TN-15-2_ExcaliburNeptunePerformanceConsiderationsNonIntrusiveUncertaintyQuantiﬁcationInf
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Excalibur-Neptune,report,2047356-TN-15-2,Task,2.5,Performance,considerations,for,non-intrusive,uncertainty,quantiﬁcation,and,the,inﬂuence,of,the,boundary,Ben,Dudson,,Peter,Hill,,Ed,Higgins,,David,Dickinson,,and,Steven,Wright,University,of,York,David,Moxey,KCL,October,28,,2022,Contents,1,Executive,summary,2,Introduction,3,Performance,considerations,4,The,inﬂuence,of,the,boundary,5,Summary,6,Acknowledgements,7,References,1,Executive,summary,1,1,2,5,14,14,15,In,this,report,we,summarise,some,performance,considerations,relevant,to,the,use,of,non-intrusive,uncertainty,quantiﬁcation,(UQ),through,tools,such,as,the,easyvvuq,package,[1,,2].,Minimising,the,number,of,simulations,and,eﬀective,use,of,workﬂow,management,tools,are,often,the,primary,route,to,improving,the,time,to,solution,and,freeing,up,researcher,time.,The,number,of,moments,required,for,converged,uncertainty,measures,near,the,boundary,is,also,explored,for,a,sample,test,case,from,the,SD1D,[3],test,cases,[4].,It,is,demonstrated,that,,depending,on,the,boundary,conditions,selected,and,the,uncertain,inputs,,convergence,can,require,between,2nd,and,5th,order,projections.,2,Introduction,In,task,83-2.4,non-intrusive,uncertainty,quantiﬁcation,(UQ),for,SD1D,[3],,a,BOUT++,[5],based,1D,ﬂuid,system,,was,explored.,The,corresponding,report,[6],introduced,the,approach,to,implementing,a,UQ,workﬂow,with,easyvvuq,,1,demonstrated,some,of,the,diﬀerent,possible,workﬂows,and,made,brief,mention,of,possible,performance,considerations.,Here,we,seek,to,build,on,this,previous,work,in,two,ways.,Firstly,,in,section,3,we,will,expand,on,some,of,the,considerations,relevant,to,optimising,the,time,to,solution,(TTS),in,a,UQ,workﬂow.,The,order,of,the,UQ,sampler,used,can,determine,the,number,of,simulations,required,,potentially,impacting,TTS,and,in,section,4,we,will,explore,the,inﬂuence,of,boundary,conditions,on,the,order,of,UQ,sampler,required,for,convergence.,3,Performance,considerations,Approaches,to,UQ,can,be,classiﬁed,as,either,intrusive,or,non-intrusive.,Intrusive,approaches,require,the,underlying,computational,model,to,be,adapted,in,order,to,eﬀectively,run,an,ensemble,of,cases,simultaneously,,increasing,the,problem,size,of,a,single,simulation.,Non-intrusive,approaches,on,the,other,hand,require,a,large,number,of,“standard”,simulations,to,be,performed,for,a,range,of,inputs.,These,approaches,have,diﬀerent,performance,considerations/characterisics.,For,example,,suppose,UQ,increases,the,amount,of,computation,required,by,a,fac-,tor,N,compared,to,a,single,simulation,which,returns,a,result,in,time,T,.,Here,intrusive,UQ,increases,the,problem,size,by,N,and,non-intrusive,UQ,requires,N,separate,simulations,to,be,performed.,If,the,weak,scaling,of,the,code,is,not,ideal,,say,due,to,collective,communication,,then,simply,increasing,the,number,of,processing,units,by,N,will,not,allow,the,intrusive,approach,to,return,a,re-,sult,in,the,same,time,T,as,previously,and,one,must,either,wait,N,T,to,get,the,result,or,accept,a,degree,of,increased,ineﬃciency.,Conversely,,the,non-intrusive,approach,can,split,the,problem,into,N,trivially,parallelisable,jobs1.,Provided,there,is,suﬃcient,computational,resource,to,runs,these,jobs,simulataneously,it,is,possible,to,return,a,result,in,T,.,However,,in,the,extreme,limit,where,it,is,only,possible,to,run,one,simulation,at,a,time,the