Kappa float, default: 1.96. Controls how much of the variance in the predicted values should be taken into account. If set to be very high, then we are favouring exploration over exploitation and vice versa. Used when the acquisition is 'LCB'. Xi float, default: 0.01. Controls how much improvement one wants over the previous best values.
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- @muhammadfahid51, optimizer.minimize function requires two argument loss and varlist. In your code replace optimizer.minimize(loss) with optimizer.minimize(loss, varlist=None). For more see this link.
- Nelder, J A, and R Mead. A Simplex Method for Function Minimization. The Computer Journal 7: 308-13. Direct search methods: Once scorned, now respectable, in Numerical Analysis 1995: Proceedings of the 1995 Dundee Biennial Conference in Numerical Analysis (Eds. D F Griffiths and G A Watson).
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Syntax
- etol = stopping tolerance for energy (unitless)
- ftol = stopping tolerance for force (force units)
- maxiter = max iterations of minimizer
- maxeval = max number of force/energy evaluations
Examples
Description
Perform an energy minimization of the system, by iteratively adjustingatom coordinates. Iterations are terminated when one of the stoppingcriteria is satisfied. At that point the configuration will hopefullybe in local potential energy minimum. More precisely, theconfiguration should approximate a critical point for the objectivefunction (see below), which may or may not be a local minimum.
The minimization algorithm used is set by themin_style command. Other options are set by themin_modify command. Minimize commands can beinterspersed with run Quiver 3 2 5. commands to alternate betweenrelaxation and dynamics. The minimizers bound the distance atoms movein one iteration, so that you can relax systems with highly overlappedatoms (large energies and forces) by pushing the atoms off of eachother.
Alternate means of relaxing a system are to run dynamics with a smallor limited timestep. Or dynamics can be runusing fix viscous to impose a damping force thatslowly drains all kinetic energy from the system. The pair_style soft potential can be used to un-overlap atoms whilerunning dynamics.un-overlap atoms while running dynamics.
Note that you can minimize some atoms in the system while holding thecoordinates of other atoms fixed by applying fix setforce to the other atoms. See a fuller discussion of usingfixes while minimizing below.
The minimization stylescg, sd, and hftninvolves an outer iteration loop which sets the search direction alongwhich atom coordinates are changed. An inner iteration is thenperformed using a line search algorithm. The line search typicallyevaluates forces and energies several times to set new coordinates.Currently, a backtracking algorithm is used which may not be optimalin terms of the number of force evaluations performed, but appears tobe more robust than previous line searches we have tried. Thebacktracking method is described in Nocedal and Wright’s NumericalOptimization (Procedure 3.1 on p 41).
The minimization stylesquickmin, fire andfire/old perform damped dynamics using an Euler integration step. Thusthey require a timestep be defined.
Note
The damped dynamic minimizers use whatever timestep you havedefined via the timestep Fonepaw android data recovery 2 8 07. command. Often theywill converge more quickly if you use a timestep about 10x largerthan you would normally use for dynamics simulations.
In all cases, the objective function being minimized is the totalpotential energy of the system as a function of the N atomcoordinates:
[begin{split}E(r_1,r_2, ldots ,r_N) = & sum_{i,j} E_{it pair}(r_i,r_j) + sum_{ij} E_{it bond}(r_i,r_j) + sum_{ijk} E_{it angle}(r_i,r_j,r_k) + & sum_{ijkl} E_{it dihedral}(r_i,r_j,r_k,r_l) + sum_{ijkl} E_{it improper}(r_i,r_j,r_k,r_l) + sum_i E_{it fix}(r_i)end{split}]
where the first term is the sum of all non-bonded pairwiseinteractions including long-range Coulombicinteractions, the second through fifth terms are bond, angle, dihedral, and improper interactionsrespectively, and the last term is energy due to fixeswhich can act as constraints or apply force to atoms, such as throughinteraction with a wall. See the discussion below about how fixcommands affect minimization.
The starting point for the minimization is the current configurationof the atoms.
The minimization procedure stops if any of several criteria are met:
- the change in energy between outer iterations is less than etol
- the 2-norm (length) of the global force vector is less than the ftol
- the line search fails because the step distance backtracks to 0.0
- the number of outer iterations or timesteps exceeds maxiter
- the number of total force evaluations exceeds maxeval
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the minimization stylespin,spin/cg, and spin/lbfgs replacethe force tolerance ftol by a torque tolerance.The minimization procedure stops if the 2-norm (length) of the torque vector on atom(defined as the cross product between theatomic spin and its precession vectors omega) is less than ftol,or if any of the other criteria are met. Torque have the same units as the energy.
Note
You can also use the fix halt command to specifya general criterion for exiting a minimization, that is acalculation performed on the state of the current system, asdefined by an equal-style variable.
For the first criterion, the specified energy tolerance etol isunitless; it is met when the energy change between successiveiterations divided by the energy magnitude is less than or equal tothe tolerance. For example, a setting of 1.0e-4 for etol means anenergy tolerance of one part in 10^4. For the damped dynamicsminimizers this check is not performed for a few steps aftervelocities are reset to 0, otherwise the minimizer would prematurelyconverge.
For the second criterion, the specified force tolerance ftol is inforce units, since it is the length of the global force vector for allatoms, e.g. a vector of size 3N for N atoms. Since many of thecomponents will be near zero after minimization, you can think offtol as an upper bound on the final force on any component of anyatom. For example, a setting of 1.0e-4 for ftol means no x, y, or zcomponent of force on any atom will be larger than 1.0e-4 (in forceunits) after minimization.
