Line data Source code
1 : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2 : Copyright (c) 2016-2021 The VES code team
3 : (see the PEOPLE-VES file at the root of this folder for a list of names)
4 :
5 : See http://www.ves-code.org for more information.
6 :
7 : This file is part of VES code module.
8 :
9 : The VES code module is free software: you can redistribute it and/or modify
10 : it under the terms of the GNU Lesser General Public License as published by
11 : the Free Software Foundation, either version 3 of the License, or
12 : (at your option) any later version.
13 :
14 : The VES code module is distributed in the hope that it will be useful,
15 : but WITHOUT ANY WARRANTY; without even the implied warranty of
16 : MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 : GNU Lesser General Public License for more details.
18 :
19 : You should have received a copy of the GNU Lesser General Public License
20 : along with the VES code module. If not, see <http://www.gnu.org/licenses/>.
21 : +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
22 :
23 : #include "bias/Bias.h"
24 : #include "core/PlumedMain.h"
25 : #include "core/ActionRegister.h"
26 : #include "tools/Communicator.h"
27 : #include "tools/Grid.h"
28 : #include "tools/File.h"
29 : //#include <algorithm> //std::fill
30 :
31 : namespace PLMD {
32 : namespace ves {
33 :
34 : //+PLUMEDOC VES_BIAS VES_DELTA_F
35 : /*
36 : Implementation of VES Delta F method
37 :
38 : Implementation of VES\f$\Delta F\f$ method \cite Invernizzi2019vesdeltaf (step two only).
39 :
40 : \warning
41 : Notice that this is a stand-alone bias Action, it does not need any of the other VES module components
42 :
43 : First you should create some estimate of the local free energy basins of your system,
44 : using e.g. multiple \ref METAD short runs, and combining them with the \ref sum_hills utility.
45 : Once you have them, you can use this bias Action to perform the VES optimization part of the method.
46 :
47 : These \f$N+1\f$ local basins are used to model the global free energy.
48 : In particular, given the conditional probabilities \f$P(\mathbf{s}|i)\propto e^{-\beta F_i(\mathbf{s})}\f$
49 : and the probabilities of being in a given basin \f$P_i\f$, we can write:
50 : \f[
51 : e^{-\beta F(\mathbf{s})}\propto P(\mathbf{s})=\sum_{i=0}^N P(\mathbf{s}|i)P_i \, .
52 : \f]
53 : We use this free energy model and the chosen bias factor \f$\gamma\f$ to build the bias potential:
54 : \f$V(\mathbf{s})=-(1-1/\gamma)F(\mathbf{s})\f$.
55 : Or, more explicitly:
56 : \f[
57 : V(\mathbf{s})=(1-1/\gamma)\frac{1}{\beta}\log\left[e^{-\beta F_0(\mathbf{s})}
58 : +\sum_{i=1}^{N} e^{-\beta F_i(\mathbf{s})} e^{-\beta \alpha_i}\right] \, ,
59 : \f]
60 : where the parameters \f$\boldsymbol{\alpha}\f$ are the \f$N\f$ free energy differences (see below) from the \f$F_0\f$ basin.
61 :
62 : By default the \f$F_i(\mathbf{s})\f$ are shifted so that \f$\min[F_i(\mathbf{s})]=0\f$ for all \f$i=\{0,...,N\}\f$.
63 : In this case the optimization parameters \f$\alpha_i\f$ are the difference in height between the minima of the basins.
64 : Using the keyword `NORMALIZE`, you can also decide to normalize the local free energies so that
65 : \f$\int d\mathbf{s}\, e^{-\beta F_i(\mathbf{s})}=1\f$.
66 : In this case the parameters will represent not the difference in height (which depends on the chosen CVs),
67 : but the actual free energy difference, \f$\alpha_i=\Delta F_i\f$.
68 :
69 : However, as discussed in Ref. \cite Invernizzi2019vesdeltaf, a better estimate of \f$\Delta F_i\f$ should be obtained through the reweighting procedure.
70 :
71 : \par Examples
72 :
73 : The following performs the optimization of the free energy difference between two metastable basins:
74 :
75 : \plumedfile
76 : cv: DISTANCE ATOMS=1,2
77 : ves: VES_DELTA_F ...
78 : ARG=cv
79 : TEMP=300
80 : FILE_F0=fesA.data
81 : FILE_F1=fesB.data
82 : BIASFACTOR=10.0
83 : M_STEP=0.1
84 : AV_STRIDE=500
85 : PRINT_STRIDE=100
86 : ...
