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g=1;g<5;g++)l.push(wa(l[0],m,g/4))}l.length===1&&(l=[...l,[...Dt(l[0],[1,1]),...l[0].slice(2)]]);let c=[{point:[l[0][0],l[0][1]],pressure:l[0][2]>=0?l[0][2]:.25,vector:[1,1],distance:0,runningLength:0}],u=!1,f=0,d=c[0],p=l.length-1;for(let m=1;m<l.length;m++){let g=i&&m===p?l[m].slice(0,2):wa(d.point,l[m],a);if(x1(d.point,g))continue;let b=$1(g,d.point);if(f+=b,m<p&&!u){if(f<r)continue;u=!0}d={point:g,pressure:l[m][2]>=0?l[m][2]:.5,vector:Ep(Tt(d.point,g)),distance:b,runningLength:f},c.push(d)}return c[0].vector=((n=c[1])==null?void 0:n.vector)||[0,0],c}function k1(e,t={}){return C1(O1(e,t),t)}function Di(e,t){return e-t}function T1(e){return e<0?-1:1}function Fi(e){return[Math.abs(e),T1(e)]}function Sp(){const e=()=>((1+Math.random())*65536|0).toString(16).substring(1);return`${e()+e()}-${e()}-${e()}-${e()}-${e()}${e()}${e()}`}var A1=2,ln=A1,js=class{constructor(e){this.drauu=e,this.event=void 0,this.point=void 0,this.start=void 0,this.el=null}onSelected(e){}onUnselected(){}onStart(e){}onMove(e){return!1}onEnd(e){}get brush(){return this.drauu.brush}get shiftPressed(){return this.drauu.shiftPressed}get altPressed(){return this.drauu.altPressed}get svgElement(){return this.drauu.el}getMousePosition(e){var t,n;const s=this.drauu.el,r=(t=this.drauu.options.coordinateScale)!=null?t:1;if(this.drauu.options.coordinateTransform===!1){const i=this.drauu.el.getBoundingClientRect();return{x:(e.pageX-i.left)*r,y:(e.pageY-i.top)*r,pressure:e.pressure}}else{const i=this.drauu.svgPoint;i.x=e.clientX,i.y=e.clientY;const a=i.matrixTransform((n=s.getScreenCTM())==null?void 0:n.inverse());return{x:a.x*r,y:a.y*r,pressure:e.pressure}}}createElement(e,t){var n;const s=document.createElementNS("http://www.w3.org/2000/svg",e),r=t?ba(ba({},this.brush),t):this.brush;return s.setAttribute("fill",(n=r.fill)!=null?n:"transparent"),s.setAttribute("stroke",r.color),s.setAttribute("stroke-width",r.size.toString()),s.setAttribute("stroke-linecap","round"),r.dasharray&&s.setAttribute("stroke-dasharray",r.dasharray),s}attr(e,t){this.el.setAttribute(e,typeof t=="string"?t:t.toFixed(ln))}_setEvent(e){this.event=e,this.point=this.getMousePosition(e)}_eventDown(e){return this._setEvent(e),this.start=this.point,this.onStart(this.point)}_eventMove(e){return this._setEvent(e),this.onMove(this.point)}_eventUp(e){return this._setEvent(e),this.onEnd(this.point)}},M1=class extends js{constructor(){super(...arguments),this.points=[]}onStart(e){return this.el=document.createElementNS("http://www.w3.org/2000/svg","path"),this.points=[e],this.attr("fill",this.brush.color),this.attr("d",this.getSvgData(this.points)),this.el}onMove(e){return this.el||this.onStart(e),this.points[this.points.length-1]!==e&&this.points.push(e),this.attr("d",this.getSvgData(this.points)),!0}onEnd(){const e=this.el;return this.el=null,!!e}getSvgData(e){const t=k1(e,ba({size:this.brush.size*2,thinning:.9,simulatePressure:!1,start:{taper:5},end:{taper:5}},this.brush.stylusOptions));if(!t.length)return"";const n=t.reduce((s,[r,i],a,l)=>{const[c,u]=l[(a+1)%l.length];return s.push(r,i,(r+c)/2,(i+u)/2),s},["M",...t[0],"Q"]);return n.push("Z"),n.map(s=>typeof s=="number"?s.toFixed(2):s).join(" ")}},I1=class extends js{onStart(e){return this.el=this.createElement("ellipse"),this.attr("cx",e.x),this.attr("cy",e.y),this.el}onMove(e){if(!this.el||!this.start)return!1;let[t,n]=Fi(e.x-this.start.x),[s,r]=Fi(e.y-this.start.y);if(this.shiftPressed){const i=Math.min(t,s);t=i,s=i}if(this.altPressed)this.attr("cx",this.start.x),this.attr("cy",this.start.y),this.attr("rx",t),this.attr("ry",s);else{const[i,a]=[this.start.x,this.start.x+t*n].sort(Di),[l,c]=[this.start.y,this.start.y+s*r].sort(Di);this.attr("cx",(i+a)/2),this.attr("cy",(l+c)/2),this.attr("rx",(a-i)/2),this.attr("ry",(c-l)/2)}return!0}onEnd(){const e=this.el;return this.el=null,!(!e||!e.getTotalLength())}};function $p(e,t){const n=document.createElementNS("http://www.w3.org/2000/svg","defs"),s=document.createElementNS("http://www.w3.org/2000/svg","marker"),r=document.createElementNS("http://www.w3.org/2000/svg","path");return r.setAttribute("fill",t),s.setAttribute("id",e),s.setAttribute("viewBox","0 -5 10 10"),s.setAttribute("refX","5"),s.setAttribute("refY","0"),s.setAttribute("markerWidth","4"),s.setAttribute("markerHeight","4"),s.setAttribute("orient","auto"),r.setAttribute("d","M0,-5L10,0L0,5"),s.appendChild(r),n.appendChild(s),n}var L1=class extends js{onStart(e){if(this.el=this.createElement("line",{fill:"transparent"}),this.attr("x1",e.x),this.attr("y1",e.y),this.attr("x2",e.x),this.attr("y2",e.y),this.brush.arrowEnd){const t=Sp(),n=document.createElementNS("http://www.w3.org/2000/svg","g");return n.append($p(t,this.brush.color)),n.append(this.el),this.attr("marker-end",`url(#${t})`),n}return this.el}onMove(e){if(!this.el)return!1;let{x:t,y:n}=e;if(this.shiftPressed){const s=e.x-this.start.x,r=e.y-this.start.y;if(r!==0){let i=s/r;i=Math.round(i),Math.abs(i)<=1?(t=this.start.x+r*i,n=this.start.y+r):(t=this.start.x+s,n=this.start.y)}}return this.altPressed?(this.attr("x1",this.start.x*2-t),this.attr("y1",this.start.y*2-n),this.attr("x2",t),this.attr("y2",n)):(this.attr("x1",this.start.x),this.attr("y1",this.start.y),this.attr("x2",t),this.attr("y2",n)),!0}onEnd(){const e=this.el;return this.el=null,!(!e||e.getTotalLength()<5)}},N1=class extends js{onStart(e){return 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theme: academic
class: text-white
coverAuthor: Laurent Fainsin
coverBackgroundUrl: >-
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title: Projet de fin d'étude
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<h2 class="opacity-50" style="font-size: 2rem;">Projet de Fin d'Étude</h2>

