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 "core/Atoms.h"
27 : #include "tools/Communicator.h"
28 : #include "tools/Grid.h"
29 : #include "tools/File.h"
30 : //#include <algorithm> //std::fill
31 :
32 : namespace PLMD {
33 : namespace ves {
34 :
35 : //+PLUMEDOC VES_BIAS VES_DELTA_F
36 : /*
37 : Implementation of VES Delta F method
38 :
39 : Implementation of VES\f$\Delta F\f$ method \cite Invernizzi2019vesdeltaf (step two only).
40 :
41 : \warning
42 : Notice that this is a stand-alone bias Action, it does not need any of the other VES module components
43 :
44 : First you should create some estimate of the local free energy basins of your system,
45 : using e.g. multiple \ref METAD short runs, and combining them with the \ref sum_hills utility.
46 : Once you have them, you can use this bias Action to perform the VES optimization part of the method.
47 :
48 : These \f$N+1\f$ local basins are used to model the global free energy.
49 : In particular, given the conditional probabilities \f$P(\mathbf{s}|i)\propto e^{-\beta F_i(\mathbf{s})}\f$
50 : and the probabilities of being in a given basin \f$P_i\f$, we can write:
51 : \f[
52 : e^{-\beta F(\mathbf{s})}\propto P(\mathbf{s})=\sum_{i=0}^N P(\mathbf{s}|i)P_i \, .
53 : \f]
54 : We use this free energy model and the chosen bias factor \f$\gamma\f$ to build the bias potential:
55 : \f$V(\mathbf{s})=-(1-1/\gamma)F(\mathbf{s})\f$.
56 : Or, more explicitly:
57 : \f[
58 : V(\mathbf{s})=(1-1/\gamma)\frac{1}{\beta}\log\left[e^{-\beta F_0(\mathbf{s})}
59 : +\sum_{i=1}^{N} e^{-\beta F_i(\mathbf{s})} e^{-\beta \alpha_i}\right] \, ,
60 : \f]
61 : where the parameters \f$\boldsymbol{\alpha}\f$ are the \f$N\f$ free energy differences (see below) from the \f$F_0\f$ basin.
62 :
63 : By default the \f$F_i(\mathbf{s})\f$ are shifted so that \f$\min[F_i(\mathbf{s})]=0\f$ for all \f$i=\{0,...,N\}\f$.
64 : In this case the optimization parameters \f$\alpha_i\f$ are the difference in height between the minima of the basins.
65 : Using the keyword `NORMALIZE`, you can also decide to normalize the local free energies so that
66 : \f$\int d\mathbf{s}\, e^{-\beta F_i(\mathbf{s})}=1\f$.
67 : In this case the parameters will represent not the difference in height (which depends on the chosen CVs),
68 : but the actual free energy difference, \f$\alpha_i=\Delta F_i\f$.
69 :
70 : However, as discussed in Ref. \cite Invernizzi2019vesdeltaf, a better estimate of \f$\Delta F_i\f$ should be obtained through the reweighting procedure.
71 :
72 : \par Examples
73 :
74 : The following performs the optimization of the free energy difference between two metastable basins:
75 :
76 : \plumedfile
77 : cv: DISTANCE ATOMS=1,2
78 : ves: VES_DELTA_F ...
79 : ARG=cv
80 : TEMP=300
81 : FILE_F0=fesA.data
82 : FILE_F1=fesB.data
83 : BIASFACTOR=10.0
84 : M_STEP=0.1
85 : AV_STRIDE=500
86 : PRINT_STRIDE=100
87 : ...