87 : PRINT FMT=%g STRIDE=500 FILE=Colvar.data ARG=cv,ves.bias,ves.rct
88 : \endplumedfile
89 :
90 : The local FES files can be obtained as described in Sec. 4.2 of Ref. \cite Invernizzi2019vesdeltaf, i.e. for example:
91 : - run 4 independent metad runs, all starting from basin A, and kill them as soon as they make the first transition (see e.g. \ref COMMITTOR)
92 : - \verbatim cat HILLS* > all_HILLS \endverbatim
93 : - \verbatim plumed sum_hills --hills all_HILLS --outfile all_fesA.dat --mintozero --min 0 --max 1 --bin 100 \endverbatim
94 : - \verbatim awk -v n_rep=4 '{if($1!="#!" && $1!="") {for(i=1+(NF-1)/2; i<=NF; i++) $i/=n_rep;} print $0}' all_fesA.dat > fesA.data \endverbatim
95 :
96 : The header of both FES files must be identical, and should be similar to the following:
97 :
98 : \auxfile{fesA.data}
99 : #! FIELDS cv file.free der_cv
100 : #! SET min_cv 0
101 : #! SET max_cv 1
102 : #! SET nbins_cv 100
103 : #! SET periodic_cv false
104 : 0 0 0
105 : \endauxfile
106 : \auxfile{fesB.data}
107 : #! FIELDS cv file.free der_cv
108 : #! SET min_cv 0
109 : #! SET max_cv 1
110 : #! SET nbins_cv 100
111 : #! SET periodic_cv false
112 : 0 0 0
113 : \endauxfile
114 :
115 : */
116 : //+ENDPLUMEDOC
117 :
118 : class VesDeltaF : public bias::Bias {
119 :
120 : private:
121 : double beta_;
122 : unsigned NumParallel_;
123 : unsigned rank_;
124 : unsigned NumWalkers_;
125 : bool isFirstStep_;
126 : bool afterCalculate_;
127 :
128 : //prob
129 : double tot_prob_;
130 : std::vector<double> prob_;
131 : std::vector< std::vector<double> > der_prob_;
132 :
133 : //local basins
134 : std::vector< std::unique_ptr<Grid> > grid_p_; //pointers because of GridBase::create
135 : std::vector<double> norm_;
136 :
137 : //optimizer-related stuff
138 : long long unsigned mean_counter_;
139 : unsigned mean_weight_tau_;
140 : unsigned alpha_size_;
141 : unsigned sym_alpha_size_;
142 : std::vector<double> mean_alpha_;
143 : std::vector<double> inst_alpha_;
144 : std::vector<double> past_increment2_;
145 : double minimization_step_;
146 : bool damping_off_;
147 : //'tg' -> 'target distribution'
148 : double inv_gamma_;
149 : unsigned tg_counter_;
150 : unsigned tg_stride_;
151 : std::vector<double> tg_dV_dAlpha_;
152 : std::vector<double> tg_d2V_dAlpha2_;
153 : //'av' -> 'ensemble average'
154 : unsigned av_counter_;
155 : unsigned av_stride_;
156 : std::vector<double> av_dV_dAlpha_;
157 : std::vector<double> av_dV_dAlpha_prod_;
158 : std::vector<double> av_d2V_dAlpha2_;
159 : //printing
160 : unsigned print_stride_;
161 : OFile alphaOfile_;
162 : //other
163 : std::vector<double> exp_alpha_;
164 : std::vector<double> prev_exp_alpha_;
165 : double work_;
166 :
167 : //functions
168 : void update_alpha();
169 : void update_tg_and_rct();
170 : inline unsigned get_index(const unsigned, const unsigned) const;
171 :
172 : public:
173 : explicit VesDeltaF(const ActionOptions&);
174 : void calculate() override;
175 : void update() override;
176 : static void registerKeywords(Keywords& keys);
177 : };
178 :
179 : PLUMED_REGISTER_ACTION(VesDeltaF,"VES_DELTA_F")
180 :
181 6 : void VesDeltaF::registerKeywords(Keywords& keys) {
182 6 : Bias::registerKeywords(keys);
183 12 : keys.add("optional","TEMP","temperature is compulsory, but it can be sometimes fetched from the MD engine");
184 : //local free energies
185 12 : keys.add("numbered","FILE_F","names of files containing local free energies and derivatives. "
186 : "The first one, FILE_F0, is used as reference for all the free energy differences.");
187 12 : keys.reset_style("FILE_F","compulsory");
188 12 : keys.addFlag("NORMALIZE",false,"normalize all local free energies so that alpha will be (approx) Delta F");
189 12 : keys.addFlag("NO_MINTOZERO",false,"leave local free energies as provided, without shifting them to zero min");
190 : //target distribution
191 12 : keys.add("compulsory","BIASFACTOR","0","the gamma bias factor used for well-tempered target p(s)."
192 : " Set to 0 for non-tempered flat target");
193 12 : keys.add("optional","TG_STRIDE","( default=1 ) number of AV_STRIDE between updates"
194 : " of target p(s) and reweighing factor c(t)");
195 : //optimization
196 12 : keys.add("compulsory","M_STEP","1.0","the mu step used for the Omega functional minimization");
197 12 : keys.add("compulsory","AV_STRIDE","500","number of simulation steps between alpha updates");
198 12 : keys.add("optional","TAU_MEAN","exponentially decaying average for alpha (rescaled using AV_STRIDE)."