<h1 style="font-size: 2.4rem; line-height: normal;">Modèles génératifs pour la représentation latente d'aubes 3D sous forme de maillages non structurés</h1>

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mon but aujourd'hui, expliquer ces 3 lignes</p>
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## Sommaire

<div class="h-100 flex items-center text-2xl">

- Présentation de Safran
- Présentation du dataset
- Modèles génératifs
- Génération par diffusion
- Résultats
- Vérifications
- Conclusion

</div>

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Petit sommaire pour cadrer prez

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- Conclu
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- Génération par diffusion
- Résultats
- Vérifications
- Conclusion

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## Présentation (rapide) de Safran

<div class="flex items-center h-full">
  <figure>
    <img src="/assets/SAF2012_0009786-1.jpg" class="h-81">
    <figcaption class="text-center">CFM56-7B</figcaption>
  </figure>

  <figure>
    <img src="/assets/SAF2013_0105143-1.jpg" class="h-81">
    <figcaption class="text-center">M88</figcaption>
  </figure>
</div>

<a href="https://medialibrary.safran-group.com/" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Safran Media Library</a>

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Rapidement, Safran grand groupe industriel technologique français. \\
principalement aéronautique, mais pas que, \\
plein d'autre filiales, mais la thématique c'est les trucs qui volent. \\
safran génère des revenus majoritairement grâce vente de moteur propulsion avion civiles

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  <figure>
    <img src="/assets/SAF2012_0009786-1.jpg" class="h-81">
    <figcaption class="text-center">CFM56-7B</figcaption>
  </figure>

  <figure>
    <img src="/assets/SAF2013_0105143-1.jpg" class="h-81">
    <figcaption class="text-center">M88</figcaption>
  </figure>
</div>

<a href="https://medialibrary.safran-group.com/" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Safran Media Library</a>`,frontmatter:{},note:`Rapidement, Safran grand groupe industriel technologique français. \\
principalement aéronautique, mais pas que, \\
plein d'autre filiales, mais la thématique c'est les trucs qui volent. \\
safran génère des revenus majoritairement grâce vente de moteur propulsion avion civiles

- à gauche: cfm56 moteur civile le plus vendu au monde, depuis 1978
- à droite: m88, moteur militaire, équipe les rafales (Dassault)
- aussi des moteur helico...`,index:2,start:56,end:84,noteHTML:`<p>Rapidement, Safran grand groupe industriel technologique français. <br>
principalement aéronautique, mais pas que, <br>
plein d'autre filiales, mais la thématique c'est les trucs qui volent. <br>
safran génère des revenus majoritairement grâce vente de moteur propulsion avion civiles</p>
<ul>
<li>à gauche: cfm56 moteur civile le plus vendu au monde, depuis 1978</li>
<li>à droite: m88, moteur militaire, équipe les rafales (Dassault)</li>
<li>aussi des moteur helico...</li>
</ul>
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## Détails d'un moteur d'avion

<div class="flex items-center h-full">
  <img src="https://avr-global.com/wp-content/uploads/2019/06/03-b-moteur-turbine-gaz-2-2.png" class="ml-20 h-full">
</div>

<a href="https://avr-global.com/aerospace/" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">AV&R Global</a>

<!--
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équipe de Safran Tech, \\
département recherche de Safran, \\
explore nouveaux procédés, nouvelles générations moteurs

Dans mon cas, \\
travaille amélioration processus génération, \\
aubes des turbines des compresseurs
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<div class="flex items-center h-full">
  <img src="https://avr-global.com/wp-content/uploads/2019/06/03-b-moteur-turbine-gaz-2-2.png" class="ml-20 h-full">
</div>

<a href="https://avr-global.com/aerospace/" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">AV&R Global</a>`,frontmatter:{},note:`Lors de mon stage, \\
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travaille amélioration processus génération, \\
aubes des turbines des compresseurs`,index:3,start:85,end:105,noteHTML:`<p>Lors de mon stage, <br>
équipe de Safran Tech, <br>
département recherche de Safran, <br>
explore nouveaux procédés, nouvelles générations moteurs</p>
<p>Dans mon cas, <br>
travaille amélioration processus génération, <br>
aubes des turbines des compresseurs</p>
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## Dataset Rotor37_1200

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<div class="flex items-center w-full h-110">

  <div class="w-65">

  1200 échantillons
  - 1000 train (87%)
  - 200 validation (13%)

  Maillages
  - 29773 nœuds
  - 59328 triangles
  - 89100 arêtes

  Champs physiques
  - Température
  - Pression
  - Énergie
  - Densité

  </div>

  <div class="w-65">

  40 paramètres de déformations

  Input CFD
  - Vitesse de rotation
  - Vitesse du vent

  Output CFD
  - Input Massflow
  - Output Massflow
  - Compression Rate
  - Isentropic efficiency
  - Polytropic efficiency

  </div>

  <div class="flex items-center flex-col bg-black h-full w-60 ml-auto">
    <img src="/assets/rotor37_surface.gif" class="m-auto h-full">
    <img src="/assets/rotor37_points.gif" class="m-auto h-full">
  </div>

</div>

<!--
Rotor37_1200, le dataset sur lequel j'ai principalement travaillé.

Donc travaille sur graphe/maillage, \\
mais connectivité "locales" (voisins proches dans l'espace) \\
donc utiliser seulement le nuage de points

Ça nous arrange, \\
car connectivité des maillages trop complexe (quadratique), \\
et techniques reconstruire surface from points

On aurait aussi pu travailler direct CAO (primitives), \\
mais bcp plus complexe car reprez pas unique via CAO, \\
et zero littérature.
-->
`,title:"Dataset Rotor37_1200",level:2,content:`## Dataset Rotor37_1200

<style scoped>
  p {
    margin-bottom: 0 !important;
  }
</style>

<div class="flex items-center w-full h-110">

  <div class="w-65">

  1200 échantillons
  - 1000 train (87%)
  - 200 validation (13%)

  Maillages
  - 29773 nœuds
  - 59328 triangles
  - 89100 arêtes

  Champs physiques
  - Température
  - Pression
  - Énergie
  - Densité

  </div>

  <div class="w-65">

  40 paramètres de déformations

  Input CFD
  - Vitesse de rotation
  - Vitesse du vent

  Output CFD
  - Input Massflow
  - Output Massflow
  - Compression Rate
  - Isentropic efficiency
  - Polytropic efficiency

  </div>

  <div class="flex items-center flex-col bg-black h-full w-60 ml-auto">
    <img src="/assets/rotor37_surface.gif" class="m-auto h-full">
    <img src="/assets/rotor37_points.gif" class="m-auto h-full">
  </div>

</div>`,frontmatter:{},note:`Rotor37_1200, le dataset sur lequel j'ai principalement travaillé.