,non-intrusive,approach,may,actually,return,a,result,slower,than,the,intrusive,approach,run,on,the,same,number,of,processors,,due,to,repetition,of,overheads.,For,example,,suppose,the,simulation,generates,a,large,mesh,as,part,of,the,initialisation,of,the,simulation.,Without,code,modiﬁcation,,time,may,then,be,wasted,in,repeatedly,generating,the,same,mesh,within,each,simulation,rather,than,reusing,this.,More,generally,,whilst,the,distribution,of,work,into,separate,simulations,used,in,non-intrusive,methods,can,make,the,additional,work,trivially,parallelisable,this,may,typi-,2,cally,make,less,eﬃcient,use,of,the,available,resources,than,intrusive,methods,due,to,the,isolation,of,each,simulation,and,hence,the,duplication,of,common,operations.,Furthermore,,the,isolation,of,separate,simulations,means,it,is,not,possible,to,take,advantage,of,the,expected,similarity,of,the,diﬀerent,cases.,For,example,,suppose,the,simulation,involves,the,iterative,solution,of,a,large,sparse,matrix,problem,for,each,case,within,the,ensemble.,In,an,intrusive,approach,one,may,envisage,using,the,solution,of,one,sample,to,provide,a,good,ﬁrst,guess,for,subsequent,samples,,accelerating,future,solves,and,limiting,the,increase,in,re-,quired,computation,to,less,than,the,factor,N,.,Such,an,approach,is,not,trivially,possible,in,non-intrusive,UQ,and,certainly,not,without,introducing,some,seri-,alisation,of,the,simulations.,Where,the,balance,lies,strongly,depends,on,both,the,simulation,problem,at,hand,as,well,as,the,properties,of,the,computational,systems,available.,Within,the,ExCALIBUR-Neptune,project,non-intrusive,ap-,proaches,are,currently,preferred,and,this,report,will,focus,on,aspects,relevant,for,these,cases.,With,non-intrusive,UQ,requiring,a,number,of,repeated,simulation,executions,with,diﬀerent,parameters,,it,is,clearly,important,to,ensure,that,individual,sim-,ulations,are,setup,as,eﬃciently,as,possible.,In,doing,so,care,must,be,taken,,however,,to,consider,the,potential,for,variation,across,the,runs,required.,For,example,,when,manually,running,a,single,simulation,one,may,be,able,to,iden-,tify,the,resolutions,required,for,the,result,to,converge,to,a,given,degree.,The,required,resolution,may,,however,,vary,with,the,inputs.,As,such,,operating,on,the,edge,of,satisfactory,resolution,for,the,nominal,case,may,lead,to,severe,under-resolution,in,other,parts,of,the,sample,space.,It,may,therefore,be,ap-,propriate,to,build,in,a,margin,of,safety,to,the,resolutions,used.,This,however,,may,degrade,the,overall,eﬃciency,of,the,problem,by,over-resolving,some,cases,and,using,more,resource,than,strictly,necessary.,Such,problems,may,be,avoided,by,the,use,of,adapative,algorithms,which,can,adapt,the,order,and,resolution,in,order,to,keep,errors,to,some,ﬁxed,level.,A,common,example,which,can,be,ob-,served,even,in,ﬁxed-grid,ﬁnite,diﬀerence,codes,,such,as,BOUT++,,is,from,time,step,adaptivity.,Here,the,limiting,time,step,may,be,strongly,dependent,on,the,uncertain,input,parameters,and,as,such,it,is,possible,to,ﬁnd,highly,variable,wall,time,requirements,for,simulations,within,a,UQ,study.,This,can,have,diﬀerent,consequences,depending,on,the,approach,to,running,the,independent,simula-,1This,is,only,true,for,non-adaptive,sampling,,which,may,not,be,the,optimal,approach,for,problems,with,a,large,number,of,uncertain,inputs.,3,tions.,Where,it,is,possible,to,deﬁne,and,launch,all,simulations,simultaneously,,variable,run,time,has,the,eﬀect,of,slowing,the,TTS,to,that,of,the,longest,sim-,ulation.,Where,runs,are,executed,sequentially,the,impact,of,variable,run,time,may,be,more,limited,if,one,expects,there,to,be,similar,numbers,of,simulations,which,go,faster,and,slower,than,the,nominal,simulation.,In,the,common,case,where,a,subset,of,the,total,number,of,simulations,are,executed,in,parallel,the,impact,on,TTS,is,less,clear,and,depends,upon,the,distribution,of,job,run,times,across,the,jobs,and,the,order,of,execution.,Where,it,is,possible,to,anticipate,the,impact,on,wall,time,requirements,as,a,function,of,input,parameters,,it,may,be,possible,to,attempt,to,load,balance,simulations,across,the,available,resource,,such,as,allocating,more,processors,to,those,problems,with,a,smaller,time,step.,When,running,a,single,simulation,the,TTS,can,often,be,minimised,by,selecting,an,optimal,number,of,processors.,The,optimal,choice,depends,upon,both,the,scaling,eﬃciency,of,the,simulation,code,as,well,as,the,impact,on,queue,time.,Queue,time,can,become,a,signiﬁcant,factor,in,determining,TTS,in,certain,sce-,narios.,This,will,depend,the,policies,of,the,queue,manager,that,have,been,set,and,will,often,become,more,signiﬁcant,when,requiring,a,substantial,fraction,of,the,resource,available.,The,impact,of,queue,time,can,be,compounded,when,at-,tempting,to,run,a,large,number,of,simulations,and,the,user,has,several,decisions,to,make,and,options,to,attempt,to,optimise,TTS.,For,example,,some,machines,may,limit,the,number,of,separate,jobs,which,can,be,submitted/running,at,any,one,time.,In,such,instances,it,may,be,beneﬁcial,to,bundle,a,number,of,sim-,ulations,into,single,jobscripts.,This,may,then,increase,the,amount,of,time,it,takes,for,each,job,to,start,running,,however,,due,to,the,increase,in,the,scale,of,resource,required.,Another,motivation,for,bundling,jobs,may,be,where,the,job,manager,policies,are,such,that,priority,is,given,to,larger,jobs.,Conversely,,a,large,number,of,small,jobs,may,be,easier,for,the,queue,manager,to,schedule,in,the,gaps,around,larger,jobs,(i.e.,using,small,jobs,for,backﬁll).,The,optimal,approach,can,therefore,be,highly,sensitive,to,the,speciﬁc,details,of,the,system,at,hand,combined,with,the,resource,requirements,and,performance,properties,of,the,simulation,code.,Fortunately,,these,concerns,are,also,not,unique,to,any,one,code,and,there,exist,tools,to,assist,the,user,in,constructing,appropriate,workﬂows,and,approaches,to,execution,such,as,FabSim3,[7],and,QCG-PilotJob,[8],integrated,within,the,VECMA,toolkit,[9].,Of,course,,whilst,optimising,individual,runs,and,the,job,strategy,can,be,helpful,,4,ultimately,the,number,of,simulations,required,plays,a,large,part,in,determin-,ing,the,TTS,and,this,is,determined,by,the,sampling,strategy,selected,and,the,order,of,the,sampler.,For,example,,with,a,polynomial-chaos-expansion,(PCE),sampler,the,number,of,simulations,is,given,by,(O,+,1)U,where,O,is,the,order,of,the,projection,and,U,is,the,number,of,uncertain,parameters.,Minimising,O,therefore,can,signiﬁcantly,reduce,the,number,of,simulations,required,,however,it,may,not,be,possible,to,determine,the,order,required,for,convergence.,Adaptive,approaches,,such,as,demonstrated,with,stochastic-collocation,(SC),in,task,2.4,[6],,oﬀer,the,potential,to,reduce,the,number,of,simulations,further,by,selectively,reﬁning,the,sampling,of,parameter,space,in,the,inputs,which,provide,the,most,information.,Furthermore,,these,oﬀer,the,ability,to,terminate,a,study,early,if,results,appear,to,be,converged.,These,gains,come,at,the