientist, p42 Vol magazine, 24 October 1998 The efficient solution to the unknown unknowns Metadynamics with machine learning Parrinello So is everything in place to be able to perform predictive, parameter free simulations for any system – ie the end of simulation as an intellectual challenge ? Not quite – need to retain data for re-use.