Donc travaille sur graphe/maillage, \\
mais connectivité "locales" (voisins proches dans l'espace) \\
donc utiliser seulement le nuage de points

Ça nous arrange, \\
car connectivité des maillages trop complexe (quadratique), \\
et techniques reconstruire surface from points

On aurait aussi pu travailler direct CAO (primitives), \\
mais bcp plus complexe car reprez pas unique via CAO, \\
et zero littérature.`,index:4,start:106,end:176,noteHTML:`<p>Rotor37_1200, le dataset sur lequel j'ai principalement travaillé.</p>
<p>Donc travaille sur graphe/maillage, <br>
mais connectivité &quot;locales&quot; (voisins proches dans l'espace) <br>
donc utiliser seulement le nuage de points</p>
<p>Ça nous arrange, <br>
car connectivité des maillages trop complexe (quadratique), <br>
et techniques reconstruire surface from points</p>
<p>On aurait aussi pu travailler direct CAO (primitives), <br>
mais bcp plus complexe car reprez pas unique via CAO, <br>
et zero littérature.</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:4,no:5},__clicksElements:[],__preloaded:!1}},{path:"6",name:"page-6",component:PP,meta:{slide:{raw:`
## Problème direct

<img src="https://git.fainsin.bzh/ENSEEIHT/projet-fin-etude-rapport/media/branch/master/assets/online_adaptative_sampling_DOE.png" class="m-auto h-100 mt-10"/>

<!--
On veut c'est générer trucs ressemblent rotor37. \\
pour ça on peut appliquer le problème direct, \\
si on veut trouver aube qui respecte un certaine critère de perf, \\
"l'exploration d'un espace paramètre"

On prend CAO, \\
on échantillone, passer sous simu, \\
relèver les perfs, on optimise pour resampler, \\
repeat ad vitam eternam.

À la fin, on a normalement au moins une aube qui nous convient.

Inconvénient, \\
c'est long, à cause de la simu, \\
nous on voudrait avoir le processus inverse \\
(perf -> aube) pas (aube -> perf)
-->
`,title:"Problème direct",level:2,content:`## Problème direct

<img src="https://git.fainsin.bzh/ENSEEIHT/projet-fin-etude-rapport/media/branch/master/assets/online_adaptative_sampling_DOE.png" class="m-auto h-100 mt-10"/>`,frontmatter:{},note:`On veut c'est générer trucs ressemblent rotor37. \\
pour ça on peut appliquer le problème direct, \\
si on veut trouver aube qui respecte un certaine critère de perf, \\
"l'exploration d'un espace paramètre"

On prend CAO, \\
on échantillone, passer sous simu, \\
relèver les perfs, on optimise pour resampler, \\
repeat ad vitam eternam.

À la fin, on a normalement au moins une aube qui nous convient.

Inconvénient, \\
c'est long, à cause de la simu, \\
nous on voudrait avoir le processus inverse \\
(perf -> aube) pas (aube -> perf)`,index:5,start:177,end:201,noteHTML:`<p>On veut c'est générer trucs ressemblent rotor37. <br>
pour ça on peut appliquer le problème direct, <br>
si on veut trouver aube qui respecte un certaine critère de perf, <br>
&quot;l'exploration d'un espace paramètre&quot;</p>
<p>On prend CAO, <br>
on échantillone, passer sous simu, <br>
relèver les perfs, on optimise pour resampler, <br>
repeat ad vitam eternam.</p>
<p>À la fin, on a normalement au moins une aube qui nous convient.</p>
<p>Inconvénient, <br>
c'est long, à cause de la simu, <br>
nous on voudrait avoir le processus inverse <br>
(perf -&gt; aube) pas (aube -&gt; perf)</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:5,no:6},__clicksElements:[],__preloaded:!1}},{path:"7",name:"page-7",component:MP,meta:{slide:{raw:`
## Problème inverse, Modèles génératifs

<img src="/assets/generative-overview.png" class="m-auto h-110"/>

<a href="https://lilianweng.github.io/posts/2021-07-11-diffusion-models/" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Lilian Weng, 2021</a>

<!--
Approximer le problème inverse, \\
solution, utiliser des réseaux de neurones, modèles génératifs.

Y'a globalement 4 grosses familles de modèles génératifs (gan, vae, nf, dm).

L'objectif de ces modèles se ressemblent un peu tous, \\
les trois premiers, on veut apprendre à génerer distrib x' qui ressemble très fortement à x.

Formelement pendant training on veut apprendre l'identité, \\
mais particularité dans leur archi, par exemple \\
VAE on passe par un goulot étranglement, espace latent, \\
GAN on a une architecture adversarial, etc. \\
NF on utilise des transfo continue reversible bijectives \\
y'a plusieurs avantages et inconvenients à chaque méthode.

Ce qui nous interesse le plus ici c'est diffusion, récent et potentiel. \\
le principe, trouver processus réversible discret stochastique \\
entre distrib données et une autre distrib qu'on connait parfaitement math
-->
`,title:"Problème inverse, Modèles génératifs",level:2,content:`## Problème inverse, Modèles génératifs

<img src="/assets/generative-overview.png" class="m-auto h-110"/>

<a href="https://lilianweng.github.io/posts/2021-07-11-diffusion-models/" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Lilian Weng, 2021</a>`,frontmatter:{},note:`Approximer le problème inverse, \\
solution, utiliser des réseaux de neurones, modèles génératifs.

Y'a globalement 4 grosses familles de modèles génératifs (gan, vae, nf, dm).

L'objectif de ces modèles se ressemblent un peu tous, \\
les trois premiers, on veut apprendre à génerer distrib x' qui ressemble très fortement à x.

Formelement pendant training on veut apprendre l'identité, \\
mais particularité dans leur archi, par exemple \\
VAE on passe par un goulot étranglement, espace latent, \\
GAN on a une architecture adversarial, etc. \\
NF on utilise des transfo continue reversible bijectives \\
y'a plusieurs avantages et inconvenients à chaque méthode.

Ce qui nous interesse le plus ici c'est diffusion, récent et potentiel. \\
le principe, trouver processus réversible discret stochastique \\
entre distrib données et une autre distrib qu'on connait parfaitement math`,index:6,start:202,end:230,noteHTML:`<p>Approximer le problème inverse, <br>
solution, utiliser des réseaux de neurones, modèles génératifs.</p>
<p>Y'a globalement 4 grosses familles de modèles génératifs (gan, vae, nf, dm).</p>
<p>L'objectif de ces modèles se ressemblent un peu tous, <br>
les trois premiers, on veut apprendre à génerer distrib x' qui ressemble très fortement à x.</p>
<p>Formelement pendant training on veut apprendre l'identité, <br>
mais particularité dans leur archi, par exemple <br>
VAE on passe par un goulot étranglement, espace latent, <br>
GAN on a une architecture adversarial, etc. <br>
NF on utilise des transfo continue reversible bijectives <br>
y'a plusieurs avantages et inconvenients à chaque méthode.</p>
<p>Ce qui nous interesse le plus ici c'est diffusion, récent et potentiel. <br>
le principe, trouver processus réversible discret stochastique <br>
entre distrib données et une autre distrib qu'on connait parfaitement math</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:6,no:7},__clicksElements:[],__preloaded:!1}},{path:"8",name:"page-8",component:FP,meta:{slide:{raw:`
## Denoising Diffusion Probabilistic Model (DDPM)

<div class="flex flex-col items-center h-100">
  <img src="/assets/ddpm_algo.png" class="m-auto w-9/10">
  <img src="/assets/ddpm_example.png" class="m-auto w-full">
</div>

<p class="absolute bottom-0 font-extralight !my-0 mr-2 right-0 text-xs">
  <a href="https://arxiv.org/abs/2006.11239">arxiv:2006.11239</a>,
  <a href="https://cvpr2022-tutorial-diffusion-models.github.io/">CVPR 2022 Diffusion Tutorial</a>
</p>

<!--
Plusieurs méthodes pour faire dla diffusion, \\
la + simple d'entre elles c'est DDPM. \\
Le principe, apprendre mapping entre données et gaussienne isotropique.