,cost,of,limiting,the,parallelisability,of,the,simulations,–,there,are,fewer,simulations,to,be,performed,at,a,time,,introducing,order,dependencies.,In,some,situations,this,may,be,of,limited,consequence,,e.g.,where,it,is,only,possible,to,run,a,small,number,of,sim-,ulations,at,a,time.,It,is,important,to,note,that,developing,sampling,strategies,with,improved,performance,properties,is,still,an,area,of,active,research,,see,for,example,[10].,4,The,inﬂuence,of,the,boundary,SD1D,evolves,the,following,plasma,equations,for,plasma,density,n,,pressure,p,and,momentum,minV||,∂n,∂t,(cid:19),p,(cid:18),3,∂,∂t,2,(cid:0)minV||,∂,∂t,=,−∇,·,(cid:0)bV||n(cid:1),+,Sn,−,S,=,−∇,·,q,+,V||∂||p,+,Sp,−,E,−,R,(cid:1),=,−∇,·,(cid:0)minV||bV||,(cid:1),−,∂||p,−,F,j||,=,Ti,=,q,=,0,p,en,1,2,Te,=,5,2,pbV||,−,κ||e∂||Te,5,where,the,heat,conduction,coeﬃcient,κ||e,is,a,nonlinear,function,of,temperature,Te:,κ||e,=,κ0T,5/2,e,and,is,given,by,the,Spitzer,conduction,κ||e,=,3.2,ne2T,τe,me,’,3.1,×,104,T,5/2,ln,Λ,A,similar,set,of,equations,can,be,included,to,describe,neutrals,[11].,In,the,1D,system,studied,by,SD1D,there,are,boundary,conditions,applied,at,ei-,ther,end,of,the,domain.,The,left,most,boundary,corresponds,to,the,“upstream”,representing,where,plasma,enters,the,scrape-oﬀ-layer,(SOL),from,the,core,at,the,outboard,mid-plane,whilst,the,right,most,boundary,corresponds,to,the,“target”,where,the,ﬁeld,line,intersects,the,material,surface,and,plasma,can,interact,with,the,wall.,In,the,presence,of,material,surfaces,plasmas,form,a,“sheath”,just,in,front,of,the,surface,which,is,a,small,region,over,which,quasi-neutrality,no,longer,holds,and,which,holds,a,negative,potential,,accelerating,ions,and,reﬂecting,elec-,trons,from,the,material,surface,such,that,the,net,ﬂux,of,ions,and,electrons,to,the,wall,is,equal.,In,SD1D,sheath,boundary,conditions,are,applied,at,the,target,and,zero,ﬂow,boundaries,are,applied,upstream.,It,is,also,necessary,to,provide,a,plasma,source,upstream,to,compensate,for,the,ﬂow,to,the,target.,There,are,multiple,options,with,which,once,can,specify,these,sources,,including,the,use,of,a,feedback,controller,to,keep,the,upstream,density,ﬁxed.,One,expects,the,neutral,density,to,be,largest,close,to,the,target,and,hence,for,the,plasma-neutral,interactions,to,dominate,here.,There,are,many,parameters,within,the,model,with,which,one,can,tune,the,behaviour,near,to,the,boundary,such,as,the,propor-,tion,of,ions,interacting,with,the,wall,which,return,to,the,system,,known,as,the,recycling,fraction,,the,energy,of,neutrals,coming,from,the,wall,,the,sheath,heat,transmission,coeﬃcient,etc.,Imposing,boundary,conditions,can,constrain,the,solution,and,the,choice,of,boundary,treatment,can,sometimes,lead,to,signifcant,diﬀerences,in,the,simulation.,It,can,therefore,be,interesting,to,consider,how,the,uncertainty,due,to,boundary,conditions,behaves.,To,explore,this,here,we,consider,test,case-04,of,SD1D,as,used,in,task,2.4,[6].,This,combines,the,full,plasma,system,given,above,with,that,for,the,neutral,gas,6,and,ﬁxed,upsteam,sources,,and,can,be,captured,by,Hermes-3.,Here,we,con-,sider,two,scenarios.,Firstly,,we,will,treat,the,upstream,density,and,pressure,sources,as,uncertain.,Secondly,,we,will,consider,uncertainty,in,the,recycling,fraction,frecycle,and,the,fraction,of,recycled,ions,redistributed,over,the,do-,main,,fredistribute2.,For,both,of,these,scenarios,we,will,also,vary,the,density,and,pressure,boundary,conditions,between,free,(constant,gradient),,zero,gradient,and,constant,ﬂux.,This,provides,six,diﬀerent,cases,to,consider,and,for,each,of,these,we,use,PCE,samples,for,all,orders,from,one,to,six,to,explore,the,convergence,of,the,results.,We,note,that,ﬁrst,order,studies,cannot,capture,higher,order,interactions,in,the,Sobol,indices,so,it,is,generally,expected,that,at,least,second,order,will,be,required,in,most,cases.,We,begin,by,considering,the,uncertain,upstream,source,cases.,Figure,1,shows,the,output,for,2nd,and,3rd,order,studies,with,free,boundary,at,the,target.,One,can,see,good,agreement,in,the,uncertainty,and,the,Sobol,indices.,It,is,interesting,to,note,that,the,5th,order,results,,shown,in,ﬁgure,2,,show,some,deviation,from,these,converged,results.,Despite,this,,the,6th,order,study,is,also,near,identical,to,the,2nd,and,3rd,order,,suggesting,good,convergence,by,2nd,order.,The,zero,gradient,study,shows,near,identical,behaviour,so,results,are,not,presented,here.,The,constant,ﬂux,boundary,condition,study,is,presented,in,ﬁgure,3.,Firstly,,one,may,clearly,note,how,the,structure,of,the,solution,has,changed,in,this,case.,From,the,plot,of,the,mean,density,it,is,not,immediately,apparent,that,there,is,any,variation,between,the,2nd,,4th,and,6th,order,results.,On,close,inspection,,one,can,see,that,the,uncertainty,near,the,target,broadens,slightly,as,the,order,increases.,This,is,a,small,relative,change,,but,does,indicate,the,results,may,not,be,fully,converged,by,this,point.,Changing,attention,to,the,Sobol,indices,,the,variation,between,the,orders,becomes,more,apparent.,Whilst,there,is,only,a,small,change,between,2nd,and,4th,order,,there,is,a,more,signiﬁcant,change,in,the,6th,order,result.,In,particular,,one,can,see,that,the,P:powerflux,index,has,reduced,somewhat,across,most,of,the,domain,,and,particularly,in,the,outer,half,of,the,domain.,This,is,matched,by,a,corresponding,increase,in,the,higher,order,indices,,with,the,Ne:flux,remaining,relatively,unchanged.,This,suggests,that,there,are,inter-dependencies,that,are,relatively,high,order,in,nature.,These,cases,serve,to,demonstrate,some,of,the,beneﬁts,and,challenges,for,adaptive,2See,section,6.2,of,[11],for,more,details.,7,methods,,such,as,those,discussed,in,task,2.4.,The,free,boundary,results,were,well,converged,by,3rd,order,whilst,going,to,6th,order,required,substantially,more,simulations,(16,vs,49,in,this,case).,A,high,order,adaptive,method,may,be,able,to,stop,early,when,convergence,is,observed.,However,,the,case,with,constant,ﬂux,boundaries,demonstrates,a,challenge,to,this,–,results,can,appear,broadly,converged,at,low,order,but,new,variation,can,arise,when,continuing,to,yet,higher,order.,One,needs,to,take,care,in,the,stopping,condition,for,adaptive,approaches.,(a),(b),(c),(d),Figure,1:,Plots,of,the,mean,normalised,plasma,density,,Ne,,as,a,function,of,parallel,arc,length,along,with,the,mean,±,the,standard,deviation,for,a,2nd,(a),and,3rd,(c),order,PCE,sampler,and,the,corresponding,ﬁrst,order,Sobol,indices,(b/d).,Free,boundary.,8,(a),(b),Figure,2:,Plots,of,the,mean,normalised,plasma,density,,Ne,,as,a,function,of,parallel,arc,length,along,with,the,mean,±,the,standard,deviation,(a),and,the,corresponding,ﬁrst,order,Sobol,indices,(b),for,a,5th,order,PCE,sampler.,Free,boundary.,9,(a),(b),(c),(d),(e),(f),Figure,3:,Plots,of,the,mean,normalised,plasma,density,,Ne,,as,a,function,of,parallel,arc,length,along,with,the,mean,±,the,standard,deviation,for,a,2nd,(a),,4th,(c),and,6th,(e),order,PCE,sampler,and,the,corresponding,ﬁrst,order