199 : " Should be used only in very specific cases");
200 12 : keys.add("optional","INITIAL_ALPHA","( default=0 ) an initial guess for the bias potential parameter alpha");
201 12 : keys.addFlag("DAMPING_OFF",false,"do not use an AdaGrad-like term to rescale M_STEP");
202 : //output parameters file
203 12 : keys.add("compulsory","ALPHA_FILE","ALPHA","file name for output minimization parameters");
204 12 : keys.add("optional","PRINT_STRIDE","( default=10 ) stride for printing to ALPHA_FILE");
205 12 : keys.add("optional","FMT","specify format for ALPHA_FILE");
206 : //debug flags
207 12 : keys.addFlag("SERIAL",false,"perform the calculation in serial even if multiple tasks are available");
208 12 : keys.addFlag("MULTIPLE_WALKERS",false,"use multiple walkers connected via MPI for the optimization");
209 6 : keys.use("RESTART");
210 :
211 : //output components
212 12 : keys.addOutputComponent("rct","default","scalar","the reweighting factor c(t)");
213 12 : keys.addOutputComponent("work","default","scalar","the work done by the bias in one AV_STRIDE");
214 6 : }
215 :
216 4 : VesDeltaF::VesDeltaF(const ActionOptions&ao)
217 : : PLUMED_BIAS_INIT(ao)
218 4 : , isFirstStep_(true)
219 4 : , afterCalculate_(false)
220 4 : , mean_counter_(0)
221 4 : , av_counter_(0)
222 4 : , work_(0)
223 : {
224 : //set beta
225 4 : const double Kb=getKBoltzmann();
226 4 : double KbT=getkBT();
227 4 : plumed_massert(KbT>0,"your MD engine does not pass the temperature to plumed, you must specify it using TEMP");
228 4 : beta_=1.0/KbT;
229 :
230 : //initialize probability grids using local free energies
231 : bool spline=true;
232 : bool sparsegrid=false;
233 4 : std::string funcl="file.free"; //typical name given by sum_hills
234 :
235 : std::vector<std::string> fes_names;
236 8 : for(unsigned n=0;; n++)//NB: here we start from FILE_F0 not from FILE_F1
237 : {
238 : std::string filename;
239 24 : if(!parseNumbered("FILE_F",n,filename))
240 : break;
241 8 : fes_names.push_back(filename);
242 8 : IFile gridfile;
243 8 : gridfile.open(filename);
244 8 : auto g=GridBase::create(funcl,getArguments(),gridfile,sparsegrid,spline,true);
245 : // we assume this cannot be sparse. in case we want it to be sparse, some of the methods
246 : // that are available only in Grid should be ported to GridBase
247 8 : auto gg=dynamic_cast<Grid*>(g.get());
248 : // if this throws, g is deleted
249 8 : plumed_assert(gg);
250 : // release ownership in order to transfer it to emplaced pointer
251 : // cppcheck-suppress ignoredReturnValue
252 : g.release();
253 8 : grid_p_.emplace_back(gg);
254 16 : }
255 4 : plumed_massert(grid_p_.size()>1,"at least 2 basins must be defined, starting from FILE_F0");
256 4 : alpha_size_=grid_p_.size()-1;
257 4 : sym_alpha_size_=alpha_size_*(alpha_size_+1)/2; //useful for symmetric matrix [alpha_size_]x[alpha_size_]
258 : //check for consistency with first local free energy
259 8 : for(unsigned n=1; n<grid_p_.size(); n++)
260 : {
261 8 : std::string error_tag="FILE_F"+std::to_string(n)+" '"+fes_names[n]+"' not compatible with reference one, FILE_F0";
262 4 : plumed_massert(grid_p_[n]->getSize()==grid_p_[0]->getSize(),error_tag);
263 4 : plumed_massert(grid_p_[n]->getMin()==grid_p_[0]->getMin(),error_tag);
264 4 : plumed_massert(grid_p_[n]->getMax()==grid_p_[0]->getMax(),error_tag);
265 4 : plumed_massert(grid_p_[n]->getBinVolume()==grid_p_[0]->getBinVolume(),error_tag);
266 : }
267 :
268 4 : bool no_mintozero=false;
269 4 : parseFlag("NO_MINTOZERO",no_mintozero);