Ce mapping apprendre via réseau débruiteur (denoising). \\
Pour se faire (algo 1), \\
on prend une de nos données (x0), \\
on la bruite (xt), \\
on la donne notre réseau, on récupère la prédiction (eps_theta), \\
on opti le réseau à prédire le bruit que l'on a ajouté (eps).

Convergence atteinte, \\
on est capable de débruiter des données.

Intéressant lorsqu'on part d'un bruit blanc (xT), \\
et que l'on demande quand même au réseau de débruiter. \\
Le réseau hallucine informations là où y'en a pas, \\
et génère finalement nouvelle donnée même distrib de celles qu'il a apprises. (algo 2)
-->
`,title:"Denoising Diffusion Probabilistic Model (DDPM)",level:2,content:`## Denoising Diffusion Probabilistic Model (DDPM)

<div class="flex flex-col items-center h-100">
  <img src="/assets/ddpm_algo.png" class="m-auto w-9/10">
  <img src="/assets/ddpm_example.png" class="m-auto w-full">
</div>

<p class="absolute bottom-0 font-extralight !my-0 mr-2 right-0 text-xs">
  <a href="https://arxiv.org/abs/2006.11239">arxiv:2006.11239</a>,
  <a href="https://cvpr2022-tutorial-diffusion-models.github.io/">CVPR 2022 Diffusion Tutorial</a>
</p>`,frontmatter:{},note:`Plusieurs méthodes pour faire dla diffusion, \\
la + simple d'entre elles c'est DDPM. \\
Le principe, apprendre mapping entre données et gaussienne isotropique.

Ce mapping apprendre via réseau débruiteur (denoising). \\
Pour se faire (algo 1), \\
on prend une de nos données (x0), \\
on la bruite (xt), \\
on la donne notre réseau, on récupère la prédiction (eps_theta), \\
on opti le réseau à prédire le bruit que l'on a ajouté (eps).

Convergence atteinte, \\
on est capable de débruiter des données.

Intéressant lorsqu'on part d'un bruit blanc (xT), \\
et que l'on demande quand même au réseau de débruiter. \\
Le réseau hallucine informations là où y'en a pas, \\
et génère finalement nouvelle donnée même distrib de celles qu'il a apprises. (algo 2)`,index:7,start:231,end:265,noteHTML:`<p>Plusieurs méthodes pour faire dla diffusion, <br>
la + simple d'entre elles c'est DDPM. <br>
Le principe, apprendre mapping entre données et gaussienne isotropique.</p>
<p>Ce mapping apprendre via réseau débruiteur (denoising). <br>
Pour se faire (algo 1), <br>
on prend une de nos données (x0), <br>
on la bruite (xt), <br>
on la donne notre réseau, on récupère la prédiction (eps_theta), <br>
on opti le réseau à prédire le bruit que l'on a ajouté (eps).</p>
<p>Convergence atteinte, <br>
on est capable de débruiter des données.</p>
<p>Intéressant lorsqu'on part d'un bruit blanc (xT), <br>
et que l'on demande quand même au réseau de débruiter. <br>
Le réseau hallucine informations là où y'en a pas, <br>
et génère finalement nouvelle donnée même distrib de celles qu'il a apprises. (algo 2)</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:7,no:8},__clicksElements:[],__preloaded:!1}},{path:"9",name:"page-9",component:KP,meta:{slide:{raw:`
## Diffusion forward process

<div class="flex items-center h-100">
  <figure>
    <div class="flex items-center w-full bg-black">
      <img src="/assets/aube_rotation.gif" class="m-auto w-full">
      <img src="/assets/aube_forward_front.gif" class="m-auto w-full">
      <img src="/assets/aube_forward_side.gif" class="m-auto w-full">
    </div>
    <figcaption class="text-center">Corruption progressive d'un échantillon, via un bruit gaussien (cf. algorithm 1)</figcaption>
  </figure>
</div>

<!--
On peut l'appliquer à nos aubes,
example du forward process sur une aube 3D, \\
(subsample 2048 points et normalisé donc un peu applati), \\
à la fin on obtient truc qui ressemble à une gaussienne.

Ce genre de données input réseau capable traiter des pointcloud, \\
comme par exemple un réseau basés sur des KPConvs, \\
ou autre archi style PointNet, \\
ou PVCNN qui travaille sur reprez voxel des points, \\
(cf rapport).
-->
`,title:"Diffusion forward process",level:2,content:`## Diffusion forward process

<div class="flex items-center h-100">
  <figure>
    <div class="flex items-center w-full bg-black">
      <img src="/assets/aube_rotation.gif" class="m-auto w-full">
      <img src="/assets/aube_forward_front.gif" class="m-auto w-full">
      <img src="/assets/aube_forward_side.gif" class="m-auto w-full">
    </div>
    <figcaption class="text-center">Corruption progressive d'un échantillon, via un bruit gaussien (cf. algorithm 1)</figcaption>
  </figure>
</div>`,frontmatter:{},note:`On peut l'appliquer à nos aubes,
example du forward process sur une aube 3D, \\
(subsample 2048 points et normalisé donc un peu applati), \\
à la fin on obtient truc qui ressemble à une gaussienne.

Ce genre de données input réseau capable traiter des pointcloud, \\
comme par exemple un réseau basés sur des KPConvs, \\
ou autre archi style PointNet, \\
ou PVCNN qui travaille sur reprez voxel des points, \\
(cf rapport).`,index:8,start:266,end:293,noteHTML:`<p>On peut l'appliquer à nos aubes,
example du forward process sur une aube 3D, <br>
(subsample 2048 points et normalisé donc un peu applati), <br>
à la fin on obtient truc qui ressemble à une gaussienne.</p>
<p>Ce genre de données input réseau capable traiter des pointcloud, <br>
comme par exemple un réseau basés sur des KPConvs, <br>
ou autre archi style PointNet, <br>
ou PVCNN qui travaille sur reprez voxel des points, <br>
(cf rapport).</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:8,no:9},__clicksElements:[],__preloaded:!1}},{path:"10",name:"page-10",component:QP,meta:{slide:{raw:`
## Diffusion reverse process

<div class="flex items-center h-100">
  <figure>
    <div class="flex items-center w-full bg-black">
      <img src="/assets/sample_rotation.gif" class="m-auto w-full">
      <img src="/assets/sample_reverse_front.gif" class="m-auto w-full">
      <img src="/assets/sample_reverse_side.gif" class="m-auto w-full">
    </div>
    <figcaption class="text-center">Débruitage itératif d'un nuage gaussien (cf. algorithm 2)</figcaption>
  </figure>
</div>

<!--
Si on effectue le reverse process, \\
nuage de point gaussien ressemble progressivement à une aube.

