From b0c4f56d95aec8406ec45a2ab8ddc6f282345df5 Mon Sep 17 00:00:00 2001 From: Your Name Date: Thu, 17 Feb 2022 12:21:08 +0100 Subject: [PATCH] images on readme --- README.md | 14 +++++++------- readme/poisson_plot.png | Bin 0 -> 44885 bytes readme/poisson_problem.png | Bin 0 -> 26673 bytes 3 files changed, 7 insertions(+), 7 deletions(-) create mode 100644 readme/poisson_plot.png create mode 100644 readme/poisson_problem.png diff --git a/README.md b/README.md index 5eb62aa..1cf69ac 100644 --- a/README.md +++ b/README.md @@ -55,13 +55,10 @@ PINN is a novel approach that involves neural networks to solve supervised learn #### Problem definition First step is formalization of the problem in the PINA framework. We take as example here a simple Poisson problem, but PINA is already able to deal with **multi-dimensional**, **parametric**, **time-dependent** problems. Consider: -$$ -\begin{cases} -\nabla u = \sin(\pi x) \sin(\pi y) & \quad\text{in}\, D,\\ -u = 0 &\quad\text{on}\, \Gamma_1 \cup\Gamma_2 \cup\Gamma_3 \cup\Gamma_4, \\ -\end{cases} -$$ -where $D= [0, 1]^2$ is a square domain, $\Gamma_1 \cup\Gamma_2 \cup\Gamma_3 \cup\Gamma_4$ are the boundaries and $u$ the unknown field. The translation in PINA code becomes a new class containing all the information about the domain, about the `conditions` and nothing more: +

+ Poisson approximation +

+where *D* is a square domain, *Gamma*s are the boundaries and *u* the unknown field. The translation in PINA code becomes a new class containing all the information about the domain, about the `conditions` and nothing more: ```python class Poisson(SpatialProblem): spatial_variables = ['x', 'y'] @@ -104,6 +101,9 @@ plotter = Plotter() plotter.plot(pinn) ``` After the training we can infer our model, save it or just plot the PINN approximation. +