270 4 : if(!no_mintozero)
271 : {
272 6 : for(unsigned n=0; n<grid_p_.size(); n++)
273 4 : grid_p_[n]->setMinToZero();
274 : }
275 4 : bool normalize=false;
276 4 : parseFlag("NORMALIZE",normalize);
277 4 : norm_.resize(grid_p_.size(),0);
278 4 : std::vector<double> c_norm(grid_p_.size());
279 : //convert the FESs to probability distributions
280 : //NB: the spline interpolation will be done on the probability distributions, not on the given FESs
281 : const unsigned ncv=getNumberOfArguments(); //just for ease
282 12 : for(unsigned n=0; n<grid_p_.size(); n++)
283 : {
284 808 : for(Grid::index_t t=0; t<grid_p_[n]->getSize(); t++)
285 : {
286 800 : std::vector<double> der(ncv);
287 800 : const double val=std::exp(-beta_*grid_p_[n]->getValueAndDerivatives(t,der));
288 1600 : for(unsigned s=0; s<ncv; s++)
289 800 : der[s]*=-beta_*val;
290 800 : grid_p_[n]->setValueAndDerivatives(t,val,der);
291 800 : norm_[n]+=val;
292 : }
293 8 : c_norm[n]=1./beta_*std::log(norm_[n]);
294 8 : if(normalize)
295 : {
296 4 : grid_p_[n]->scaleAllValuesAndDerivatives(1./norm_[n]);
297 4 : norm_[n]=1;
298 : }
299 : }
300 :
301 : //get target
302 4 : double biasfactor=0;
303 4 : parse("BIASFACTOR",biasfactor);
304 4 : plumed_massert(biasfactor==0 || biasfactor>1,"BIASFACTOR must be zero (for uniform target) or greater than one");
305 4 : if(biasfactor==0)
306 2 : inv_gamma_=0;
307 : else
308 2 : inv_gamma_=1./biasfactor;
309 4 : tg_counter_=0;
310 4 : tg_stride_=1;
311 4 : parse("TG_STRIDE",tg_stride_);
312 4 : tg_dV_dAlpha_.resize(alpha_size_,0);
313 4 : tg_d2V_dAlpha2_.resize(sym_alpha_size_,0);
314 :
315 : //setup optimization stuff
316 4 : minimization_step_=1;
317 4 : parse("M_STEP",minimization_step_);
318 :
319 4 : av_stride_=500;
320 4 : parse("AV_STRIDE",av_stride_);
321 4 : av_dV_dAlpha_.resize(alpha_size_,0);
322 4 : av_dV_dAlpha_prod_.resize(sym_alpha_size_,0);
323 4 : av_d2V_dAlpha2_.resize(sym_alpha_size_,0);
324 :
325 4 : mean_weight_tau_=0;
326 4 : parse("TAU_MEAN",mean_weight_tau_);
327 4 : if(mean_weight_tau_!=1) //set it to 1 for basic SGD
328 : {
329 4 : plumed_massert((mean_weight_tau_==0 || mean_weight_tau_>av_stride_),"TAU_MEAN is rescaled with AV_STRIDE, so it has to be greater");
330 4 : mean_weight_tau_/=av_stride_; //this way you can look at the number of simulation steps to choose TAU_MEAN
331 : }
332 :
333 8 : parseVector("INITIAL_ALPHA",mean_alpha_);
334 4 : if(mean_alpha_.size()>0)
335 : {
336 2 : plumed_massert(mean_alpha_.size()==alpha_size_,"provide one INITIAL_ALPHA for each basin beyond the first one");
337 : }
338 : else
339 2 : mean_alpha_.resize(alpha_size_,0);
340 4 : inst_alpha_=mean_alpha_;
341 4 : exp_alpha_.resize(alpha_size_);
342 8 : for(unsigned i=0; i<alpha_size_; i++)
343 4 : exp_alpha_[i]=std::exp(-beta_*mean_alpha_[i]);
344 4 : prev_exp_alpha_=exp_alpha_;
345 :
346 4 : damping_off_=false;
347 4 : parseFlag("DAMPING_OFF",damping_off_);
348 4 : if(damping_off_)
349 2 : past_increment2_.resize(alpha_size_,1);
350 : else
351 2 : past_increment2_.resize(alpha_size_,0);
352 :
353 : //file printing options
354 4 : std::string alphaFileName("ALPHA");
355 4 : parse("ALPHA_FILE",alphaFileName);
356 4 : print_stride_=10;
357 8 : parse("PRINT_STRIDE",print_stride_);
358 : std::string fmt;
359 4 : parse("FMT",fmt);
360 :
361 : //other flags, mainly for debugging
362 4 : NumParallel_=comm.Get_size();
363 4 : rank_=comm.Get_rank();
364 4 : bool serial=false;
365 4 : parseFlag("SERIAL",serial);
366 4 : if(serial)
367 : {