88 : PRINT FMT=%g STRIDE=500 FILE=Colvar.data ARG=cv,ves.bias,ves.rct
89 : \endplumedfile
90 :
91 : The local FES files can be obtained as described in Sec. 4.2 of Ref. \cite Invernizzi2019vesdeltaf, i.e. for example:
92 : - 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)
93 : - \verbatim cat HILLS* > all_HILLS \endverbatim
94 : - \verbatim plumed sum_hills --hills all_HILLS --outfile all_fesA.dat --mintozero --min 0 --max 1 --bin 100 \endverbatim
95 : - \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
96 :
97 : The header of both FES files must be identical, and should be similar to the following:
98 :
99 : \auxfile{fesA.data}
100 : #! FIELDS cv file.free der_cv
101 : #! SET min_cv 0
102 : #! SET max_cv 1
103 : #! SET nbins_cv 100
104 : #! SET periodic_cv false
105 : 0 0 0
106 : \endauxfile
107 : \auxfile{fesB.data}
108 : #! FIELDS cv file.free der_cv
109 : #! SET min_cv 0
110 : #! SET max_cv 1
111 : #! SET nbins_cv 100
112 : #! SET periodic_cv false
113 : 0 0 0
114 : \endauxfile
115 :
116 : */
117 : //+ENDPLUMEDOC
118 :
119 : class VesDeltaF : public bias::Bias {
120 :
121 : private:
122 : double beta_;
123 : unsigned NumParallel_;
124 : unsigned rank_;
125 : unsigned NumWalkers_;
126 : bool isFirstStep_;
127 : bool afterCalculate_;
128 :
129 : //prob
130 : double tot_prob_;
131 : std::vector<double> prob_;
132 : std::vector< std::vector<double> > der_prob_;
133 :
134 : //local basins
135 : std::vector< std::unique_ptr<Grid> > grid_p_; //pointers because of GridBase::create
136 : std::vector<double> norm_;
137 :
138 : //optimizer-related stuff
139 : long long unsigned mean_counter_;
140 : unsigned mean_weight_tau_;
141 : unsigned alpha_size_;
142 : unsigned sym_alpha_size_;
143 : std::vector<double> mean_alpha_;
144 : std::vector<double> inst_alpha_;
145 : std::vector<double> past_increment2_;
146 : double minimization_step_;
147 : bool damping_off_;
148 : //'tg' -> 'target distribution'
149 : double inv_gamma_;
150 : unsigned tg_counter_;
151 : unsigned tg_stride_;
152 : std::vector<double> tg_dV_dAlpha_;
153 : std::vector<double> tg_d2V_dAlpha2_;
154 : //'av' -> 'ensemble average'
155 : unsigned av_counter_;
156 : unsigned av_stride_;
157 : std::vector<double> av_dV_dAlpha_;
158 : std::vector<double> av_dV_dAlpha_prod_;
159 : std::vector<double> av_d2V_dAlpha2_;
160 : //printing
161 : unsigned print_stride_;
162 : OFile alphaOfile_;
163 : //other
164 : std::vector<double> exp_alpha_;
165 : std::vector<double> prev_exp_alpha_;
166 : double work_;
167 :
168 : //functions
169 : void update_alpha();
170 : void update_tg_and_rct();
171 : inline unsigned get_index(const unsigned, const unsigned) const;
172 :
173 : public:
174 : explicit VesDeltaF(const ActionOptions&);
175 : void calculate() override;
176 : void update() override;
177 : static void registerKeywords(Keywords& keys);
178 : };
179 :
180 13793 : PLUMED_REGISTER_ACTION(VesDeltaF,"VES_DELTA_F")
181 :
182 8 : void VesDeltaF::registerKeywords(Keywords& keys) {
183 8 : Bias::registerKeywords(keys);
184 8 : keys.use("ARG");
185 16 : keys.add("optional","TEMP","temperature is compulsory, but it can be sometimes fetched from the MD engine");
186 : //local free energies
187 16 : keys.add("numbered","FILE_F","names of files containing local free energies and derivatives. "
188 : "The first one, FILE_F0, is used as reference for all the free energy differences.");
189 16 : keys.reset_style("FILE_F","compulsory");
190 16 : keys.addFlag("NORMALIZE",false,"normalize all local free energies so that alpha will be (approx) Delta F");
191 16 : keys.addFlag("NO_MINTOZERO",false,"leave local free energies as provided, without shifting them to zero min");
192 : //target distribution
193 16 : keys.add("compulsory","BIASFACTOR","0","the gamma bias factor used for well-tempered target p(s)."
194 : " Set to 0 for non-tempered flat target");
195 16 : keys.add("optional","TG_STRIDE","( default=1 ) number of AV_STRIDE between updates"
196 : " of target p(s) and reweighing factor c(t)");
197 : //optimization
198 16 : keys.add("compulsory","M_STEP","1.0","the mu step used for the Omega functional minimization");
199 16 : keys.add("compulsory","AV_STRIDE","500","number of simulation steps between alpha updates");
200 16 : keys.add("optional","TAU_MEAN","exponentially decaying average for alpha (rescaled using AV_STRIDE)."
