The Julia programming language in applications for electrochemical systems simulation

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The Julia programming language in applications for electrochemical systems simulation
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Julia is a new computer language with multidimensional arrays as first class data types designed for numerical computations. Compared to other languagues with similar purpose (Matlab, python/numpy, R), Julia follows a number of promising paradigms. Julia was designed around a just-in-time compilation strategy which guarantees high single thread performance. At the same time it supports various parallelization approaches (shared/distributed memory, GPU offloading). Programming paradigms like multiple dispatch and reflection provide a high level of expressivity. The talk will give an overview on these features of Julia. Based on first principles of nonequilibrium thermodynamics, at WIAS, a modeling and simulation strategy for electrochemical systems has been developed which accurately accounts for phenomena which are poorly reflected in classical models like finite ion size and constraints, solvation phenomena. These models result in highly nonlinear systems of partial differential equations. The talk presents first steps towards a Julia based implementation of a finite volume bases numerical solution strategy for these systems.>
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and this nice place and fully on a lesser so who have total mean to be here and going on between him OK my talk I will mostly focus on on Newell a programming language so I'm looking into submission of electric
and the systems and the question is can we used as language in this context so this of some kind of test and we have started to
load 1st projects which are using doing effect and and we got some experience from this and that I would try to sheds so some back of computer
languages so most of you in on this of course compiled languages also basically the that same the preview languages and scientific computing are compiled languages which allow I highly optimized
forward and Jezek this is of course what from 49 modern photon put on a 77 which is some kind deal for because language and scientific computing gear has lots of land use in libraries and but it's very hard
to write complicated for programs so complex problems in part on 77 because lots of structuring tools for not 1 and Fortran and thought and I devoted to the the for to those made is much better with in this respect but a day from my point of view can make this this developing destructuring and
so did in most momentum among new programmers but of course fans of larger problem problem using 1 of photons and you could say and so that's just my personal point of view so and see essentially to go off trimester as a language which provide structuring tools and C. plus plus a not
currently believed to be the football for a and language which is a superset of C which is not so full of pools of structuring get the cold C. plus plus 11 was a quantum leap the many new features of the language should show essentially fortified it's quite a bit the the the problem C plus plus is of course that it's a very steep learning coughs and and you don't need also lots of to combine libraries in this languages and so on OK so that's and that's very sort of writing codons languages isn't and some very use because they're they're very rigid and so on so and so on and of
course if you sign of the scripting languages for many smaller parcels of a larger projects like
Math-Net Python like the servers similar Sunday KSUless kind of boilerplate cortices as necessary more to perform some tasks and they're
executed in an intrepid out when usually d interpreter works in such a way that at 1st DDD language code as on-the-fly compiled to some byte code and by cortisone and a printed efficiently and and this of course this is kind of co-training has so surprised essentially accord show you why does very far away from the CPU so is usually significantly slower than the quadrature can can get from the compiling interests so you can have a lesser type-checking where these 2 feeling to you have listed in strict type-checking because languages and operated they have all for introspection capabilities forms of it so that you have which allows to look into components of a structure and in English which is for instance impossible in C. C plus plus you have an intermediate workflow you've just by the court in restaurant and L 2 twist which interface to fort unsealed C. plus plus and and Saudi kind of senate very many people for instance we are working with for for for all 4 of the simulation project a study of some kind of core components which on a compiled language and then we have a Python interface vision loss of flexible and control 450 indeed is core components underscore which is so poor language problem 1 wants to have some called language which is fast and flexible language for the use of and this is all of these 2 and then a smell some kind of trend to go to just-in-time compiling just-in-time combining from I'm kind of music kind of technology evolution in computer languages which are just as 70 before wise essentially the ideas that we don't compile to some intermediate byte code which is done in the printer but that they just compile commission caught on the fly and it's that's the basic idea and that this is a essentially and on and on and in many cases for instance modern rollers use just-in-time compilers for speeding up the job could things which are running in the role at the graded this low-level return machine compiler infrastructure which is essentially a library which is allow us to to to to right just-in-time compilers does a project which tries to speed up I've known as are small tokens is storable language which already had something like this and projects for just-in-time compilers are available job there's a language called jewel of it is more of a interest also just-in-time compiling pool and then we have to which is based also on his VN compiler infrastructure which essentially is a just-in-time compiled language which is for the the progress of scientific computing and so just new competent just I learned about recently you look at roles are component essentially no has instead of the and their wars began which is also just-in-time compiler that thing did this could go