368 2 : log.printf(" -- SERIAL: running without loop parallelization\n");
369 2 : NumParallel_=1;
370 2 : rank_=0;
371 : }
372 :
373 4 : bool multiple_walkers=false;
374 4 : parseFlag("MULTIPLE_WALKERS",multiple_walkers);
375 4 : if(!multiple_walkers)
376 2 : NumWalkers_=1;
377 : else
378 : {
379 2 : if(comm.Get_rank()==0)//multi_sim_comm works well on first rank only
380 2 : NumWalkers_=multi_sim_comm.Get_size();
381 2 : if(comm.Get_size()>1) //if each walker has more than one processor update them all
382 0 : comm.Bcast(NumWalkers_,0);
383 : }
384 :
385 4 : checkRead();
386 :
387 : //restart if needed
388 4 : if(getRestart())
389 : {
390 2 : IFile ifile;
391 2 : ifile.link(*this);
392 2 : if(NumWalkers_>1)
393 4 : ifile.enforceSuffix("");
394 2 : if(ifile.FileExist(alphaFileName))
395 : {
396 2 : log.printf(" Restarting from: %s\n",alphaFileName.c_str());
397 2 : log.printf(" all options (also PRINT_STRIDE) must be consistent!\n");
398 2 : log.printf(" any INITIAL_ALPHA will be overwritten\n");
399 2 : ifile.open(alphaFileName);
400 : double time;
401 2 : std::vector<double> damping(alpha_size_);
402 20 : while(ifile.scanField("time",time)) //room for improvements: only last line is important
403 : {
404 16 : for(unsigned i=0; i<alpha_size_; i++)
405 : {
406 8 : const std::string index(std::to_string(i+1));
407 8 : prev_exp_alpha_[i]=std::exp(-beta_*mean_alpha_[i]);
408 16 : ifile.scanField("alpha_"+index,mean_alpha_[i]);
409 16 : ifile.scanField("auxiliary_"+index,inst_alpha_[i]);
410 16 : ifile.scanField("damping_"+index,damping[i]);
411 : }
412 8 : ifile.scanField();
413 8 : mean_counter_+=print_stride_;
414 : }
415 4 : for(unsigned i=0; i<alpha_size_; i++)
416 : {
417 2 : exp_alpha_[i]=std::exp(-beta_*mean_alpha_[i]);
418 2 : past_increment2_[i]=damping[i]*damping[i];
419 : }
420 : //sync all walkers and treads. Not sure is mandatory but is no harm
421 2 : comm.Barrier();
422 2 : if(comm.Get_rank()==0)
423 2 : multi_sim_comm.Barrier();
424 : }
425 : else
426 0 : log.printf(" -- WARNING: restart requested, but no '%s' file found!\n",alphaFileName.c_str());
427 2 : }
428 :
429 : //setup output file with Alpha values
430 4 : alphaOfile_.link(*this);
431 4 : if(NumWalkers_>1)
432 : {
433 2 : if(comm.Get_rank()==0 && multi_sim_comm.Get_rank()>0)
434 : alphaFileName="/dev/null"; //only first walker writes on file
435 4 : alphaOfile_.enforceSuffix("");
436 : }
437 4 : alphaOfile_.open(alphaFileName);
438 4 : if(fmt.length()>0)
439 8 : alphaOfile_.fmtField(" "+fmt);
440 :
441 : //add other output components
442 12 : addComponent("rct"); componentIsNotPeriodic("rct");
443 8 : addComponent("work"); componentIsNotPeriodic("work");
444 :
445 : //print some info
446 4 : log.printf(" Temperature T: %g\n",1./(Kb*beta_));
447 4 : log.printf(" Beta (1/Kb*T): %g\n",beta_);
448 4 : log.printf(" Local free energy basins files and normalization constants:\n");
449 12 : for(unsigned n=0; n<grid_p_.size(); n++)
450 8 : log.printf(" F_%d filename: %s c_%d=%g\n",n,fes_names[n].c_str(),n,c_norm[n]);
451 4 : if(no_mintozero)
452 2 : log.printf(" -- NO_MINTOZERO: local free energies are not shifted to be zero at minimum\n");
453 4 : if(normalize)
454 2 : log.printf(" -- NORMALIZE: F_n+=c_n, alpha=DeltaF\n");
455 4 : log.printf(" Using target distribution with 1/gamma = %g\n",inv_gamma_);
456 4 : log.printf(" and updated with stride %d\n",tg_stride_);
457 4 : log.printf(" Step for the minimization algorithm: %g\n",minimization_step_);