201 : " Should be used only in very specific cases");
202 16 : keys.add("optional","INITIAL_ALPHA","( default=0 ) an initial guess for the bias potential parameter alpha");
203 16 : keys.addFlag("DAMPING_OFF",false,"do not use an AdaGrad-like term to rescale M_STEP");
204 : //output parameters file
205 16 : keys.add("compulsory","ALPHA_FILE","ALPHA","file name for output minimization parameters");
206 16 : keys.add("optional","PRINT_STRIDE","( default=10 ) stride for printing to ALPHA_FILE");
207 16 : keys.add("optional","FMT","specify format for ALPHA_FILE");
208 : //debug flags
209 16 : keys.addFlag("SERIAL",false,"perform the calculation in serial even if multiple tasks are available");
210 16 : keys.addFlag("MULTIPLE_WALKERS",false,"use multiple walkers connected via MPI for the optimization");
211 8 : keys.use("RESTART");
212 :
213 : //output components
214 8 : componentsAreNotOptional(keys);
215 16 : keys.addOutputComponent("rct","default","the reweighting factor c(t)");
216 16 : keys.addOutputComponent("work","default","the work done by the bias in one AV_STRIDE");
217 8 : }
218 :
219 4 : VesDeltaF::VesDeltaF(const ActionOptions&ao)
220 : : PLUMED_BIAS_INIT(ao)
221 4 : , isFirstStep_(true)
222 4 : , afterCalculate_(false)
223 4 : , mean_counter_(0)
224 4 : , av_counter_(0)
225 4 : , work_(0) {
226 : //set beta
227 4 : const double Kb=plumed.getAtoms().getKBoltzmann();
228 4 : double temp=0;
229 4 : parse("TEMP",temp);
230 4 : double KbT=Kb*temp;
231 4 : if(KbT==0) {
232 0 : KbT=plumed.getAtoms().getKbT();
233 0 : plumed_massert(KbT>0,"your MD engine does not pass the temperature to plumed, you must specify it using TEMP");
234 : }
235 4 : beta_=1.0/KbT;
236 :
237 : //initialize probability grids using local free energies
238 : bool spline=true;
239 : bool sparsegrid=false;
240 4 : std::string funcl="file.free"; //typical name given by sum_hills
241 :
242 : std::vector<std::string> fes_names;
243 8 : for(unsigned n=0;; n++) { //NB: here we start from FILE_F0 not from FILE_F1
244 : std::string filename;
245 24 : if(!parseNumbered("FILE_F",n,filename)) {
246 : break;
247 : }
248 8 : fes_names.push_back(filename);
249 8 : IFile gridfile;
250 8 : gridfile.open(filename);
251 8 : auto g=GridBase::create(funcl,getArguments(),gridfile,sparsegrid,spline,true);
252 : // we assume this cannot be sparse. in case we want it to be sparse, some of the methods
253 : // that are available only in Grid should be ported to GridBase
254 8 : auto gg=dynamic_cast<Grid*>(g.get());
255 : // if this throws, g is deleted
256 8 : plumed_assert(gg);
257 : // release ownership in order to transfer it to emplaced pointer
258 : g.release();
259 8 : grid_p_.emplace_back(gg);
260 16 : }
261 4 : plumed_massert(grid_p_.size()>1,"at least 2 basins must be defined, starting from FILE_F0");
262 4 : alpha_size_=grid_p_.size()-1;
263 4 : sym_alpha_size_=alpha_size_*(alpha_size_+1)/2; //useful for symmetric matrix [alpha_size_]x[alpha_size_]
264 : //check for consistency with first local free energy
265 8 : for(unsigned n=1; n<grid_p_.size(); n++) {
266 8 : std::string error_tag="FILE_F"+std::to_string(n)+" '"+fes_names[n]+"' not compatible with reference one, FILE_F0";
267 4 : plumed_massert(grid_p_[n]->getSize()==grid_p_[0]->getSize(),error_tag);
268 4 : plumed_massert(grid_p_[n]->getMin()==grid_p_[0]->getMin(),error_tag);
269 4 : plumed_massert(grid_p_[n]->getMax()==grid_p_[0]->getMax(),error_tag);