+ Poisson approximation +

## Dependencies and installation diff --git a/readme/poisson_plot.png b/readme/poisson_plot.png new file mode 100644 index 0000000000000000000000000000000000000000..cb3d6d8d6f3bc67b38b8c30710046fbcb6038ef3 GIT binary patch literal 44885 zcmeFZby!vFx(7ND=@tb9Bn3oC>8?qMq>7YuNlQryNT-M(ASnXUA`Jr4Ad)I6NFzw2 z5|Z~Fy7u1ZoW0I-&$;o}z4KXXZx`yAbB^(S@B9Ah3)fInB*Lf0N1;$e%1UT06bkD( z3WZ^Yiw!^Njw@=0{}XYQ*Kxh!Xz6<2#MuI+YU1i-=jdv8*ObBC!rA4nqXQq802eO@ zgSD%xlZz-fxBWl=0GFe)75Avg_XfBKo|BTU3kpSIg8Yk-CzX2_g?iPZjF!3Sk-GZD z+u)|#vD79dCB``%^uyRw&0GP6cV{Ewz9v7Rnz#IzAfFtT%#{>iq#{JVW=Z+m8c*a{vF7_<;M7hih zI8M^neg6DekCg16FWsbuL2?GBf4-om^`+NCR3THC_OKjf;@3yX@H_9XFIE@~MXKDur6;M|wG`=RCKe1}Iz zr4C=-3`>w*6eE1Dd{)R|LVD`$gV@y6iK4B=zBD;B`ZS&AJQ=N&FKxMHZ_9jFT&ef2 zL#)*`^hFZ=Dmxij*;8l8$?vU>^8Q>Kr!+A!sc~M27~2XZq3WA^Mj(2va*b}HifABYS`=7Jn>JT;+fI;9p1Zn>z2vJWW&J9 z_R@GYH}VrILTt_c#1TBE7YVV;qGadJ1*fLcX6NRbbw0X)Jd>AdX_xnZeHWEM4_e#1K{e)ezoU!jv zgTB8O5~Ck^!vETyY=%lD*?E6`W@Xdb(t=JsPZsM#NGtqWP*6~N&&AEntvDt|eQmZq zviFhS{*K9y|F z$j4VcDFn~M z`uaK*kFh@wD?k6)ot>R`@86e={?a`KYt+0u-ZyP;f2D-ixCvFiJLz4s@~Y11%BYbT*^T4X>)s<}Wmj+Byjihax^XD(?Cu^?US8f+ z1=}a{&704wi__me<@VCmW%jF@tq{)n(a@M#S%o^j{e^AT5hatWmS*heNW#s{ot=}D z>9W|zDXxES3l@~=>o$Q?8XImc#ym~k-QDxPii(OJ9v)$n1^GG1ZQxb%OtW5xKXU9g zyE<0Bw_dj~Jv$q~-FSFr$H;weMp9qZEb9+#z!??l`q>5-n@A;te?lu%S%Q;$z``y+NPneA2~XzG9V9Dgw ze)dY+T$v=hT~e_sYN9d{mYhrtCCud0OI0Tq7fcj~eifm*#P(V3A{~<*6|@!w_P|8~ zye0==pAFQblpFb0Fq&suwOpp{MC1q=WKZ(oLkk(q}sn2K|-j|_0bF zRA9HtzIt&ZSFQMSkHBB~nmzs4FAMT7hw$R=#(s}sv zr>osW4H-Nn`<-7Ay-!BMzbIBLExqS5N1vX!R4g;fAXivI*0i?LR#_;(d2GikS(REs z4m)yk_7=P@ad6me-peuVT4`%}5I8gYK7%dKllai9aq!0LgH~o zhNo$}Q>v8iaf?NF;G64crEOwY6@2I=*EiU^cb9Ifr;3TTv{$CJFDjuwDivNZc0ah0 zY{n_7rtkN3cxZ_DRhr%zy~$TjP}f;ctob{;y71s8y?ghrDT&w2VdKt?z^Ev~w)XaC zUlemcF)}k_LR~&nHFPvVh>Pp5T_~@h5VA?q_TFP6gs?E^CbVxAjS@tz0@O?SLB=ro-cm= zxkH3>;#B(84)S;JvK!pFgMpGd`boaJwx)l_Q|)_8##^PcIXOAPzK6n(=%t9K-GA)Q zb;dADNzpg0*#zQ|v*OO>s-}dLTlLQ_BpP+V_ANDS$M@M8vkHreNi^L@XQMI_e|9di z9Oa~kv|qe<(HKhWXw5xlXBQXV2m7uQHTN(-eE5L!hf5hx)_b<>J>#=t;^ZV!N#trr zuI4l&>jUMeMT%!_b(P0MIn%zqG(s1$dTkw8_1Lki;Qfoxi>dG zH^;n;^e5+vUA^bZdv*lQM3e6XJcJ}PEDN~Yq=#6rSijmcEUvWW-^g`3+`D&{g5pI@ z&FK7(3#fGObrIKZAF<$@Kw~&dOeY>D;_}t_W45wgW9FGdy+rgDG@7|sMLM!$yThR> z)u9j|p^o1L56nhB+!h4R#qEMQAYL1DRFOCDQBCAXBIjqdK{ z>lY6!yj^129Dv0`MYuFlLjUpO#~^vB?>~O1UVcjNwZxeH@}=qV;jg{%spF7?^*R!x z2ixbocGo$hkgj=eu7l`$n&>%sd3j_|fxkOF>s&{e4aHYUMWq!6rHGl<(5$kuGk$xm z^qVDqM+DHI&u#m7LJ74w&;E)W_4@87R#?;~ZDC}uVVRnnUzFTmV*Y@%{U_x51ZmOn zRN|PgYp2JQ`bNSxH=Pcl>yaNHP6v{ls%c;)a;lqh^YRk4>`8ivfr=dG_P zj(W%8Ov8gtK%k?(bJl6K89Xq1DWHp#aK`KlR1#Yc9fZDw&6=Z(7WKROQQ6nze$kKcd3c!8Egh`in4`COT6e6OuW9p{ z5<8VNas}ifs>Vx)Vj=x#b57(B|9&YAQHh^CYUU%;rTOP|wJwD8y^N<5$0W=MkB`9M zCnL)zKKOl+G1id2ue?62Ozgb=tbct9d9zKsbm{;r{~5m6kI0XevuWZFNZJ%Db92&9 zk;N__%~gkHr^}{9ZTRRcvy+nL)5$G{@OrQ^iI@N+vVSqpP+O_z-ADK;{2c|mgpxz? 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