458 4 : log.printf(" Stride for the ensemble average: %d\n",av_stride_);
459 4 : if(mean_weight_tau_>1)
460 2 : log.printf(" Exponentially decaying average with weight=tau/av_stride=%d\n",mean_weight_tau_);
461 4 : if(mean_weight_tau_==1)
462 0 : log.printf(" +++ WARNING +++ setting TAU_MEAN=1 is equivalent to use simple SGD, without mean alpha nor hessian contribution\n");
463 4 : log.printf(" Initial guess for alpha:\n");
464 8 : for(unsigned i=0; i<alpha_size_; i++)
465 4 : log.printf(" alpha_%d = %g\n",i+1,mean_alpha_[i]);
466 4 : if(damping_off_)
467 2 : log.printf(" -- DAMPING_OFF: the minimization step will NOT become smaller as the simulation goes on\n");
468 4 : log.printf(" Printing on file %s with stride %d\n",alphaFileName.c_str(),print_stride_);
469 4 : if(serial)
470 2 : log.printf(" -- SERIAL: running without loop parallelization\n");
471 4 : if(NumParallel_>1)
472 2 : log.printf(" Using multiple threads per simulation: %d\n",NumParallel_);
473 4 : if(multiple_walkers)
474 : {
475 2 : log.printf(" -- MULTIPLE_WALKERS: multiple simulations will combine statistics for the optimization\n");
476 2 : if(NumWalkers_>1)
477 : {
478 2 : log.printf(" number of walkers: %d\n",NumWalkers_);
479 2 : log.printf(" walker rank: %d\n",multi_sim_comm.Get_rank()); //only comm.Get_rank()=0 prints, so this is fine
480 : }
481 : else
482 0 : log.printf(" +++ WARNING +++ only one replica found: are you sure you are running MPI-connected simulations?\n");
483 : }
484 4 : log.printf(" Bibliography ");
485 8 : log<<plumed.cite("Invernizzi and Parrinello, J. Chem. Theory Comput. 15, 2187-2194 (2019)");
486 8 : log<<plumed.cite("Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)");
487 4 : if(inv_gamma_>0)
488 4 : log<<plumed.cite("Valsson and Parrinello, J. Chem. Theory Comput. 11, 1996-2002 (2015)");
489 :
490 : //last initializations
491 4 : prob_.resize(grid_p_.size());
492 4 : der_prob_.resize(grid_p_.size(),std::vector<double>(getNumberOfArguments()));
493 4 : update_tg_and_rct();
494 8 : }
495 :
496 804 : void VesDeltaF::calculate()
497 : {
498 : //get CVs
499 804 : const unsigned ncv=getNumberOfArguments(); //just for ease
500 804 : std::vector<double> cv(ncv);
501 1608 : for(unsigned s=0; s<ncv; s++)
502 804 : cv[s]=getArgument(s);
503 : //get probabilities for each basin, and total one
504 2412 : for(unsigned n=0; n<grid_p_.size(); n++)
505 1608 : prob_[n]=grid_p_[n]->getValueAndDerivatives(cv,der_prob_[n]);
506 804 : tot_prob_=prob_[0];
507 1608 : for(unsigned i=0; i<alpha_size_; i++)
508 804 : tot_prob_+=prob_[i+1]*exp_alpha_[i];
509 :
510 : //update bias and forces: V=-(1-inv_gamma_)*fes
511 804 : setBias((1-inv_gamma_)/beta_*std::log(tot_prob_));
512 1608 : for(unsigned s=0; s<ncv; s++)
513 : {
514 804 : double dProb_dCV_s=der_prob_[0][s];
515 1608 : for(unsigned i=0; i<alpha_size_; i++)
516 804 : dProb_dCV_s+=der_prob_[i+1][s]*exp_alpha_[i];
517 804 : setOutputForce(s,-(1-inv_gamma_)/beta_/tot_prob_*dProb_dCV_s);
518 : }
519 804 : afterCalculate_=true;
520 804 : }
521 :
522 804 : void VesDeltaF::update()
523 : {
524 : //skip first step to sync getTime() and av_counter_, as in METAD
525 804 : if(isFirstStep_)
526 : {
527 4 : isFirstStep_=false;
528 4 : return;
529 : }
530 800 : plumed_massert(afterCalculate_,"VesDeltaF::update() must be called after VesDeltaF::calculate() to work properly");
531 800 : afterCalculate_=false;
532 :
533 : //calculate derivatives for ensemble averages
534 800 : std::vector<double> dV_dAlpha(alpha_size_);