Le résultat (kp-fcnn) est pas mal, \\
mais reste une bonne quantité de bruit, \\
(bonne chance reconstruction surface), \\
surement améliorable hyperparmètres, \\
mais meilleurs méthodes depuis 2020.
-->
`,title:"Diffusion reverse process",level:2,content:`## Diffusion reverse process

<div class="flex items-center h-100">
  <figure>
    <div class="flex items-center w-full bg-black">
      <img src="/assets/sample_rotation.gif" class="m-auto w-full">
      <img src="/assets/sample_reverse_front.gif" class="m-auto w-full">
      <img src="/assets/sample_reverse_side.gif" class="m-auto w-full">
    </div>
    <figcaption class="text-center">Débruitage itératif d'un nuage gaussien (cf. algorithm 2)</figcaption>
  </figure>
</div>`,frontmatter:{},note:`Si on effectue le reverse process, \\
nuage de point gaussien ressemble progressivement à une aube.

Le résultat (kp-fcnn) est pas mal, \\
mais reste une bonne quantité de bruit, \\
(bonne chance reconstruction surface), \\
surement améliorable hyperparmètres, \\
mais meilleurs méthodes depuis 2020.`,index:9,start:294,end:319,noteHTML:`<p>Si on effectue le reverse process, <br>
nuage de point gaussien ressemble progressivement à une aube.</p>
<p>Le résultat (kp-fcnn) est pas mal, <br>
mais reste une bonne quantité de bruit, <br>
(bonne chance reconstruction surface), <br>
surement améliorable hyperparmètres, <br>
mais meilleurs méthodes depuis 2020.</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:9,no:10},__clicksElements:[],__preloaded:!1}},{path:"11",name:"page-11",component:iC,meta:{slide:{raw:`
## Latent Diffusion Model (LDM)

<div class="flex items-center w-full h-full flex-col justify-evenly">

  <div class="flex items-center w-full h-72 justify-evenly">
    <figure>
      <img src="https://ar5iv.labs.arxiv.org/html/2112.10752/assets/img/generativevscompressive4.jpg" class="m-auto h-70">
    </figure>

  <div>

  $\\displaystyle x_0 \\approx \\hat{x}_0 = \\frac{ x_t - \\sqrt{1 - \\overline\\alpha_t} \\epsilon_\\theta(x_t) }{ \\sqrt{\\overline\\alpha_t} }$

  $\\displaystyle \\text{RMSE} = \\sqrt{ \\frac{ \\| x_0 - \\hat{x}_0 \\|^2_2 }{ D } }$

  $$\\begin{align*}
    \\text{Rate} &= \\frac{1}{2 \\sigma^2_q(t)} \\frac{ \\overline\\alpha_{t-1} ( 1 - \\alpha_t )^2 }{ (1 - \\overline\\alpha_t)^2 } \\| x_0 - \\hat{x}_0 \\|^2_2 \\\\
                &= \\text{D}_{\\text{KL}} \\left[ q(x_{t-1} | x_t, x_0) \\| p_\\theta(x_{t-1} | x_t) \\right]
  \\end{align*}$$

  </div>

  </div>

  <figure>
    <img src="/assets/ldm-simplified.png" class="w-160">
    <figcaption class="text-center">Nouvelle pipeline, ajout d'une transformation en amont</figcaption>
  </figure>

</div>

<a href="https://arxiv.org/abs/2112.10752" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">arxiv:2112.10752</a>

<!--
Présentation des LDM qui permettent de traiter plus efficacement nos données.

Part du constat que si l'on trace pour t, \\
l'erreur de reconstruction (RMSE, distortion) en fonction de t, \\
(on prend x_0, on le bruite x_t, on prédit x_0_hat, pour chaque t), \\
le Rate (issue de l'ELBO, une KLD) en fonction de t, \\
(KLD=#bits nécéssaire pour passer de P à Q), \\
on combine les deux pour avoir distortion en fonction de rate. \\

On observe qu'on a deux domaine dans le processus de diffusion, \\
un domaine nécéssite bcp de bits et encode peu de distortion, \\
l'autre inverse, peu bits, bcp de distortion, \\
donc un peu du gachi de réseau neurone le perceptuel, \\
on aimerait travailler uniquement sur la partie semantique. \\

On peut le faire si trouve espace alternatif aux données, \\
Espace latent sont une possibilité, \\
utilisation, par ex, d'autoencoder, qui s'occuper du perceptuel, \\
la diffusion préoccupe que du semantic. \\

Ça revient à modifier la pipeline de diffusion comme suit:

avantage, latent space plus petit, donc modèle plus petit, simple, rapide...
-->
`,title:"Latent Diffusion Model (LDM)",level:2,content:`## Latent Diffusion Model (LDM)

<div class="flex items-center w-full h-full flex-col justify-evenly">

  <div class="flex items-center w-full h-72 justify-evenly">
    <figure>
      <img src="https://ar5iv.labs.arxiv.org/html/2112.10752/assets/img/generativevscompressive4.jpg" class="m-auto h-70">
    </figure>

  <div>

  $\\displaystyle x_0 \\approx \\hat{x}_0 = \\frac{ x_t - \\sqrt{1 - \\overline\\alpha_t} \\epsilon_\\theta(x_t) }{ \\sqrt{\\overline\\alpha_t} }$

  $\\displaystyle \\text{RMSE} = \\sqrt{ \\frac{ \\| x_0 - \\hat{x}_0 \\|^2_2 }{ D } }$

  $$\\begin{align*}
    \\text{Rate} &= \\frac{1}{2 \\sigma^2_q(t)} \\frac{ \\overline\\alpha_{t-1} ( 1 - \\alpha_t )^2 }{ (1 - \\overline\\alpha_t)^2 } \\| x_0 - \\hat{x}_0 \\|^2_2 \\\\
                &= \\text{D}_{\\text{KL}} \\left[ q(x_{t-1} | x_t, x_0) \\| p_\\theta(x_{t-1} | x_t) \\right]
  \\end{align*}$$

  </div>

  </div>

  <figure>
    <img src="/assets/ldm-simplified.png" class="w-160">
    <figcaption class="text-center">Nouvelle pipeline, ajout d'une transformation en amont</figcaption>
  </figure>

</div>

<a href="https://arxiv.org/abs/2112.10752" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">arxiv:2112.10752</a>`,frontmatter:{},note:`Présentation des LDM qui permettent de traiter plus efficacement nos données.

Part du constat que si l'on trace pour t, \\
l'erreur de reconstruction (RMSE, distortion) en fonction de t, \\
(on prend x_0, on le bruite x_t, on prédit x_0_hat, pour chaque t), \\
le Rate (issue de l'ELBO, une KLD) en fonction de t, \\
(KLD=#bits nécéssaire pour passer de P à Q), \\
on combine les deux pour avoir distortion en fonction de rate. \\

On observe qu'on a deux domaine dans le processus de diffusion, \\
un domaine nécéssite bcp de bits et encode peu de distortion, \\
l'autre inverse, peu bits, bcp de distortion, \\
donc un peu du gachi de réseau neurone le perceptuel, \\
on aimerait travailler uniquement sur la partie semantique. \\

On peut le faire si trouve espace alternatif aux données, \\
Espace latent sont une possibilité, \\
utilisation, par ex, d'autoencoder, qui s'occuper du perceptuel, \\
la diffusion préoccupe que du semantic. \\