,Sobol,indices,(b/d/f).,Constant,ﬂux,boundary.,10,We,now,turn,attention,to,the,case,where,we,treat,the,recycling,fraction,,frecycle,,and,the,redistribution,,fredistribute,,as,uncertain,inputs.,Here,we,adopt,a,uniform,distribution,with,minimum,of,0,and,maximum,of,1,for,both,parame-,ters.,Figure,4,shows,the,2nd,,4th,and,6th,order,results,for,the,free,boundary,case.,This,demonstrates,reasonable,convergence,at,4th,order,and,the,5th,and,6th,order,results,are,near,identical.,Again,,the,zero,gradient,results,give,very,similar,behaviour,so,are,ommitted.,The,constant,ﬂux,results,are,shown,in,ﬁg-,ure,5.,Although,hard,to,see,,this,shows,that,there,is,variation,in,the,uncertainty,on,the,measured,Ne,between,4th,and,6th,order,,particular,near,the,target.,This,is,,again,,more,visible,in,the,Sobol,indices,,especially,in,the,higher,order,and,sd1d:fredistribute,parameters.,These,results,shown,that,at,least,5th,order,It,is,important,to,note,that,the,conﬁdence,is,required,for,convergence,here.,intervals,shown,here,include,unphysical,negative,densities,which,cannot,have,been,found,in,any,simulation.,In,such,situations,one,may,wish,to,work,with,logarithmic,variables.,11,(a),(b),(c),(d),(e),(f),Figure,4:,Plots,of,the,mean,normalised,plasma,density,,Ne,,as,a,function,of,parallel,arc,length,along,with,the,mean,±,the,standard,deviation,for,a,2nd,(a),,4th,(c),and,6th,(e),order,PCE,sampler,and,the,corresponding,ﬁrst,order,Sobol,indices,(b/d/f).,Free,boundary.,12,(a),(b),(c),(d),(e),(f),(g),(h),Figure,5:,Plots,of,the,mean,normalised,plasma,density,,Ne,,as,a,function,of,13,parallel,arc,length,along,with,the,mean,±,the,standard,deviation,for,a,2nd,(a),,4th,(c),,5th,(e),and,6th,(g),order,PCE,sampler,and,the,corresponding,ﬁrst,order,Sobol,indices,(b/d/f/h).,Constant,ﬂux,boundary.,5,Summary,In,this,report,we,have,discussed,some,of,the,relevant,performance,considerations,when,performing,UQ,studies,with,a,toolkit,such,as,easyvvuq.,Whilst,there,are,many,aspects,that,can,inﬂuence,the,time,to,solution,,two,of,the,most,signiﬁcant,aspects,which,impact,the,eﬃciency,of,such,studies,are,minimising,the,number,of,simulations,required,and,eﬀective,use,of,tools,to,help,automate,and,manage,complex,workﬂows.,The,latter,frees,the,user,from,having,to,micro-manage,the,simulations,and,analysis,,allowing,them,to,focus,on,other,aspects,of,the,work.,In,a,crude,sense,,the,number,of,simulations,to,be,performed,is,controlled,by,the,order,of,the,projection,and,the,number,of,uncertain,inputs.,However,,adaptive,schemes,can,optimise,the,approach,to,sampling,such,that,simulations,are,tar-,geted,to,reﬁne,in,the,directions,returning,the,most,useful,information.,This,,combined,with,a,method,to,test,for,convergence,,can,allow,for,a,signiﬁcant,reduction,in,the,number,of,simulations,required.,We,demonstrated,how,Sobol,indices,and,the,population,distribution,estimates,required,diﬀerent,projection,orders,to,converge,depending,on,the,uncertain,parameters,and,boundary,condi-,tions,used,,ranging,from,2nd,to,6th,order.,This,highlights,one,possible,advantage,of,adaptive,schemes,,but,also,gave,a,demonstration,of,challenges,to,be,faced,in,testing,for,convergence,where,Sobol,indices,were,observed,to,roughly,converge,by,4th,order,,only,for,signiﬁcant,change,to,be,found,at,5th,and,6th,order.,For,the,simple,test,case,considered,here,it,was,possible,to,perform,high,order,PCE,studies,in,under,ten,minutes,using,a,single,node,of,Archer2.,More,expensive,systems,would,likely,beneﬁt,from