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.

ONETEPLinear scaling quantum mechanical calculations

Peter Haynes

Arash Mostofi

Imperial College, London

Chris Kriton Skylaris

University of Southampton

0

10

20

30

40

50

60

0 500 1000 1500 2000 2500

Number of atoms

To

tal t

ime

(h)ONETEP

CASTEP

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 1 10 100 1000 1,000,000Time 0 0 ps ns s

0

0.0001 eV

qualitative

topological

0.01 eV

Tight binding

empirical

DFT

QMCCI

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 1991.

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. Kermode1, T. Albaret2, D. Sherman3, N. Bernstein4,P. Gumbsch5,6, MCP, G. Csányi7 & A. De Vita8,9

1. TCM Group, Cavendish Laboratory2. 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 Freiburg7. 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 ofstress fields around the crack tip

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

Multiscalemodelling

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 1 10 100 1000 1,000,000Time 0 0 ps ns s

0

0.0001 eV

qualitative

topological

0.01 eV

Tight binding

empirical

DFT

QMCCI

Accuracy

But larger systems have longer timescales

Mark Buchanan, New Scientist, p42 Vol. 2157 magazine, 24 October 1998

The timescale problem

Some sampling based approaches:Simulated annealingRandom sampling – Needs and PickardGeneric algorithms – Nested sampling – Csanyi and Bartok-Partay

Mark Buchanan, New Scientist, p42 Vol. 2157 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. 2157 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 – VoterMetadynamics – Parrinello

Mark Buchanan, New Scientist, p42 Vol. 2157 magazine, 24 October 1998

The efficient solution to the unknown unknowns

Metadynamics with machine learningParrinello

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.