270 4 : plumed_massert(grid_p_[n]->getBinVolume()==grid_p_[0]->getBinVolume(),error_tag);
271 : }
272 :
273 4 : bool no_mintozero=false;
274 4 : parseFlag("NO_MINTOZERO",no_mintozero);
275 4 : if(!no_mintozero) {
276 6 : for(unsigned n=0; n<grid_p_.size(); n++) {
277 4 : grid_p_[n]->setMinToZero();
278 : }
279 : }
280 4 : bool normalize=false;
281 4 : parseFlag("NORMALIZE",normalize);
282 4 : norm_.resize(grid_p_.size(),0);
283 4 : std::vector<double> c_norm(grid_p_.size());
284 : //convert the FESs to probability distributions
285 : //NB: the spline interpolation will be done on the probability distributions, not on the given FESs
286 : const unsigned ncv=getNumberOfArguments(); //just for ease
287 12 : for(unsigned n=0; n<grid_p_.size(); n++) {
288 808 : for(Grid::index_t t=0; t<grid_p_[n]->getSize(); t++) {
289 800 : std::vector<double> der(ncv);
290 800 : const double val=std::exp(-beta_*grid_p_[n]->getValueAndDerivatives(t,der));
291 1600 : for(unsigned s=0; s<ncv; s++) {
292 800 : der[s]*=-beta_*val;
293 : }
294 800 : grid_p_[n]->setValueAndDerivatives(t,val,der);
295 800 : norm_[n]+=val;
296 : }
297 8 : c_norm[n]=1./beta_*std::log(norm_[n]);
298 8 : if(normalize) {
299 4 : grid_p_[n]->scaleAllValuesAndDerivatives(1./norm_[n]);
300 4 : norm_[n]=1;
301 : }
302 : }
303 :
304 : //get target
305 4 : double biasfactor=0;
306 4 : parse("BIASFACTOR",biasfactor);
307 4 : plumed_massert(biasfactor==0 || biasfactor>1,"BIASFACTOR must be zero (for uniform target) or greater than one");
308 4 : if(biasfactor==0) {
309 2 : inv_gamma_=0;
310 : } else {
311 2 : inv_gamma_=1./biasfactor;
312 : }
313 4 : tg_counter_=0;
314 4 : tg_stride_=1;
315 4 : parse("TG_STRIDE",tg_stride_);
316 4 : tg_dV_dAlpha_.resize(alpha_size_,0);
317 4 : tg_d2V_dAlpha2_.resize(sym_alpha_size_,0);
318 :
319 : //setup optimization stuff
320 4 : minimization_step_=1;
321 4 : parse("M_STEP",minimization_step_);
322 :
323 4 : av_stride_=500;
324 4 : parse("AV_STRIDE",av_stride_);
325 4 : av_dV_dAlpha_.resize(alpha_size_,0);
326 4 : av_dV_dAlpha_prod_.resize(sym_alpha_size_,0);
327 4 : av_d2V_dAlpha2_.resize(sym_alpha_size_,0);
328 :
329 4 : mean_weight_tau_=0;
330 4 : parse("TAU_MEAN",mean_weight_tau_);
331 4 : if(mean_weight_tau_!=1) { //set it to 1 for basic SGD
332 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");
333 4 : mean_weight_tau_/=av_stride_; //this way you can look at the number of simulation steps to choose TAU_MEAN
334 : }
335 :
336 8 : parseVector("INITIAL_ALPHA",mean_alpha_);
337 4 : if(mean_alpha_.size()>0) {
338 2 : plumed_massert(mean_alpha_.size()==alpha_size_,"provide one INITIAL_ALPHA for each basin beyond the first one");
339 : } else {
340 2 : mean_alpha_.resize(alpha_size_,0);
341 : }
342 4 : inst_alpha_=mean_alpha_;
343 4 : exp_alpha_.resize(alpha_size_);
344 8 : for(unsigned i=0; i<alpha_size_; i++) {
345 4 : exp_alpha_[i]=std::exp(-beta_*mean_alpha_[i]);
346 : }
347 4 : prev_exp_alpha_=exp_alpha_;
348 :
349 4 : damping_off_=false;
350 4 : parseFlag("DAMPING_OFF",damping_off_);
351 4 : if(damping_off_) {
352 2 : past_increment2_.resize(alpha_size_,1);
353 : } else {
354 2 : past_increment2_.resize(alpha_size_,0);
355 : }
356 :
357 : //file printing options
358 4 : std::string alphaFileName("ALPHA");
359 4 : parse("ALPHA_FILE",alphaFileName);
360 4 : print_stride_=10;
361 8 : parse("PRINT_STRIDE",print_stride_);
362 : std::string fmt;
363 4 : parse("FMT",fmt);
364 :
365 : //other flags, mainly for debugging
366 4 : NumParallel_=comm.Get_size();