on so and this means that a just-in-time compiling which you can have powerful syndics features like like is interpreted languages have some competition denied
committed combination in a style of a but just could be mediated by caching caught and you can get high performance and this is of course the idea
that young which you draw the project was started in 2 dozen mind at the MIT and just essentially to talk essentially 9 years to go to version 1 comma decimal 0 that sure there was an error
available since last some there just appeared minus review on new during which Judea and in 2018 jury of 1 year victims and price
from America suffered the Chosin given every 4 years and not many projects get his due due due to about esteem to try article but should goddess and not bureaucrats and yeah so so doing version 1 comma decimal 0 I didn't really work this truly I had to somehow on on my screen but I thought OK so they will have breaking changes into court which did indeed happened and and so it goes some limitations in time in noticeable that this but 1 time 0 and we can really tried this all at and invest in court with all to new danger that things change quickly there are lots of resources on 9 available decimal bridge of did you booked somewhere and and in introduction face and I won't give them some kind of introduction how to write a formal in Judea but I will focus on
some features of 2 which which might have might be attractive and so OK so how to characterize you do we have 1 could say OK it's just like magnet but to its faster because it's just-in-time compared or you can say OK it's just like about it but what resources and resource project all I can say it's like pies by which is of course some current alternative also too much but it's fast so once again because of 2 just sometime in future compiling feature and all errors come from 1 instead of from 0 so what so that's that's that's an interesting problem anyway so men propose essentially as really scientific computing and and where so we have Monday the areas injuria as 1st class objects like in Fortran in MATLAB but unlike C. plus plus C. plus plus lakes modern images errors as 1st as object if you will want to work this Monday dimension errors and C. plus plus you need to choose the form 1 of several every libraries and all these other new languages which are somehow will popping up of swift trust more difficult have stages as
well so softly and essentially Morocco analysis and really certain field which which it's this kind of data structures so as I would
said users are coming from 1 so far unimodal offensive and be happy with this and people come from C plus plus and Python and hate this even just pairs so if you come from UCLA also from pattern by you know how to work with slicing all these kind of 4 features on Judea we have already an extensive library of standard functions of linear algebra operations and we also has a very large package ecosystem already in flight sophisticated package manager which and essentially has it up and down that package if it's installed into your computer or Donaldson particle version of a package show from get up and and and puts it on a computer so it has been developed from
scratch using modern notation language development department of course and humankind essential some murdered lots of law chargeable from the Deligne Mitchell and and and just to do the developers of course could could build on this the language vi valued and not always just specified happening just all of a strongly typed the incest and strong typing means that and you can compiled just UDD language called proved their performance called I will say something more about what had been dispatching sense in a C plus plus speak all functions of our century templates the polarization pose availability languages reflexes you have a model system and model you have some kind of command-line we divide print loop and ok data as a foreign function interface to see Fortran you can wrap levels from the blast let's particle of
interfacing to foot on this is rather straightforward that reflexivity also allows for for just grading proxy orders from another male and interpreted language for instance the PICO Audigier package which
loads a loss to load essentially any Python model into Duluth and using this means you can for instance use ordered prodding tools which are available from Python you find useful new here the value of intrinsic put sort of imitation profiling testing you have code inspection of the the intermediate court and also of genitive similar court Desai the integration packages far available for instance intermediate or dead just to buy on notebooks addition law and adjective working this truly near although like this is also quite often done with Python some features so wanted this
page OK so we can define a function you know just believe some kind of 1st in the fight standard function then this function let's just have a function which does its 2 numbers we write it like this and the can you don't specify the data types you inviting dysfunction became corners function which different the 5th this Parliament also of different data types Yubico dysfunction of this and really no must as of road floating point numbers as parameters and the Rococo dysfunction and the fractional numbers them as Parliament of so doing as good immigration numbers and if you notice the function would be a just-in-time compiled in 2 instances the B 1 version for real now mass and another version for formation anomalous and everything will be optimized for for for for these numbers and if you look at the result of this you can get as a result than just a real of course is some or you could get as a result duration number which is the sum of these 2 operations them so that's that's in some kind of basic idea and C. plus plus 14 you can write this kind of code for those as a template function which shares sometime upon medicine which also has an altruist specify which essentially determines studio data type after did you to package and then used to need an expression Template Library for aeration and numbers that you could install from was for instance in C. plus plus but if you compare the in the historical forgetting just to run and for doing this they you see some kind of advantage of you in this context OK so once we can have
