fire: fast inertial relaxation engine for optimization on all...
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![Page 1: FIRE: Fast Inertial Relaxation Engine for Optimization on All Scalesusers.jyu.fi/~pekkosk/resources/pdf/FIRE.pdf · 2013-01-17 · FIRE: Fast Inertial Relaxation Engine for Optimization](https://reader033.vdocuments.us/reader033/viewer/2022052722/5f0cd6107e708231d4375f34/html5/thumbnails/1.jpg)
FIREFIRE: Fast Inertial Relaxation Enginefor Optimization on All Scales
P. KoskinenE. Bitzek, F. Gähler, M. Moseler, and P. Gumbsch
Funding: Academy of Finland Fraunhofer MAVO for Multiscale Materials Modeling
Fraunhofer Institut
Werksoffmechanik
P. Koskinen 19. September 2006 Multiscale Materials Modeling
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Optimization
Local optimization:●structure optimization●constrained optimization●transition state (barrier) calculations●stability analysis●etc...
Global minimization●often uses local minimization methods
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Optimization
Local optimization:●structure optimization●constrained optimization●transition state (barrier) calculations●stability analysis●etc... Steepest Descent (SD)
Conjugate Gradient (CG)Molecular Dynamics (MD) ('quenching')Quasi-Newton (QN) (BFGS, L-BFGS)Truncated Newton (TN)etc...
Toolbox:
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Choose your weapon
![Page 5: FIRE: Fast Inertial Relaxation Engine for Optimization on All Scalesusers.jyu.fi/~pekkosk/resources/pdf/FIRE.pdf · 2013-01-17 · FIRE: Fast Inertial Relaxation Engine for Optimization](https://reader033.vdocuments.us/reader033/viewer/2022052722/5f0cd6107e708231d4375f34/html5/thumbnails/5.jpg)
P. Koskinen 19. September 2006 Multiscale Materials Modeling
Choose your weapon
![Page 6: FIRE: Fast Inertial Relaxation Engine for Optimization on All Scalesusers.jyu.fi/~pekkosk/resources/pdf/FIRE.pdf · 2013-01-17 · FIRE: Fast Inertial Relaxation Engine for Optimization](https://reader033.vdocuments.us/reader033/viewer/2022052722/5f0cd6107e708231d4375f34/html5/thumbnails/6.jpg)
P. Koskinen 19. September 2006 Multiscale Materials Modeling
Choose your weapon
– computational cost● function calls● computational overhead
– memory requirements ~ N↔N2
– robustness – easy to use? (parameters, implementation)– convergence criteria (E, F, max(F), r,...)
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Choose your weapon
– computational cost● function calls● computational overhead
– memory requirements ~ N↔N2
– robustness – easy to use? (parameters, implementation)– convergence criteria (E, F, max(F), r,...)
Molecular Dynamics (MD) ('quenching')
![Page 8: FIRE: Fast Inertial Relaxation Engine for Optimization on All Scalesusers.jyu.fi/~pekkosk/resources/pdf/FIRE.pdf · 2013-01-17 · FIRE: Fast Inertial Relaxation Engine for Optimization](https://reader033.vdocuments.us/reader033/viewer/2022052722/5f0cd6107e708231d4375f34/html5/thumbnails/8.jpg)
P. Koskinen 19. September 2006 Multiscale Materials Modeling
Clever skier
start here
minimum
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Clever (blind) skier
start here
minimum?
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Snapshot at t=ti
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Snapshot at t=ti
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Considerations
●if we go uphill ⇒ stop●use MD with discrete t: optimize t in a stable manner: right direction? ⇒increase t where to go? ⇒decrease t t should have max limit no hasty decisions●steer in the beginning, then let it go too heavy steering ⇒ SD let inertia decide the direction
All dimensions should be comparablevectors are 3N-dimensional
Fast Inertial Relaxation Engine (FIRE)
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
The algorithm
MD: calculate x, F = − ∇E(x), and v using any common MD integrator; check for convergence F1: calculate P = F · v F2: set v → (1 − α) · v + α · F/|F| · |v| F3: if P > 0 and the number of steps since P was negative is larger than N
min, increase the time step
∆t → min(∆t · finc
, ∆tmax
) and decrease α → α · fα
F4: if P ≤ 0, decrease time step ∆t → ∆t · fdec
, freeze
the system v → 0 and set α back to αstart
F5: return to MD E. Bizek, P. Koskinen, F. Gähler, M. Moseler, P. Gumbch, PRL (to appear)
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Sample code (!)
subroutine FIRE(it,dt,n,v[n],F[n],done) if( max(F) < crit ) done
P = V*F V = (1-a)*V + a*F*norm(V)/norm(F)
if( P<0 ) V = 0 cut = it dt = dt * f_dec a = a_start else if( P>=0 and it-cut>N_min ) dt = min( dt*f_inc, dt_max ) a = a * f_dec
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Results
Fenretinide (N=62)
FIRE
CG
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Results
function calls
Small convergence criteria: Na71
-
FIRE
CG
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Results
Convergence criteria: FRMS
or Fmax
<10-3 eV/Å (10-6 eV/Å)
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Summary
FIRE competes with sophisticated methods!
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Summary
FIRE competes with sophisticated methods!
Furthermore:●robust relaxation for all N●memory usage small●small computational overhead●gradient-based: stability analysis●gradient based: small convergence criteria●non-harmonic energy landscapes●stable against errors in E(x) and F(x)●constrained minimization easy●intuitive, easy adaption to new problems●application to non-atomistic problems
![Page 20: FIRE: Fast Inertial Relaxation Engine for Optimization on All Scalesusers.jyu.fi/~pekkosk/resources/pdf/FIRE.pdf · 2013-01-17 · FIRE: Fast Inertial Relaxation Engine for Optimization](https://reader033.vdocuments.us/reader033/viewer/2022052722/5f0cd6107e708231d4375f34/html5/thumbnails/20.jpg)
P. Koskinen 19. September 2006 Multiscale Materials Modeling
FIRE code
subroutine FIRE(it,dt,n,v[n],F[n],done) if( max(F) < crit ) done
P = V*F V = (1-a)*V + a*F*norm(V)/norm(F)
if( P<0 ) V = 0 cut = it dt = dt * f_dec a = a_start else if( P>=0 and it-cut>N_min ) dt = min( dt*f_inc, dt_max ) a = a * f_dec
Have fun!
Have fun!
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Do not click, clicking is not allowed.
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
Spiral
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P. Koskinen 19. September 2006 Multiscale Materials Modeling
FIRE, CG and L-BFGS