367 4 : rank_=comm.Get_rank();
368 4 : bool serial=false;
369 4 : parseFlag("SERIAL",serial);
370 4 : if(serial) {
371 2 : log.printf(" -- SERIAL: running without loop parallelization\n");
372 2 : NumParallel_=1;
373 2 : rank_=0;
374 : }
375 :
376 4 : bool multiple_walkers=false;
377 4 : parseFlag("MULTIPLE_WALKERS",multiple_walkers);
378 4 : if(!multiple_walkers) {
379 2 : NumWalkers_=1;
380 : } else {
381 2 : if(comm.Get_rank()==0) { //multi_sim_comm works well on first rank only
382 2 : NumWalkers_=multi_sim_comm.Get_size();
383 : }
384 2 : if(comm.Get_size()>1) { //if each walker has more than one processor update them all
385 0 : comm.Bcast(NumWalkers_,0);
386 : }
387 : }
388 :
389 4 : checkRead();
390 :
391 : //restart if needed
392 4 : if(getRestart()) {
393 2 : IFile ifile;
394 2 : ifile.link(*this);
395 2 : if(NumWalkers_>1) {
396 4 : ifile.enforceSuffix("");
397 : }
398 2 : if(ifile.FileExist(alphaFileName)) {
399 2 : log.printf(" Restarting from: %s\n",alphaFileName.c_str());
400 2 : log.printf(" all options (also PRINT_STRIDE) must be consistent!\n");
401 2 : log.printf(" any INITIAL_ALPHA will be overwritten\n");
402 2 : ifile.open(alphaFileName);
403 : double time;
404 2 : std::vector<double> damping(alpha_size_);
405 20 : while(ifile.scanField("time",time)) { //room for improvements: only last line is important
406 16 : for(unsigned i=0; i<alpha_size_; i++) {
407 8 : const std::string index(std::to_string(i+1));
408 8 : prev_exp_alpha_[i]=std::exp(-beta_*mean_alpha_[i]);
409 16 : ifile.scanField("alpha_"+index,mean_alpha_[i]);
410 16 : ifile.scanField("auxiliary_"+index,inst_alpha_[i]);
411 16 : ifile.scanField("damping_"+index,damping[i]);
412 : }
413 8 : ifile.scanField();
414 8 : mean_counter_+=print_stride_;
415 : }
416 4 : for(unsigned i=0; i<alpha_size_; i++) {
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 : }
428 2 : }
429 :
430 : //setup output file with Alpha values
431 4 : alphaOfile_.link(*this);
432 4 : if(NumWalkers_>1) {
433 2 : if(comm.Get_rank()==0 && multi_sim_comm.Get_rank()>0) {
434 : alphaFileName="/dev/null"; //only first walker writes on file
435 : }
436 4 : alphaOfile_.enforceSuffix("");
437 : }
438 4 : alphaOfile_.open(alphaFileName);
439 4 : if(fmt.length()>0) {
440 8 : alphaOfile_.fmtField(" "+fmt);
441 : }
442 :
443 : //add other output components
444 4 : addComponent("rct");
445 4 : componentIsNotPeriodic("rct");
446 4 : addComponent("work");
447 4 : componentIsNotPeriodic("work");
448 :
449 : //print some info
450 4 : log.printf(" Temperature T: %g\n",1./(Kb*beta_));
451 4 : log.printf(" Beta (1/Kb*T): %g\n",beta_);
452 4 : log.printf(" Local free energy basins files and normalization constants:\n");
453 12 : for(unsigned n=0; n<grid_p_.size(); n++) {
454 8 : log.printf(" F_%d filename: %s c_%d=%g\n",n,fes_names[n].c_str(),n,c_norm[n]);
455 : }
456 4 : if(no_mintozero) {
457 2 : log.printf(" -- NO_MINTOZERO: local free energies are not shifted to be zero at minimum\n");
458 : }
459 4 : if(normalize) {
460 2 : log.printf(" -- NORMALIZE: F_n+=c_n, alpha=DeltaF\n");
461 : }
462 4 : log.printf(" Using target distribution with 1/gamma = %g\n",inv_gamma_);
463 4 : log.printf(" and updated with stride %d\n",tg_stride_);
464 4 : log.printf(" Step for the minimization algorithm: %g\n",minimization_step_);
465 4 : log.printf(" Stride for the ensemble average: %d\n",av_stride_);
466 4 : if(mean_weight_tau_>1) {
467 2 : log.printf(" Exponentially decaying average with weight=tau/av_stride=%d\n",mean_weight_tau_);