different number types I aggression and muscle real what you can also have with them when I must this
ring you can define during the Lunar must by just user using some kind of AppSec number love at Cylon various shapes Alaska's you will
it's like you had hired to relational due to real enormous and you're going to public stand was but I stress minus 1 and a tooth for a 0 and this creates a ring of numbers and
Michigan also just represent as a subset of poor little that was us and if you look at hollowed polynomial have then you're just a group called of the justice discounted when number and if you collect that you could do you do reside in such a components so boring 1 part and you components before it's turned on the 2nd part you see that you have a relation of 2 function and its derivatives at the same time and then you can of course generalize this to an integer the function and this means using us as numbers which you can can using a computer language you get an automatic in relation of functions and derivatives months and this means you can go to full of mode automatic differentiation with result lots of could provide this can be generalized to watch it to source functions of multiple components scored and modulate do anonymous in C plus plus you can get this also by using some expression Template Library difficulty by government which also see the Chern you to put together the
so-called and dismay and you I have you to do
and I must Bergeaud package and was peckish form understood stodgier which you can run and install new during installation and you can write code for a functional cumulative relation of intuitive for free so that's something that but interesting I wanna
said so can I will just do it with foster this another feature of juniors
the colonization you can have experimental you already have my experiment modifying so supportive support for multiprocessing like MPI there's also Dell's already packages for doing GPU programming and and pushing them and you Yabucoa knows riding appeal into here so maybe this is delivered to go from moving target but but this is something that you can start
using the of structuring tools slide models like at stake tireless which and also to control module dispatcher in the winter you can have starch which compile you date that essentially then if you write functions like all function and then you get something like duck typing in the open literature look plus plus the typical duck typing it's a technique extensively used in C plus plus standard worry libraries essentially DAT and any method of IT pomade a method works and if it has a particle interphase so dysfunction adverts for all didn't harvested should know how to do the class and so and you have a very flexible of of of wide Incan packages and you know glorious also quite
interesting if you have a package which provides a function which has 2 parameters 1 parameter is a function which depends on 1 variable and you have a 2nd parameter which shows should rule does something in this and I want to use this package of the function which needs another but empowerment and or a two-pass my own data from this function UCB would be to have a comic function which shows an additional has to have watched star parliament or something like this which should be done by the package design of new package C. plus plus we would be that I have some kind of basis base class but I can be like my data from and during a so-called killed us can essentially that the function the the data objects into a new function and then you can pass this to the package manager and a package manager doesn't have to propagation and designer doesn't have to care about which stayed out to pasture the function applied interesting feature and I got stumble on this when I tried all the 1st steps on on on on an automatic differentiation June OK so the question is
now a language ready for prime time I've already made the a lot of statements minus which can be good and OK but they're also is maybe some pitfalls use languages throughout flesh is at a moving target so now we have a degree of 1 comma decimal you and if you compare this with the competing languages I already mentioned we see that C plus plus is a much more of a moving target currently in and Python is moving part target as well depriving tool to present to transition is still and it's so well OK maybe that's not give them before that the biggest problem I think we have this an investment into existing code but this means we can try to use did you study what he had to use an existing get filamentation patients and for dancing C. plus plus self or important components the those tools which are given to us from the viewer echo ecosystem and all from the particle system so in just this is possible and then of course there also are new kinds of design paradigms so 1 refinement object-orientation C plus plus then 1 needs to think about is Monteverde dispatch things and so on still for libraries developers to sodium at but it seems to be easier to design and by programming gives which is used to understand from 1 experience user steps that students do you have been the idea here OK so now
electrochemistry there's not much time on this so but that's my main work
in the field of and in electrochemistry electrochemical systems if you want to monitor that duty big challenges to the affair quiet day a complicated character models which they're they're just on every level we have summoned interesting features to C and D problems which come out of this or clients nonlinear highly nonlinear directions terms so depending on electrostatic potential and therefore a strongly covered motion of files electrolytes and so on and I just voted to try to give a