Ça revient à modifier la pipeline de diffusion comme suit:

avantage, latent space plus petit, donc modèle plus petit, simple, rapide...`,index:10,start:320,end:380,noteHTML:`<p>Présentation des LDM qui permettent de traiter plus efficacement nos données.</p>
<p>Part du constat que si l'on trace pour t, <br>
l'erreur de reconstruction (RMSE, distortion) en fonction de t, <br>
(on prend x_0, on le bruite x_t, on prédit x_0_hat, pour chaque t), <br>
le Rate (issue de l'ELBO, une KLD) en fonction de t, <br>
(KLD=#bits nécéssaire pour passer de P à Q), <br>
on combine les deux pour avoir distortion en fonction de rate. \\</p>
<p>On observe qu'on a deux domaine dans le processus de diffusion, <br>
un domaine nécéssite bcp de bits et encode peu de distortion, <br>
l'autre inverse, peu bits, bcp de distortion, <br>
donc un peu du gachi de réseau neurone le perceptuel, <br>
on aimerait travailler uniquement sur la partie semantique. \\</p>
<p>On peut le faire si trouve espace alternatif aux données, <br>
Espace latent sont une possibilité, <br>
utilisation, par ex, d'autoencoder, qui s'occuper du perceptuel, <br>
la diffusion préoccupe que du semantic. \\</p>
<p>Ça revient à modifier la pipeline de diffusion comme suit:</p>
<p>avantage, latent space plus petit, donc modèle plus petit, simple, rapide...</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:10,no:11},__clicksElements:[],__preloaded:!1}},{path:"12",name:"page-12",component:gC,meta:{slide:{raw:`
## Générations par diffusion latente (non conditionnée)

<div class="grid grid-cols-4 col-auto self-center justify-items-center w-full h-100 bg-black">
  <img src="/assets/gen_points_1.gif" class="w-50">
  <img src="/assets/gen_points_2.gif" class="w-50">
  <img src="/assets/gen_points_3.gif" class="w-50">
  <img src="/assets/gen_points_4.gif" class="w-50">
  <img src="/assets/gen_points_5.gif" class="w-50">
  <img src="/assets/gen_points_6.gif" class="w-50">
  <img src="/assets/gen_points_7.gif" class="w-50">
  <img src="/assets/gen_surface_1.gif" class="w-50">
</div>

<!--
Si on applique nos diffusion latente via une PCA, \\
on obtient ceci.

Nuages de point de très bonne qualité, \\
on a plus le bruit qu'on avait avec KP-FCNN, \\
bonus PCA, même ordre des points, on peut copier connectivité aube nominale, \\
pas besoin méthode reconstruction dans ce cas.
-->
`,title:"Générations par diffusion latente (non conditionnée)",level:2,content:`## Générations par diffusion latente (non conditionnée)

<div class="grid grid-cols-4 col-auto self-center justify-items-center w-full h-100 bg-black">
  <img src="/assets/gen_points_1.gif" class="w-50">
  <img src="/assets/gen_points_2.gif" class="w-50">
  <img src="/assets/gen_points_3.gif" class="w-50">
  <img src="/assets/gen_points_4.gif" class="w-50">
  <img src="/assets/gen_points_5.gif" class="w-50">
  <img src="/assets/gen_points_6.gif" class="w-50">
  <img src="/assets/gen_points_7.gif" class="w-50">
  <img src="/assets/gen_surface_1.gif" class="w-50">
</div>`,frontmatter:{},note:`Si on applique nos diffusion latente via une PCA, \\
on obtient ceci.

Nuages de point de très bonne qualité, \\
on a plus le bruit qu'on avait avec KP-FCNN, \\
bonus PCA, même ordre des points, on peut copier connectivité aube nominale, \\
pas besoin méthode reconstruction dans ce cas.`,index:11,start:381,end:405,noteHTML:`<p>Si on applique nos diffusion latente via une PCA, <br>
on obtient ceci.</p>
<p>Nuages de point de très bonne qualité, <br>
on a plus le bruit qu'on avait avec KP-FCNN, <br>
bonus PCA, même ordre des points, on peut copier connectivité aube nominale, <br>
pas besoin méthode reconstruction dans ce cas.</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:11,no:12},__clicksElements:[],__preloaded:!1}},{path:"13",name:"page-13",component:xC,meta:{slide:{raw:`
## Classifier-free Guidance (CFG)

<img src="https://perceptron.blog/assets/images/diffusion_models/diffusion_gradients_free.gif" class="m-auto h-55">
<img src="https://perceptron.blog/assets/images/diffusion_models/diffusion_free_guided_results.gif" class="m-auto h-55">

<a href="https://perceptron.blog/defusing-diffusion/" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Paweł Pierzchlewicz</a>

<!--
Jusqu'à présent, avec tout ce que j'ai dit, \\
capable de générer des données ressemble certaine densité proba. \\
(non conditionné)

Cependant on veut générer données ressemblent densité proba jointe avec classe. \\
(conditionné).

Il existe plusieurs méthode pour faire cela, \\
l'un d'entre elle etant cfg.

Principe entrainer notre réseau diffusion conjointement, \\
prédiction non conditionnée et conditionnée.

On complexifie un peu plus l'apprentissage, \\
mais sampling pouvoir choisir quel densité de proba on veut gen.

On pourrait très bien entrainer un modèle par classe, \\
mais c'est long et en plus nous on a pas de classes discète, \\
là on fait tout en même temps...
-->
`,title:"Classifier-free Guidance (CFG)",level:2,content:`## Classifier-free Guidance (CFG)

<img src="https://perceptron.blog/assets/images/diffusion_models/diffusion_gradients_free.gif" class="m-auto h-55">
<img src="https://perceptron.blog/assets/images/diffusion_models/diffusion_free_guided_results.gif" class="m-auto h-55">

<a href="https://perceptron.blog/defusing-diffusion/" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Paweł Pierzchlewicz</a>`,frontmatter:{},note:`Jusqu'à présent, avec tout ce que j'ai dit, \\
capable de générer des données ressemble certaine densité proba. \\
(non conditionné)

Cependant on veut générer données ressemblent densité proba jointe avec classe. \\
(conditionné).

Il existe plusieurs méthode pour faire cela, \\
l'un d'entre elle etant cfg.

Principe entrainer notre réseau diffusion conjointement, \\
prédiction non conditionnée et conditionnée.

On complexifie un peu plus l'apprentissage, \\
mais sampling pouvoir choisir quel densité de proba on veut gen.

On pourrait très bien entrainer un modèle par classe, \\
mais c'est long et en plus nous on a pas de classes discète, \\
là on fait tout en même temps...`,index:12,start:406,end:436,noteHTML:`<p>Jusqu'à présent, avec tout ce que j'ai dit, <br>
capable de générer des données ressemble certaine densité proba. <br>
(non conditionné)</p>
<p>Cependant on veut générer données ressemblent densité proba jointe avec classe. <br>
(conditionné).</p>
<p>Il existe plusieurs méthode pour faire cela, <br>
l'un d'entre elle etant cfg.</p>
<p>Principe entrainer notre réseau diffusion conjointement, <br>
prédiction non conditionnée et conditionnée.</p>
<p>On complexifie un peu plus l'apprentissage, <br>
mais sampling pouvoir choisir quel densité de proba on veut gen.</p>
<p>On pourrait très bien entrainer un modèle par classe, <br>
mais c'est long et en plus nous on a pas de classes discète, <br>
là on fait tout en même temps...</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:12,no:13},__clicksElements:[],__preloaded:!1}},{path:"14",name:"page-14",component:IC,meta:{slide:{raw:`
## Générations par diffusion latente (conditionnée)

<div class="grid grid-cols-4 col-auto self-center justify-items-center w-full h-100 bg-black">
  <img src="/assets/gen_surface_1.gif" class="w-50">
  <img src="/assets/gen_surface_2.gif" class="w-50">
  <img src="/assets/gen_surface_3.gif" class="w-50">
  <img src="/assets/gen_surface_4.gif" class="w-50">
  <img src="/assets/gen_surface_5.gif" class="w-50">
  <img src="/assets/gen_surface_6.gif" class="w-50">
  <img src="/assets/gen_surface_7.gif" class="w-50">
  <img src="/assets/gen_surface_8.gif" class="w-50">
</div>

<!--
Si on fait génération conditionné, ça marche encore.