468 : }
469 4 : if(mean_weight_tau_==1) {
470 0 : log.printf(" +++ WARNING +++ setting TAU_MEAN=1 is equivalent to use simple SGD, without mean alpha nor hessian contribution\n");
471 : }
472 4 : log.printf(" Initial guess for alpha:\n");
473 8 : for(unsigned i=0; i<alpha_size_; i++) {
474 4 : log.printf(" alpha_%d = %g\n",i+1,mean_alpha_[i]);
475 : }
476 4 : if(damping_off_) {
477 2 : log.printf(" -- DAMPING_OFF: the minimization step will NOT become smaller as the simulation goes on\n");
478 : }
479 4 : log.printf(" Printing on file %s with stride %d\n",alphaFileName.c_str(),print_stride_);
480 4 : if(serial) {
481 2 : log.printf(" -- SERIAL: running without loop parallelization\n");
482 : }
483 4 : if(NumParallel_>1) {
484 2 : log.printf(" Using multiple threads per simulation: %d\n",NumParallel_);
485 : }
486 4 : if(multiple_walkers) {
487 2 : log.printf(" -- MULTIPLE_WALKERS: multiple simulations will combine statistics for the optimization\n");
488 2 : if(NumWalkers_>1) {
489 2 : log.printf(" number of walkers: %d\n",NumWalkers_);
490 2 : log.printf(" walker rank: %d\n",multi_sim_comm.Get_rank()); //only comm.Get_rank()=0 prints, so this is fine
491 : } else {
492 0 : log.printf(" +++ WARNING +++ only one replica found: are you sure you are running MPI-connected simulations?\n");
493 : }
494 : }
495 4 : log.printf(" Bibliography ");
496 8 : log<<plumed.cite("Invernizzi and Parrinello, J. Chem. Theory Comput. 15, 2187-2194 (2019)");
497 8 : log<<plumed.cite("Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)");
498 4 : if(inv_gamma_>0) {
499 4 : log<<plumed.cite("Valsson and Parrinello, J. Chem. Theory Comput. 11, 1996-2002 (2015)");
500 : }
501 :
502 : //last initializations
503 4 : prob_.resize(grid_p_.size());
504 4 : der_prob_.resize(grid_p_.size(),std::vector<double>(getNumberOfArguments()));
505 4 : update_tg_and_rct();
506 8 : }
507 :
508 804 : void VesDeltaF::calculate() {
509 : //get CVs
510 804 : const unsigned ncv=getNumberOfArguments(); //just for ease
511 804 : std::vector<double> cv(ncv);
512 1608 : for(unsigned s=0; s<ncv; s++) {
513 804 : cv[s]=getArgument(s);
514 : }
515 : //get probabilities for each basin, and total one
516 2412 : for(unsigned n=0; n<grid_p_.size(); n++) {
517 1608 : prob_[n]=grid_p_[n]->getValueAndDerivatives(cv,der_prob_[n]);
518 : }
519 804 : tot_prob_=prob_[0];
520 1608 : for(unsigned i=0; i<alpha_size_; i++) {
521 804 : tot_prob_+=prob_[i+1]*exp_alpha_[i];
522 : }
523 :
524 : //update bias and forces: V=-(1-inv_gamma_)*fes
525 804 : setBias((1-inv_gamma_)/beta_*std::log(tot_prob_));
526 1608 : for(unsigned s=0; s<ncv; s++) {
527 804 : double dProb_dCV_s=der_prob_[0][s];
528 1608 : for(unsigned i=0; i<alpha_size_; i++) {
529 804 : dProb_dCV_s+=der_prob_[i+1][s]*exp_alpha_[i];
530 : }
531 804 : setOutputForce(s,-(1-inv_gamma_)/beta_/tot_prob_*dProb_dCV_s);
532 : }
533 804 : afterCalculate_=true;
534 804 : }
535 :
536 804 : void VesDeltaF::update() {
537 : //skip first step to sync getTime() and av_counter_, as in METAD
538 804 : if(isFirstStep_) {
539 4 : isFirstStep_=false;
540 4 : return;
541 : }
542 800 : plumed_massert(afterCalculate_,"VesDeltaF::update() must be called after VesDeltaF::calculate() to work properly");
543 800 : afterCalculate_=false;
544 :
545 : //calculate derivatives for ensemble averages
546 800 : std::vector<double> dV_dAlpha(alpha_size_);
547 800 : std::vector<double> d2V_dAlpha2(sym_alpha_size_);