,the,use,of,FabSim3,[7].,6,Acknowledgements,We,gratefully,acknowledge,compute,time,provided,on,CIRRUS,and,Archer2,through,the,Excalibur,SEAVEA,project,[12].,14,7,References,[1],Wright,,David,W.,and,Richardson,,Robin,A.,and,Edeling,,Wouter,and,Lakhlili,,Jalal,and,Sinclair,,Robert,C.,and,Jancauskas,,Vytautas,and,Suleimenova,,Diana,and,Bosak,,Bartosz,and,Kulczewski,,Michal,and,Pio-,ntek,,Tomasz,and,Kopta,,Piotr,and,Chirca,,Irina,and,Arabnejad,,Hamid,and,Luk,,Onnie,O.,and,Hoenen,,Olivier,and,Weglarz,,Jan,and,Crommelin,,Daan,and,Groen,,Derek,and,Coveney,,Peter,V.,Building,conﬁdence,in,simulation:,Applications,of,easyvvuq.,Advanced,Theory,and,Simulations,,3(8):1900246,,2020,,doi:https://doi.org/10.1002/adts.201900246.,[2],Richardson,,Robin,A.,and,Wright,,David,W.,and,Edeling,,Wouter,and,Jan-,causkas,,Vytautas,and,Lakhlili,,Jalal,and,Coveney,,Peter,V.,EasyVVUQ:,A,library,for,veriﬁcation,,validation,and,uncertainty,quantiﬁcation,in,high,performance,computing.,Journal,of,Open,Research,Software,,8(1):1–8,,2020,,doi:10.5334/JORS.303.,[3],Benjamin,Dudson.,SD1D:,Sol,and,Divertor,in,1D.,https://github.com/,boutproject/SD1D.,[4],Benjamin,Dudson,,Peter,Hill,,Ed,Higgins,,David,Dickinson,,Steven,Wright,and,David,Moxey.,1D,ﬂuid,model,tests.,https:,//github.com/ExCALIBUR-NEPTUNE/Documents/blob/main/reports/,2047356/TN-04.pdf.,[5],Benjamin,Daniel,Dudson,,Peter,Alec,Hill,,David,Dickinson,,Joseph,Parker,,Adam,Dempsey,,Andrew,Allen,,Arka,Bokshi,,Brendan,Shanahan,,Brett,Friedman,,Chenhao,Ma,,David,Bold,,Dmitry,Meyerson,,Eric,Grinaker,,George,Breyiannis,,Hasan,Muhammed,,Haruki,Seto,,Hong,Zhang,,Ilon,Joseph,,Jarrod,Leddy,,Jed,Brown,,Jens,Madsen,,John,Omotani,,Joshua,Sauppe,,Kevin,Savage,,Licheng,Wang,,Luke,Easy,,Marta,Estarellas,,Matt,Thomas,,Maxim,Umansky,,Michael,Løiten,,Minwoo,Kim,,M,Leconte,,Nicholas,Walkden,,Olivier,Izacard,,Pengwei,Xi,,Peter,Naylor,,Fabio,Riva,,Sanat,Tiwari,,Sean,Farley,,Simon,Myers,,Tianyang,Xia,,Tongnyeol,Rhee,,Xiang,Liu,,Xueqiao,Xu,,Zhanhui,Wang,,Sajidah,Ahmed,,and,Toby,James.,BOUT++,,3,2022.,[6],Benjamin,Dudson,,Peter,Hill,,Ed,Higgins,,David,Dickinson,,Steven,Wright,and,David,Moxey.,Non-intrusive,UQ,with,BOUT++,1D,15,ﬂuid,solver.,blob/main/reports/2047356/TN-08-1.pdf.,https://github.com/ExCALIBUR-NEPTUNE/Documents/,[7],Derek,Groen,,Agastya,P.,Bhati,,James,Suter,,James,Hetherington,,Ste-,fan,J.,Zasada,,and,Peter,V.,Coveney.,FabSim:,Facilitating,compu-,tational,research,through,automation,on,large-scale,and,distributed,e-,infrastructures.,Computer,Physics,Communications,,207:375–385,,2016,,doi:10.1016/j.cpc.2016.05.020.,[8],Tomasz,Piontek,Piotr,Kopta,and,Bartosz,Bosak.,QCG-PilotJob.,https:,//github.com/psnc-qcg/QCG-PilotJob.,[9],VECMA,Team.,Veriﬁed,Exascale,Computing,for,Multiscale,Applications.,https://www.vecma.eu.,[10],Linus,Seelinger,,Anne,Reinarz,,Leonhard,Rannabauer,,Michael,Bader,,Pe-,ter,Bastian,,and,Robert,Scheichl.,High,performance,uncertainty,quan-,tiﬁcation,with,parallelized,multilevel,markov,chain,monte,carlo.,In,Pro-,ceedings,of,the,International,Conference,for,High,Performance,Computing,,Networking,,Storage,and,Analysis,,SC,’21,,New,York,,NY,,USA,,2021.,As-,sociation,for,Computing,Machinery.,[11],Benjamin,Dudson,and,others.,SD1D,Manual.,https://github.com/,boutproject/SD1D/tree/master/doc.,[12],SEAVEA,Team.,Software,Environment,for,Actionable,and,VVUQ-,evaluated,Exascale,Applications.,https://excalibur.ac.uk/projects/,seavea/.,16

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