Problème, \\
incapable visuellement différence entre aubes conditionné, \\
là par exemple toutes conditonnés même critère physqiue, \\
et ça se voit pas trop.

Une solution ça serait simu cfd, mais trop long, \\
donc on va utiliser des modèles de regression, plus légers et rapides.
-->
`,title:"Générations par diffusion latente (conditionnée)",level:2,content:`## Générations par diffusion latente (conditionnée)

<div class="grid grid-cols-4 col-auto self-center justify-items-center w-full h-100 bg-black">
  <img src="/assets/gen_surface_1.gif" class="w-50">
  <img src="/assets/gen_surface_2.gif" class="w-50">
  <img src="/assets/gen_surface_3.gif" class="w-50">
  <img src="/assets/gen_surface_4.gif" class="w-50">
  <img src="/assets/gen_surface_5.gif" class="w-50">
  <img src="/assets/gen_surface_6.gif" class="w-50">
  <img src="/assets/gen_surface_7.gif" class="w-50">
  <img src="/assets/gen_surface_8.gif" class="w-50">
</div>`,frontmatter:{},note:`Si on fait génération conditionné, ça marche encore.

Problème, \\
incapable visuellement différence entre aubes conditionné, \\
là par exemple toutes conditonnés même critère physqiue, \\
et ça se voit pas trop.

Une solution ça serait simu cfd, mais trop long, \\
donc on va utiliser des modèles de regression, plus légers et rapides.`,index:13,start:437,end:463,noteHTML:`<p>Si on fait génération conditionné, ça marche encore.</p>
<p>Problème, <br>
incapable visuellement différence entre aubes conditionné, <br>
là par exemple toutes conditonnés même critère physqiue, <br>
et ça se voit pas trop.</p>
<p>Une solution ça serait simu cfd, mais trop long, <br>
donc on va utiliser des modèles de regression, plus légers et rapides.</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:13,no:14},__clicksElements:[],__preloaded:!1}},{path:"15",name:"page-15",component:DC,meta:{slide:{raw:`
## Gaussian Process (GP)

<div class="flex items-center h-100" style="overflow: hidden;">
  <div style="overflow: hidden;">
    <iframe scrolling="no" style="height: 50rem; margin-top: -18rem; width: 75rem; margin-left: -10rem;" src="https://distill.pub/2019/visual-exploration-gaussian-processes/">
    </iframe>
  </div>
</div>

<a href="https://distill.pub/2019/visual-exploration-gaussian-processes/" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Distill</a>

<!--
On pourrait entrainer un réseau de neurones pour faire regression entre nuage de points et critère de perf. Mais y'a plus simples.

Les GP c'est des méthodes à noyau, probabilistiques.
* supervisé, au même sens que SVM, K-NN, ...
* non paramétrique (techniquement hyper-paramétrique, à cause noyau).
* fournir des intervals de confiance
-->
`,title:"Gaussian Process (GP)",level:2,content:`## Gaussian Process (GP)

<div class="flex items-center h-100" style="overflow: hidden;">
  <div style="overflow: hidden;">
    <iframe scrolling="no" style="height: 50rem; margin-top: -18rem; width: 75rem; margin-left: -10rem;" src="https://distill.pub/2019/visual-exploration-gaussian-processes/">
    </iframe>
  </div>
</div>

<a href="https://distill.pub/2019/visual-exploration-gaussian-processes/" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Distill</a>`,frontmatter:{},note:`On pourrait entrainer un réseau de neurones pour faire regression entre nuage de points et critère de perf. Mais y'a plus simples.

Les GP c'est des méthodes à noyau, probabilistiques.
* supervisé, au même sens que SVM, K-NN, ...
* non paramétrique (techniquement hyper-paramétrique, à cause noyau).
* fournir des intervals de confiance`,index:14,start:464,end:485,noteHTML:`<p>On pourrait entrainer un réseau de neurones pour faire regression entre nuage de points et critère de perf. Mais y'a plus simples.</p>
<p>Les GP c'est des méthodes à noyau, probabilistiques.</p>
<ul>
<li>supervisé, au même sens que SVM, K-NN, ...</li>
<li>non paramétrique (techniquement hyper-paramétrique, à cause noyau).</li>
<li>fournir des intervals de confiance</li>
</ul>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:14,no:15},__clicksElements:[],__preloaded:!1}},{path:"16",name:"page-16",component:zC,meta:{slide:{raw:`
## "Entrainement" d'un GP sur Rotor37_1200

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_train_30_pca.png" class="m-auto w-full">
</div>

<!--
Donc on peut utiliser des GPs pour relation modes pca et perfs.

On s'assure juste que leurs prédictions sont correctes par rapport à des données de test, ici coeff détermination ~= 1 donc correct.
-->
`,title:`"Entrainement" d'un GP sur Rotor37_1200`,level:2,content:`## "Entrainement" d'un GP sur Rotor37_1200

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_train_30_pca.png" class="m-auto w-full">
</div>`,frontmatter:{},note:`Donc on peut utiliser des GPs pour relation modes pca et perfs.

On s'assure juste que leurs prédictions sont correctes par rapport à des données de test, ici coeff détermination ~= 1 donc correct.`,index:15,start:486,end:499,noteHTML:`<p>Donc on peut utiliser des GPs pour relation modes pca et perfs.</p>
<p>On s'assure juste que leurs prédictions sont correctes par rapport à des données de test, ici coeff détermination ~= 1 donc correct.</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:15,no:16},__clicksElements:[],__preloaded:!1}},{path:"17",name:"page-17",component:GC,meta:{slide:{raw:`
## Analyse de générations non conditionnées

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_unconditional.png" class="m-auto w-full">
</div>
`,title:"Analyse de générations non conditionnées",level:2,content:`## Analyse de générations non conditionnées

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_unconditional.png" class="m-auto w-full">
</div>`,frontmatter:{},index:16,start:500,end:507,noteHTML:"",filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:16,no:17},__clicksElements:[],__preloaded:!1}},{path:"18",name:"page-18",component:QC,meta:{slide:{raw:`
## Analyse de générations progressivement conditionnées

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_guidance.gif" class="m-auto w-full">
</div>

<!--
je fais varier gamma entre 0 et 1.

conditionné sur out_massflow = -1
-->
`,title:"Analyse de générations progressivement conditionnées",level:2,content:`## Analyse de générations progressivement conditionnées

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_guidance.gif" class="m-auto w-full">
</div>`,frontmatter:{},note:`je fais varier gamma entre 0 et 1.

conditionné sur out_massflow = -1`,index:17,start:508,end:521,noteHTML:`<p>je fais varier gamma entre 0 et 1.</p>
<p>conditionné sur out_massflow = -1</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:17,no:18},__clicksElements:[],__preloaded:!1}},{path:"19",name:"page-19",component:rO,meta:{slide:{raw:`
## Analyse de générations conditionnées (massflow)

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_massflow.gif" class="m-auto w-full">
</div>

<!--
on fait varier entre -3 et 3.

gamma = 2.5.