Either or both of the etol and ftol values can be set to 0.0, inwhich case some other criterion will terminate the minimization.
During a minimization, the outer iteration count is treated as atimestep. Output is triggered by this timestep, e.g. thermodynamicoutput or dump and restart files.
Using the thermo_style custom command with thefmax or fnorm keywords can be useful for monitoring the progressof the minimization. Note that these outputs will be calculated onlyfrom forces on the atoms, and will not include any extra degrees offreedom, such as from the fix box/relax command.
Following minimization, a statistical summary is printed that listswhich convergence criterion caused the minimizer to stop, as well asinformation about the energy, force, final line search, and iterationcounts. An example is as follows:
The 3 energy values are for before and after the minimization and onthe next-to-last iteration. This is what the etol parameter checks.
The two-norm force values are the length of the global force vectorbefore and after minimization. This is what the ftol parameterchecks.
The max-component force values are the absolute value of the largestcomponent (x,y,z) in the global force vector, i.e. the infinity-normof the force vector.
The alpha parameter for the line-search, when multiplied by the maxforce component (on the last iteration), gives the max distance anyatom moved during the last iteration. Alpha will be 0.0 if the linesearch could not reduce the energy. Even if alpha is non-zero, if the“max atom move” distance is tiny compared to typical atom coordinates,then it is possible the last iteration effectively caused no atommovement and thus the evaluated energy did not change and theminimizer terminated. Said another way, even with non-zero forces,it’s possible the effect of those forces is to move atoms a distanceless than machine precision, so that the energy cannot be furtherreduced.
The iterations and force evaluation values are what is checked by themaxiter and maxeval parameters.
Note
There are several force fields in LAMMPS which havediscontinuities or other approximations which may prevent you fromperforming an energy minimization to high tolerances. For example,you should use a pair style that goes to 0.0 at thecutoff distance when performing minimization (even if you later changeit when running dynamics). If you do not do this, the total energy ofthe system will have discontinuities when the relative distancebetween any pair of atoms changes from cutoff+epsilon tocutoff-epsilon and the minimizer may behave poorly. Some of themany-body potentials use splines and other internal cutoffs thatinherently have this problem. The long-range Coulombic styles (PPPM, Ewald) are approximate to within theuser-specified tolerance, which means their energy and forces may notagree to a higher precision than the Kspace-specified tolerance. Inall these cases, the minimizer may give up and stop before finding aminimum to the specified energy or force tolerance.
Note that a cutoff Lennard-Jones potential (and others) can be shiftedso that its energy is 0.0 at the cutoff via thepair_modify command. See the doc pages forindividual pair styles for details. Note thatCoulombic potentials always have a cutoff, unless versions with along-range component are used (e.g. pair_style lj/cut/coul/long). The CHARMM potentials go to 0.0 atthe cutoff (e.g. pair_style lj/charmm/coul/charmm),as do the GROMACS potentials (e.g. pair_style lj/gromacs).
If a soft potential (pair_style soft) is used theAstop value is used for the prefactor (no time dependence).
The fix box/relax command can be used to apply anexternal pressure to the simulation box and allow it to shrink/expandduring the minimization.
Only a few other fixes (typically those that add forces) are invokedduring minimization. See the doc pages for individual fixcommands to see which ones are relevant. Current examples of fixesthat can be used include:
Note
Some fixes which are invoked during minimization have anassociated potential energy. For that energy to be included in thetotal potential energy of the system (the quantity being minimized),you MUST enable the fix_modifyenergy option forthat fix. The doc pages for individual fix commandsspecify if this should be done.
Note
The minimizers in LAMMPS do not allow for bonds (or angles, etc)to be held fixed while atom coordinates are being relaxed, e.g. viafix shake or fix rigid. See moreinfo in the Restrictions section below.
Styles with a gpu, intel, kk, omp, or opt suffix arefunctionally the same as the corresponding style without the suffix.They have been optimized to run faster, depending on your availablehardware, as discussed on the Speed packages docpage. The accelerated styles take the same arguments and shouldproduce the same results, except for round-off and precision issues.
These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,USER-OMP and OPT packages, respectively. They are only enabled ifLAMMPS was built with those packages. See the Build package doc page for more info.
You can specify the accelerated styles explicitly in your input scriptby including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use thesuffix command in your input script.
![Minimizer 100061 Minimizer 100061](https://is5-ssl.mzstatic.com/image/thumb/Purple22/v4/08/db/94/08db94b3-fa0f-1d91-e118-dec5f17355a5/source/1920x1080bb.png)
See the Speed packages doc page for moreinstructions on how to use the accelerated styles effectively.
Restrictions
Features that are not yet implemented are listed here, in case someoneknows how they could be coded:
It is an error to use fix shake with minimizationbecause it turns off bonds that should be included in the potentialenergy of the system. The effect of a fix shake can be approximatedduring a minimization by using stiff spring constants for the bondsand/or angles that would normally be constrained by the SHAKEalgorithm.
Minimizer 100079
Fix rigid is also not supported by minimization. Itis not an error to have it defined, but the energy minimization willnot keep the defined body(s) rigid during the minimization. Note thatif bonds, angles, etc internal to a rigid body have been turned off(e.g. via neigh_modify exclude), they will notcontribute to the potential energy which is probably not what isdesired.
Minimizer 100061
Pair potentials that produce torque on a particle (e.g. granular potentials or the GayBerne potential for ellipsoidal particles) are notrelaxed by a minimization. More specifically, radial relaxations areinduced, but no rotations are induced by a minimization, so such asystem will not fully relax.
Default
none
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