535 800 : std::vector<double> d2V_dAlpha2(sym_alpha_size_);
536 1600 : for(unsigned i=0; i<alpha_size_; i++)
537 800 : dV_dAlpha[i]=-(1-inv_gamma_)/tot_prob_*prob_[i+1]*exp_alpha_[i];
538 1600 : for(unsigned i=0; i<alpha_size_; i++)
539 : {
540 800 : d2V_dAlpha2[get_index(i,i)]=-beta_*dV_dAlpha[i];
541 1600 : for(unsigned j=i; j<alpha_size_; j++)
542 800 : d2V_dAlpha2[get_index(i,j)]-=beta_/(1-inv_gamma_)*dV_dAlpha[i]*dV_dAlpha[j];
543 : }
544 : //update ensemble averages
545 800 : av_counter_++;
546 1600 : for(unsigned i=0; i<alpha_size_; i++)
547 : {
548 800 : av_dV_dAlpha_[i]+=(dV_dAlpha[i]-av_dV_dAlpha_[i])/av_counter_;
549 1600 : for(unsigned j=i; j<alpha_size_; j++)
550 : {
551 800 : const unsigned ij=get_index(i,j);
552 800 : av_dV_dAlpha_prod_[ij]+=(dV_dAlpha[i]*dV_dAlpha[j]-av_dV_dAlpha_prod_[ij])/av_counter_;
553 800 : av_d2V_dAlpha2_[ij]+=(d2V_dAlpha2[ij]-av_d2V_dAlpha2_[ij])/av_counter_;
554 : }
555 : }
556 : //update work
557 800 : double prev_tot_prob=prob_[0];
558 1600 : for(unsigned i=0; i<alpha_size_; i++)
559 800 : prev_tot_prob+=prob_[i+1]*prev_exp_alpha_[i];
560 800 : work_+=(1-inv_gamma_)/beta_*std::log(tot_prob_/prev_tot_prob);
561 :
562 : //update coefficients
563 800 : if(av_counter_==av_stride_)
564 : {
565 16 : update_alpha();
566 16 : tg_counter_++;
567 16 : if(tg_counter_==tg_stride_)
568 : {
569 12 : update_tg_and_rct();
570 12 : tg_counter_=0;
571 : }
572 : //reset the ensemble averages
573 16 : av_counter_=0;
574 : std::fill(av_dV_dAlpha_.begin(),av_dV_dAlpha_.end(),0);
575 : std::fill(av_dV_dAlpha_prod_.begin(),av_dV_dAlpha_prod_.end(),0);
576 : std::fill(av_d2V_dAlpha2_.begin(),av_d2V_dAlpha2_.end(),0);
577 : }
578 : }
579 :
580 16 : void VesDeltaF::update_tg_and_rct()
581 : {
582 : //calculate target averages
583 16 : double Z_0=norm_[0];
584 32 : for(unsigned i=0; i<alpha_size_; i++)
585 16 : Z_0+=norm_[i+1]*exp_alpha_[i];
586 16 : double Z_tg=0;
587 : std::fill(tg_dV_dAlpha_.begin(),tg_dV_dAlpha_.end(),0);
588 : std::fill(tg_d2V_dAlpha2_.begin(),tg_d2V_dAlpha2_.end(),0);
589 1116 : for(Grid::index_t t=rank_; t<grid_p_[0]->getSize(); t+=NumParallel_)
590 : { //TODO can we recycle some code?
591 1100 : std::vector<double> prob(grid_p_.size());
592 3300 : for(unsigned n=0; n<grid_p_.size(); n++)
593 2200 : prob[n]=grid_p_[n]->getValue(t);
594 1100 : double tot_prob=prob[0];
595 2200 : for(unsigned i=0; i<alpha_size_; i++)
596 1100 : tot_prob+=prob[i+1]*exp_alpha_[i];
597 1100 : std::vector<double> dV_dAlpha(alpha_size_);
598 1100 : std::vector<double> d2V_dAlpha2(sym_alpha_size_);
599 2200 : for(unsigned i=0; i<alpha_size_; i++)
600 1100 : dV_dAlpha[i]=-(1-inv_gamma_)/tot_prob*prob[i+1]*exp_alpha_[i];
601 2200 : for(unsigned i=0; i<alpha_size_; i++)
602 : {
603 1100 : d2V_dAlpha2[get_index(i,i)]=-beta_*dV_dAlpha[i];
604 2200 : for(unsigned j=i; j<alpha_size_; j++)
605 1100 : d2V_dAlpha2[get_index(i,j)]-=beta_/(1-inv_gamma_)*dV_dAlpha[i]*dV_dAlpha[j];
606 : }
607 1100 : const double unnorm_tg_p=std::pow(tot_prob,inv_gamma_);
608 1100 : Z_tg+=unnorm_tg_p;
609 2200 : for(unsigned i=0; i<alpha_size_; i++)
610 1100 : tg_dV_dAlpha_[i]+=unnorm_tg_p*dV_dAlpha[i];
611 2200 : for(unsigned ij=0; ij<sym_alpha_size_; ij++)
612 1100 : tg_d2V_dAlpha2_[ij]+=unnorm_tg_p*d2V_dAlpha2[ij];
613 : }
614 16 : if(NumParallel_>1)
615 : {
616 10 : comm.Sum(Z_tg);
617 10 : comm.Sum(tg_dV_dAlpha_);
618 10 : comm.Sum(tg_d2V_dAlpha2_);
619 : }
620 32 : for(unsigned i=0; i<alpha_size_; i++)
621 16 : tg_dV_dAlpha_[i]/=Z_tg;
622 32 : for(unsigned ij=0; ij<sym_alpha_size_; ij++)
623 16 : tg_d2V_dAlpha2_[ij]/=Z_tg;
624 16 : getPntrToComponent("rct")->set(-1./beta_*std::log(Z_tg/Z_0)); //Z_tg is the best available estimate of Z_V
625 16 : }
626 :
627 16 : void VesDeltaF::update_alpha()
628 : {
629 : //combining the averages of multiple walkers
630 16 : if(NumWalkers_>1)
631 : {
632 8 : if(comm.Get_rank()==0) //sum only once: in the first rank of each walker
633 : {
634 8 : multi_sim_comm.Sum(av_dV_dAlpha_);
635 8 : multi_sim_comm.Sum(av_dV_dAlpha_prod_);
636 8 : multi_sim_comm.Sum(av_d2V_dAlpha2_);
637 16 : for(unsigned i=0; i<alpha_size_; i++)
638 8 : av_dV_dAlpha_[i]/=NumWalkers_;
639 16 : for(unsigned ij=0; ij<sym_alpha_size_; ij++)
640 : {
641 8 : av_dV_dAlpha_prod_[ij]/=NumWalkers_;
642 8 : av_d2V_dAlpha2_[ij]/=NumWalkers_;
643 : }
644 : }
645 8 : if(comm.Get_size()>1)//if there are more ranks for each walker, everybody has to know
646 : {
647 0 : comm.Bcast(av_dV_dAlpha_,0);
648 0 : comm.Bcast(av_dV_dAlpha_prod_,0);
649 0 : comm.Bcast(av_d2V_dAlpha2_,0);
650 : }
651 : }
652 : //set work and reset it
653 16 : getPntrToComponent("work")->set(work_);
654 16 : work_=0;
655 :
656 : //build the gradient and the Hessian of the functional
657 16 : std::vector<double> grad_omega(alpha_size_);
658 16 : std::vector<double> hess_omega(sym_alpha_size_);
659 32 : for(unsigned i=0; i<alpha_size_; i++)
660 : {
661 16 : grad_omega[i]=tg_dV_dAlpha_[i]-av_dV_dAlpha_[i];
662 32 : for(unsigned j=i; j<alpha_size_; j++)
663 : {
664 16 : const unsigned ij=get_index(i,j);
665 16 : hess_omega[ij]=beta_*(av_dV_dAlpha_prod_[ij]-av_dV_dAlpha_[i]*av_dV_dAlpha_[j])+tg_d2V_dAlpha2_[ij]-av_d2V_dAlpha2_[ij];
666 : }
667 : }
668 : //calculate the increment and update alpha
669 16 : mean_counter_++;
670 : long long unsigned mean_weight=mean_counter_;
671 16 : if(mean_weight_tau_>0 && mean_weight_tau_<mean_counter_)
672 : mean_weight=mean_weight_tau_;
673 16 : std::vector<double> damping(alpha_size_);
674 32 : for(unsigned i=0; i<alpha_size_; i++)
675 : {
676 16 : double increment_i=grad_omega[i];
677 32 : for(unsigned j=0; j<alpha_size_; j++)
678 16 : increment_i+=hess_omega[get_index(i,j)]*(inst_alpha_[j]-mean_alpha_[j]);
679 16 : if(!damping_off_)
680 8 : past_increment2_[i]+=increment_i*increment_i;
681 16 : damping[i]=std::sqrt(past_increment2_[i]);
682 16 : prev_exp_alpha_[i]=std::exp(-beta_*mean_alpha_[i]);
683 16 : inst_alpha_[i]-=minimization_step_/damping[i]*increment_i;
684 16 : mean_alpha_[i]+=(inst_alpha_[i]-mean_alpha_[i])/mean_weight;
685 16 : exp_alpha_[i]=std::exp(-beta_*mean_alpha_[i]);
686 : }
687 :
688 : //update the Alpha file
689 16 : if(mean_counter_%print_stride_==0)
690 : {
691 16 : alphaOfile_.printField("time",getTime());
692 32 : for(unsigned i=0; i<alpha_size_; i++)
693 : {
694 16 : const std::string index(std::to_string(i+1));
695 32 : alphaOfile_.printField("alpha_"+index,mean_alpha_[i]);
696 32 : alphaOfile_.printField("auxiliary_"+index,inst_alpha_[i]);
697 32 : alphaOfile_.printField("damping_"+index,damping[i]);
698 : }
699 16 : alphaOfile_.printField();
700 : }
701 16 : }
702 :
703 : //mapping of a [alpha_size_]x[alpha_size_] symmetric matrix into a vector of size sym_alpha_size_, useful for the communicator
704 4632 : inline unsigned VesDeltaF::get_index(const unsigned i, const unsigned j) const
705 : {
706 4632 : if(i<=j)
707 4632 : return j+i*(alpha_size_-1)-i*(i-1)/2;
708 : else
709 0 : return get_index(j,i);
710 : }
711 :
712 : }
713 : }
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