certain impression what how these things work on this level from the basic electrolyte if you look at the implementation of the new discussed you find about method for convection diffusion problems that we have some connective diffusive transport of a species in some field this is the flux and this it's a continued creation which essentially has been derived from Interational for the representative elementary volume and all they had to work with this kind of problem is to adjust explicitly constructed representative elementary volumes and derive a discrete system from this construction that's the idea of definable method which many of you of course will and in order to
do this so we can construct an explicit in order
to do this we need an expression of 2 fluxes between 2 neighboring control rooms from if you had speech concerned concentration is controllable components and for this there some classical exponential fitting out the numerical fluxes which can be used the and that's so coach offered a woman discretization and assess a generalization for nonlinear problems and if you go make into
electrochemistry maybe our writing date creation as 2 simple so infected concentration always depends on what on the chemical potential for species walk on the chemical potential of all the species which which are out so that's that's so you have to serve in the semiconductor context can have this dependence on the chemical potential 1 species America chemistry to chemical potentials of all species and and solution are linked together and then digestion is how to
them express it is not can endure creation we can define an excess chemical potential or the activity coefficient in order to express geez this gelatines and from this you get different formulations then of do you diffusion flux fish are improve on on the symbol representation I showed before and you can have for instance and formulation adjusted based on some so-called diffusion announcement so this novel nonidentity pops up as a nonlinear diffusion coefficient on this case essentially conformity Cimflex is just another under transformation that the an excess chemical potential depending ones and concentration in addition of why force and from this you can and defined different nonlinear 2 point flux expressions for our dreadful diffusion system when we see that these are a few we have that really function which is exponential function here the goal don't you have to come and potential system give depend on concentrations and these are highly nonlinear expressions and in order to solve systems and you market to all method of choices Newton's method and for Newton's method in all we need all the derivatives of these terms and if you writers accessible language result automatic differentiation it's quite a lot of work to to to to to get to this
and this is much easier so the ideas
from from this kind of structure of data we can have wide you often programming interface to define and for method for this kind class of assistant creation then you just need to implement stored trekking flux terms as use of functions and all the rest is time just an economic of a given a discretization worked and and so the implementation of these functions have lost will we get to you just could not and operator and for Newton's method you have to be able to look dissonant operator this has been implemented in some
cooling which caught in the vitamin C. plus plus of course and they tried to solid null also for some new projects in electrochemistry enjoy and for instance
they have this kind of you you for our charge transport in semiconductors The was such a 6 which would be the same as sensible modern form phone ionically could therefore nonlinear degenerating diffusion coefficient and in addition given potentially creationists gives us do you did you did is potential field and from solving this kind of problem you get a natural limitation of concentrations in longer close to working electrode and finite double-decker persistence which are significant improvements or the classical model that we wouldn't have to Stygian or is it turning and
what we will need to write to flux in Judea as the use of function this just as the need and and mentation of disbelief function and the right this kind of function which then is it related to this real none last August numbers and there's no need to work this all these complicated to derivatives of 2 bodily function do do disarmament and so on and so on and you can so this is everything necessary to estimate the flux bird from part of the nonlinear operator and integer commentaries the started to work this summer hello boy
project partners and PhD students on a rule but really it was so much easier way to work toward tool to understand what is happening in court and then with all its use C. O. C. plus plus a python implementation and installation enjoy no is quite easy no fiddling with a bit system you can of also soldiery often package as ministers and you know systems there are also lots of useful packages in statistics ordinary differential equations and so on so what I missed was as a library designer for this kind of things for something like concepts which is also discussed for C plus plus 2 is this duck typing features and Angelia graphics is not did they are so essentially you collect would prove to graphics which not that fast there is passed ladies 1st task could be improved maybe we can can discussed has also which could be prolonged wing the Judea world just long implementation from C plus plus so for me it just as a conclusion it's worth to try this alternative maybe at 1st and a smaller project in order to see how how things work all day and then I hope this study can really goal was just language as some kind of replacement of toward language kind of system and we we are currently having this and Python and and and and C. plus plus so thank you so much
the it was