ça suit bien le conditionnement, \\
sur les bords ça déconne un peu, pas très grave, \\
mais ça doit venir du GP qui ne généralise pas la regression, \\
car génération correctes visuellement, \\
il faudrait verif avec une CFD là.

correlation avec in_massflow et compression_rate, \\
normal car correlé physiquement.
-->
`,title:"Analyse de générations conditionnées (massflow)",level:2,content:`## Analyse de générations conditionnées (massflow)

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_massflow.gif" class="m-auto w-full">
</div>`,frontmatter:{},note:`on fait varier entre -3 et 3.

gamma = 2.5.

ça suit bien le conditionnement, \\
sur les bords ça déconne un peu, pas très grave, \\
mais ça doit venir du GP qui ne généralise pas la regression, \\
car génération correctes visuellement, \\
il faudrait verif avec une CFD là.

correlation avec in_massflow et compression_rate, \\
normal car correlé physiquement.`,index:18,start:522,end:544,noteHTML:`<p>on fait varier entre -3 et 3.</p>
<p>gamma = 2.5.</p>
<p>ça suit bien le conditionnement, <br>
sur les bords ça déconne un peu, pas très grave, <br>
mais ça doit venir du GP qui ne généralise pas la regression, <br>
car génération correctes visuellement, <br>
il faudrait verif avec une CFD là.</p>
<p>correlation avec in_massflow et compression_rate, <br>
normal car correlé physiquement.</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:18,no:19},__clicksElements:[],__preloaded:!1}},{path:"20",name:"page-20",component:cO,meta:{slide:{raw:`
## Analyse de générations conditionnées (efficiency)

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_efficiency.gif" class="m-auto w-full">
</div>

<!--
pareil, mais pour l'efficiency
-->
`,title:"Analyse de générations conditionnées (efficiency)",level:2,content:`## Analyse de générations conditionnées (efficiency)

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_efficiency.gif" class="m-auto w-full">
</div>`,frontmatter:{},note:"pareil, mais pour l'efficiency",index:19,start:545,end:556,noteHTML:`<p>pareil, mais pour l'efficiency</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:19,no:20},__clicksElements:[],__preloaded:!1}},{path:"21",name:"page-21",component:mO,meta:{slide:{raw:`
## Analyse de générations conditionnées (double)

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_double.gif" class="m-auto w-full">
</div>

<!--
pareil, mais là on conditionne \\
efficiency = 1 \\
massflow = [-3, 3]
-->
`,title:"Analyse de générations conditionnées (double)",level:2,content:`## Analyse de générations conditionnées (double)

<div class="flex flex-col items-center h-100">
  <img src="/assets/gp_double.gif" class="m-auto w-full">
</div>`,frontmatter:{},note:`pareil, mais là on conditionne \\
efficiency = 1 \\
massflow = [-3, 3]`,index:20,start:557,end:570,noteHTML:`<p>pareil, mais là on conditionne <br>
efficiency = 1 <br>
massflow = [-3, 3]</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:20,no:21},__clicksElements:[],__preloaded:!1}},{path:"22",name:"page-22",component:_O,meta:{slide:{raw:`
## Conclusion

<div class="h-100 flex flex-col text-2xl justify-center">

### Travail réalisé

- Génération conditionnée d'aubes par diffusion
- Release d'un code réutilisable en interne
- Rédaction d'une déclaration d'invention

</div>
`,title:"Conclusion",level:2,content:`## Conclusion

<div class="h-100 flex flex-col text-2xl justify-center">

### Travail réalisé

- Génération conditionnée d'aubes par diffusion
- Release d'un code réutilisable en interne
- Rédaction d'une déclaration d'invention

</div>`,frontmatter:{},index:21,start:571,end:584,noteHTML:"",filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:21,no:22},__clicksElements:[],__preloaded:!1}},{path:"23",name:"page-23",component:xO,meta:{slide:{raw:`
## Conclusion

<div class="h-100 flex flex-col text-2xl justify-center">

### Perspectives

- Vérifier le conditionnement par simulation CFD
- Remplacer la PCA par une méthode paramétrique
- Travailler directement sur les CAOs
- Tester des méthodes par RL

</div>
`,title:"Conclusion",level:2,content:`## Conclusion

<div class="h-100 flex flex-col text-2xl justify-center">

### Perspectives

- Vérifier le conditionnement par simulation CFD
- Remplacer la PCA par une méthode paramétrique
- Travailler directement sur les CAOs
- Tester des méthodes par RL

</div>`,frontmatter:{},index:22,start:585,end:599,noteHTML:"",filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:22,no:23},__clicksElements:[],__preloaded:!1}},{path:"24",name:"page-24",component:$O,meta:{slide:{raw:`
<div class="h-full w-full flex justify-center items-center">

# Annexes

</div>
`,title:"Annexes",level:1,content:`<div class="h-full w-full flex justify-center items-center">

# Annexes

</div>`,frontmatter:{},index:23,start:600,end:607,noteHTML:"",filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:23,no:24},__clicksElements:[],__preloaded:!1}},{path:"25",name:"page-25",component:AO,meta:{slide:{raw:`
## GraphVAE

<div class="flex items-center w-full bg-black">
  <img src="/assets/graphvae_surface.gif" class="m-auto w-full">
  <img src="/assets/graphvae_points.gif" class="m-auto w-full">
</div>
`,title:"GraphVAE",level:2,content:`## GraphVAE

<div class="flex items-center w-full bg-black">
  <img src="/assets/graphvae_surface.gif" class="m-auto w-full">
  <img src="/assets/graphvae_points.gif" class="m-auto w-full">
</div>`,frontmatter:{},index:24,start:608,end:616,noteHTML:"",filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:24,no:25},__clicksElements:[],__preloaded:!1}},{path:"26",name:"page-26",component:RO,meta:{slide:{raw:`
## PVD

<div class="flex items-center w-full bg-black">
  <img src="/assets/pvd_points.gif" class="m-auto h-100">
</div>

<!--
bon résultats, mais y'a des points au milieu de l'aube, donc c'est chiant pour reconstruction surface. En plus on peut moins facilement appliquer ce qu'on a fait avec les GPs ici.
-->
`,title:"PVD",level:2,content:`## PVD

<div class="flex items-center w-full bg-black">
  <img src="/assets/pvd_points.gif" class="m-auto h-100">
</div>`,frontmatter:{},note:"bon résultats, mais y'a des points au milieu de l'aube, donc c'est chiant pour reconstruction surface. En plus on peut moins facilement appliquer ce qu'on a fait avec les GPs ici.",index:25,start:617,end:628,noteHTML:`<p>bon résultats, mais y'a des points au milieu de l'aube, donc c'est chiant pour reconstruction surface. En plus on peut moins facilement appliquer ce qu'on a fait avec les GPs ici.</p>
`,filepath:"/home/laurent/Documents/Cours/ENSEEIHT/PFE/etude-biblio/slides/slides.md",id:25,no:26},__clicksElements:[],__preloaded:!1}},{path:"27",name:"page-27",component:FO,meta:{slide:{raw:`
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