Simulations“sharpen”theirtools

ThecommunityofphysicistsvalidatestheprecisionofnumericalmethodsApril6,2016Forseveralyearsnow,numericalsimulationshavebeenrecognisedasanimportantmethodofscientificinvestigationinthefieldofthephysicsofmaterials(amongstothers).Withsimulations,realityisreproduced,bymeansofcomputercalculations,toanecessarydegreeofapproximation(whichmayproduceerrors)thatexpertsrefertoas“precision”.AnarticleinScience,authoredbyalargegroupofscientistsfrom44internationalinstitutions,marksthebeginningofamajorprocessofvalidationofalgorithmsandmethodswhich,thoughdifferent,convergeonthesame“problems”.Thefirsttestwascarriedoutontheequationsofstateofelementalcrystals:thesoftwareandmethodsexamined(includingthemostcommonlyusedtoday)showedgreatconsistencyofpredictions,confirmingtheirprecision.AmongtheauthorsofthearticleareanumberofSISSAresearchfellowsandprofessors.

Inscience,thereistheory:afairlygeneral“statement”thatdescribestheworld.Forexample(simplifyingsomewhat)takethestatement“theEarthrotatesarounditsownaxisandaroundtheSun”.Totestthistheory,weneedtoproducepredictionsthatweareabletocomparebymeansofmeasurements(whenthesearepossible).Andtodothis,weneedmorespecificmodelstranslatedintoamathematicallanguage.However,theremaybeseveral,slightlydifferentmodelsorevenmodelsbasedonradicallydifferentmethodologiesthatpredictthesamething.Forexample,goingbacktoour“theory”presentedabove,weknowthatitimpliesthatdayandnightalternateontheEarth,sowecandecidetocalculatewhentheSunwillrisetomorrowandthencheckthecorrectnessofofthepredictioninreallife.Thiscanbedoneinseveralways.Byusingarecordofallthesunrisetimesoverthepastmonths,wecantrytoidentifyregularpatternsandproduceamathematicalfunctionthatdescribesthepastandprovidesanestimateofthefuture,includingthetimeatwhichthesunwillrisetomorrow–allwithoutknowinganythingabouttheEarthoritsrotationspeed,etc.Alternatively,wecanusemathematicalmethodstoreconstructthephysicalsystemoftheEarthrevolvingaroundtheSun(enteringdataontheplanet’sdiameter,rotationspeed,axisinclination,etc.),andcalculatetomorrow’ssunrisetimeusingthismethod.Theresultsofthetwomethodscanbecomparedwithreal-lifeobservationandwitheachother.Twotypesoferrorcanoccur:thetheoryiswrong,theEarthdoesnotrevolvearoundtheSunanditisonlybychancethatthepredictionscoincideordonotcoincidewithreality,butsoonerorlatersomemajorinconsistencywillemergeandthetheorywillhavetobereviewed(imaginethatourstartingtheoryhadbeen“theSunrevolvesaroundtheEarth”).Thisisaproblemof“accuracy”andconcernsourknowledgeofreality(andmuchbroaderprocessesofreview,debateandreasoningwithinthescientificcommunity).However,anothertypeofproblemmayarise:thetheoryiscorrect,butthemathematicaltoolsweareusingarewrong,foravarietyofreasons.Inthiscase,wetalkabout“precision”ameasurementthatcanbeobtained,forexample,bycomparingtheresultsofthedifferentmethods:iftheyareconsistent(inourcasetheyyieldthesamesunrisetime)thenwecanconsiderthemtobereliableandcontinuetousethem.This,thoughinafarmorecomplexmanner,iswhatwasdonebythescientists(includingStefanodeGironcoliandAndreaDalCorso,professorsatSISSA/CNR-IOMDemocritos,EmineKüçükbenliSISSAresearchscientist,andPaoloGiannozzi,professorattheUniversityofUdine)forthenumericalsimulationmethodsthatarewidelyusedinthephysicsofmaterials.Indeed,todayphysicistsstudythenatureofmatterbysimulatingitspropertieswithdifferentmethodsand

software.“Duringanimportantconferenceheldafewyearsago,wecametotheconclusionthatitwastimetodosomethingwehadnotdonebefore–atleastnotsystematically–andwhichchemists,inafieldquiteclosetoours,hadalreadystartedtodo,thatis,totesttheprecisionofourinstruments”,explainsdeGironcoli.“Westartedwithsimplethings,butclearlywestillhavealongwaytogo.Nonethelesstheresultswerepositive”continuesdeGironcoli.Thegroupofscientistsstartedfromthebasisofphysics,theequationofstate,andtesteditonthesimplestmaterials:crystalsmadeupofoneelementonly(doingitforallelementsoftheperiodictable).Wetestednolessthan40methods,implementedwith15differentsoftwarepackages.AmongthemisalsoQuantumESPRESSO,oneofthemostimportantsoftwarepackagescurrentlyinuse,producedbyaconsortiuminwhichalsoSISSAandtheUniversityofUdineparticipate.“Weareverysatisfied:notonlydodifferentsoftwarepackagesimplementingthesamemethodsyieldthesameresults,butnowwealsogetthesameresultswiththemostcommonlyusedmainclassesofmethods(therearetwo)”commentsGiannozzi.Obviously,thisisonlythestart-thegroupisalreadyconsideringextendingthetesttomorecomplexmaterials–butitisstillanimportantconfirmation:“precisionishigh”,concludesdeGironcoli,“sowecanrelaxalittleandconcentrateonaccuracy,thatis,ontheoreticalspeculation”.Amongtheotherinstitutionstakingpartinthestudy,coordinatedbytheGhentUniversity(Belgium),areHarvardUniversity(USA),theUniversitiesofOxfordandCambridge(UK),theÉcolePolytechniqueFédéraledeLausanne(Switzerland),theMax-PlanckInstituteofMicrostructurePhysics(Germany),tonamejustafew.USEFULLINKS:

• OriginalpaperinScience:http://goo.gl/ZoJE2b

IMAGES:

• Bismuthcrystals-Credits:MaximBilovitskiy(Wikimediacommons:https://goo.gl/4fRRNa)

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