548 1600 : for(unsigned i=0; i<alpha_size_; i++) {
549 800 : dV_dAlpha[i]=-(1-inv_gamma_)/tot_prob_*prob_[i+1]*exp_alpha_[i];
550 : }
551 1600 : for(unsigned i=0; i<alpha_size_; i++) {
552 800 : d2V_dAlpha2[get_index(i,i)]=-beta_*dV_dAlpha[i];
553 1600 : for(unsigned j=i; j<alpha_size_; j++) {
554 800 : d2V_dAlpha2[get_index(i,j)]-=beta_/(1-inv_gamma_)*dV_dAlpha[i]*dV_dAlpha[j];
555 : }
556 : }
557 : //update ensemble averages
558 800 : av_counter_++;
559 1600 : for(unsigned i=0; i<alpha_size_; i++) {
560 800 : av_dV_dAlpha_[i]+=(dV_dAlpha[i]-av_dV_dAlpha_[i])/av_counter_;
561 1600 : for(unsigned j=i; j<alpha_size_; j++) {
562 800 : const unsigned ij=get_index(i,j);
563 800 : av_dV_dAlpha_prod_[ij]+=(dV_dAlpha[i]*dV_dAlpha[j]-av_dV_dAlpha_prod_[ij])/av_counter_;
564 800 : av_d2V_dAlpha2_[ij]+=(d2V_dAlpha2[ij]-av_d2V_dAlpha2_[ij])/av_counter_;
565 : }
566 : }
567 : //update work
568 800 : double prev_tot_prob=prob_[0];
569 1600 : for(unsigned i=0; i<alpha_size_; i++) {
570 800 : prev_tot_prob+=prob_[i+1]*prev_exp_alpha_[i];
571 : }
572 800 : work_+=(1-inv_gamma_)/beta_*std::log(tot_prob_/prev_tot_prob);
573 :
574 : //update coefficients
575 800 : if(av_counter_==av_stride_) {
576 16 : update_alpha();
577 16 : tg_counter_++;
578 16 : if(tg_counter_==tg_stride_) {
579 12 : update_tg_and_rct();
580 12 : tg_counter_=0;
581 : }
582 : //reset the ensemble averages
583 16 : av_counter_=0;
584 : std::fill(av_dV_dAlpha_.begin(),av_dV_dAlpha_.end(),0);
585 : std::fill(av_dV_dAlpha_prod_.begin(),av_dV_dAlpha_prod_.end(),0);
586 : std::fill(av_d2V_dAlpha2_.begin(),av_d2V_dAlpha2_.end(),0);
587 : }
588 : }
589 :
590 16 : void VesDeltaF::update_tg_and_rct() {
591 : //calculate target averages
592 16 : double Z_0=norm_[0];
593 32 : for(unsigned i=0; i<alpha_size_; i++) {
594 16 : Z_0+=norm_[i+1]*exp_alpha_[i];
595 : }
596 16 : double Z_tg=0;
597 : std::fill(tg_dV_dAlpha_.begin(),tg_dV_dAlpha_.end(),0);
598 : std::fill(tg_d2V_dAlpha2_.begin(),tg_d2V_dAlpha2_.end(),0);
599 1116 : for(Grid::index_t t=rank_; t<grid_p_[0]->getSize(); t+=NumParallel_) {
600 : //TODO can we recycle some code?
601 1100 : std::vector<double> prob(grid_p_.size());
602 3300 : for(unsigned n=0; n<grid_p_.size(); n++) {
603 2200 : prob[n]=grid_p_[n]->getValue(t);
604 : }
605 1100 : double tot_prob=prob[0];
606 2200 : for(unsigned i=0; i<alpha_size_; i++) {
607 1100 : tot_prob+=prob[i+1]*exp_alpha_[i];
608 : }
609 1100 : std::vector<double> dV_dAlpha(alpha_size_);
610 1100 : std::vector<double> d2V_dAlpha2(sym_alpha_size_);
611 2200 : for(unsigned i=0; i<alpha_size_; i++) {
612 1100 : dV_dAlpha[i]=-(1-inv_gamma_)/tot_prob*prob[i+1]*exp_alpha_[i];
613 : }
614 2200 : for(unsigned i=0; i<alpha_size_; i++) {
615 1100 : d2V_dAlpha2[get_index(i,i)]=-beta_*dV_dAlpha[i];
616 2200 : for(unsigned j=i; j<alpha_size_; j++) {
617 1100 : d2V_dAlpha2[get_index(i,j)]-=beta_/(1-inv_gamma_)*dV_dAlpha[i]*dV_dAlpha[j];
618 : }
619 : }
620 1100 : const double unnorm_tg_p=std::pow(tot_prob,inv_gamma_);
621 1100 : Z_tg+=unnorm_tg_p;
622 2200 : for(unsigned i=0; i<alpha_size_; i++) {
623 1100 : tg_dV_dAlpha_[i]+=unnorm_tg_p*dV_dAlpha[i];
624 : }
625 2200 : for(unsigned ij=0; ij<sym_alpha_size_; ij++) {
626 1100 : tg_d2V_dAlpha2_[ij]+=unnorm_tg_p*d2V_dAlpha2[ij];
627 : }
628 : }
629 16 : if(NumParallel_>1) {
630 10 : comm.Sum(Z_tg);
631 10 : comm.Sum(tg_dV_dAlpha_);
632 10 : comm.Sum(tg_d2V_dAlpha2_);
633 : }
634 32 : for(unsigned i=0; i<alpha_size_; i++) {
635 16 : tg_dV_dAlpha_[i]/=Z_tg;
636 : }
637 32 : for(unsigned ij=0; ij<sym_alpha_size_; ij++) {
638 16 : tg_d2V_dAlpha2_[ij]/=Z_tg;
639 : }
640 16 : getPntrToComponent("rct")->set(-1./beta_*std::log(Z_tg/Z_0)); //Z_tg is the best available estimate of Z_V
641 16 : }
642 :
643 16 : void VesDeltaF::update_alpha() {
644 : //combining the averages of multiple walkers
645 16 : if(NumWalkers_>1) {
646 8 : if(comm.Get_rank()==0) { //sum only once: in the first rank of each walker
647 8 : multi_sim_comm.Sum(av_dV_dAlpha_);
648 8 : multi_sim_comm.Sum(av_dV_dAlpha_prod_);
649 8 : multi_sim_comm.Sum(av_d2V_dAlpha2_);
650 16 : for(unsigned i=0; i<alpha_size_; i++) {
651 8 : av_dV_dAlpha_[i]/=NumWalkers_;
652 : }
653 16 : for(unsigned ij=0; ij<sym_alpha_size_; ij++) {
654 8 : av_dV_dAlpha_prod_[ij]/=NumWalkers_;
655 8 : av_d2V_dAlpha2_[ij]/=NumWalkers_;
656 : }
657 : }
658 8 : if(comm.Get_size()>1) { //if there are more ranks for each walker, everybody has to know
659 0 : comm.Bcast(av_dV_dAlpha_,0);
660 0 : comm.Bcast(av_dV_dAlpha_prod_,0);
661 0 : comm.Bcast(av_d2V_dAlpha2_,0);
662 : }
663 : }
664 : //set work and reset it
665 16 : getPntrToComponent("work")->set(work_);
666 16 : work_=0;
667 :
668 : //build the gradient and the Hessian of the functional
669 16 : std::vector<double> grad_omega(alpha_size_);
670 16 : std::vector<double> hess_omega(sym_alpha_size_);
671 32 : for(unsigned i=0; i<alpha_size_; i++) {
672 16 : grad_omega[i]=tg_dV_dAlpha_[i]-av_dV_dAlpha_[i];
673 32 : for(unsigned j=i; j<alpha_size_; j++) {
674 16 : const unsigned ij=get_index(i,j);
675 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];
676 : }
677 : }
678 : //calculate the increment and update alpha
679 16 : mean_counter_++;
680 : long long unsigned mean_weight=mean_counter_;
681 16 : if(mean_weight_tau_>0 && mean_weight_tau_<mean_counter_) {
682 : mean_weight=mean_weight_tau_;
683 : }
684 16 : std::vector<double> damping(alpha_size_);
685 32 : for(unsigned i=0; i<alpha_size_; i++) {
686 16 : double increment_i=grad_omega[i];
687 32 : for(unsigned j=0; j<alpha_size_; j++) {
688 16 : increment_i+=hess_omega[get_index(i,j)]*(inst_alpha_[j]-mean_alpha_[j]);
689 : }
690 16 : if(!damping_off_) {
691 8 : past_increment2_[i]+=increment_i*increment_i;
692 : }
693 16 : damping[i]=std::sqrt(past_increment2_[i]);
694 16 : prev_exp_alpha_[i]=std::exp(-beta_*mean_alpha_[i]);
695 16 : inst_alpha_[i]-=minimization_step_/damping[i]*increment_i;
696 16 : mean_alpha_[i]+=(inst_alpha_[i]-mean_alpha_[i])/mean_weight;
697 16 : exp_alpha_[i]=std::exp(-beta_*mean_alpha_[i]);
698 : }
699 :
700 : //update the Alpha file
701 16 : if(mean_counter_%print_stride_==0) {
702 16 : alphaOfile_.printField("time",getTime());
703 32 : for(unsigned i=0; i<alpha_size_; i++) {
704 16 : const std::string index(std::to_string(i+1));
705 32 : alphaOfile_.printField("alpha_"+index,mean_alpha_[i]);
706 32 : alphaOfile_.printField("auxiliary_"+index,inst_alpha_[i]);
707 32 : alphaOfile_.printField("damping_"+index,damping[i]);
708 : }
709 16 : alphaOfile_.printField();
710 : }
711 16 : }
712 :
713 : //mapping of a [alpha_size_]x[alpha_size_] symmetric matrix into a vector of size sym_alpha_size_, useful for the communicator
714 4632 : inline unsigned VesDeltaF::get_index(const unsigned i, const unsigned j) const {
715 4632 : if(i<=j) {
716 4632 : return j+i*(alpha_size_-1)-i*(i-1)/2;
717 : } else {
718 0 : return get_index(j,i);
719 : }
720 : }
721 :
722 : }
723 : }
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