SINGLE Francisco (Paco) Chinesta IGPSC, Arcachon, 18 Juin 2018
Sommaire 1. Pensées profondes 2. Dressant la complexité «Single equation» «Single model» «Single data» 3. Epiloge
1 - Pensées profondes Il est tellement difficile changer le paradigme dès l intérieur du paradigme! Einstein
Alessandro Volta Académie des Sciences de Paris, 1801 Napoleon: Monsieur Volta, pensez-vous que l'électricité servira un jour pour quelque chose d autre que faire sauter des grenouilles?
Gauss: Il est étrange et injuste à la fois, la preuve de l arbitraire et affligeante existence, d être né dans une époque particulière, et devenir prisonnier d elle, l ayant ou pas voulu. Cela vous confère un indécent avantage par rapport au passé et au même temps vous transforme en un clown devant le futur.
L'apprentissage peut se comparer au fait de verser un liquide très chaud sur une sphère en cire (représentant le cerveau). L écoulement creusera des rivages, et puis, n importe quel autre liquide (représentant les données et informations collectées) s écoulera par les mêmes rivages. L innovation, la découverte, nécessite de quitter ces rivages et remonter explorer le plateau, malgré les préjugés des années de formation réglée.
Où se posaient les hirondelles avenant l invention du téléphone? Gregoire Lacroix
Tout au debut, était l observation Astronomie en Babylonie
les modèles furent après Ptolémée, Copernic, Kepler, Galilée, Newton,, Einstein,
Galilée 5/15 = 1/3 15/25 = 3/5 25/35 = 5/7
5/15 = 1/3 15/25 = 3/5 F 25/35 = 5/7 g = m d2 x dt 2
Physique OU Donnés?
Component ou système Virtual Twin Modèle, Calibration & Contrôle basé sur FT Engineering Digital & Hybrid Twin + Données pour la prise de décision en temps réel Augmented Engineering Manufacturing Manufact4.0 In service IoT
Data Parametric model Calibration AI-based decision making Data-Driven Enriched Model Virtual Digital Hybrid
Physique ET Données Vers une ingénierie hybride combinant physique et données Le jumeau virtuel Le jumeau digital Le jumeau hybride
Le jumeau virtuel
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sha1_base64="aaot2ihkj/azagezmngq7vif/ci=">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</latexit> Le jumeau hybride Données Ẋ model (t, µ) Calibrage : Ẋ model (t, µ ) Ignorance : Ẋ ign (t) =Ẋ(t) Ẋmodel (t, µ ) Modèle de l ignorance Prise de décision basée sur des données
2 - Dressant la complexité
«Single equation» «Single model» «Single data
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sha1_base64="bivhvm1fjt0wvlirrean8dsqsgc=">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</latexit> <latexit sha1_base64="bivhvm1fjt0wvlirrean8dsqsgc=">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</latexit> «Single equation» POD X(t) =Bx(t) eliminant les correlations KX(t) =F(t) kx(t) =f(t) PGD X(t, µ 1,µ 2,,µ P ) X i T i (t) PY j=1 M j i (µ j)
Abaque d usinage
Airbag paramétrique
Crash paramétrique
Tracking system 2"m"
«Material Hybrid Lab»
«Single model» L idée 0 K 11 K 12 K 1N K 21 K 22 K 2N B....... @..... 1 C A 0 B @ U 1 U 2... 1 C A = 0 B @ F 1 F 2... 1 C A K N1 K N2 K NN U N F N Modèle Sortie Entrée Connaissant (F i, U i ), i = 1,...,P on obtient le modèle K = U 1 F
Variantes Deep-Learning, Tensor learning, Dictionary learning, Manifold learning, Linear and nonlinear regression (incl. decision tress), Sparse identification (compressed sensing), Dynamic model decomposition, Data-driven operator, spgd
«Single data»
En fait, c est quoi un arbre? Combien de paramètres permettent le définir?
η ξ
Intelligence artificielle: apprentissage de «variétés» D. Gonzalez, E. Cueto & F. Ch., Annals of Biomedical Engineering, 2015
«Towards smart data» Newton, Schrodinger, Dirac, MICRO x i, v i Maxwell, Boltzmann, Fokker, Planck, Liouville, MESO f(x, v, t) Navier, Stokes, Hooke, Carnot, Clausius, MACRO V, P, T
«Towards smart data» Newton, Schrodinger, Dirac, MICRO x i, v i Data Maxwell, Boltzmann, Fokker, Planck, Liouville, MESO f(x, v, t) Navier, Stokes, Hooke, Carnot, Clausius, MACRO V, P, T
«Towards smart data» Newton, Schrodinger, Dirac, MICRO x i, v i Data Maxwell, Boltzmann, Fokker, Planck, Liouville, MESO f(x, v, t) Information Navier, Stokes, Hooke, Carnot, Clausius, MACRO V, P, T
«Towards smart data» Newton, Schrodinger, Dirac, MICRO x i, v i Data Maxwell, Boltzmann, Fokker, Planck, Liouville, MESO f(x, v, t) Information Navier, Stokes, Hooke, Carnot, Clausius, MACRO V, P, T Knowledge
The hybrid twin THE$BIG$PICTURE$ Parametric$ determinis6c$ contribu6on$ PGD$ Data;Driven$ correc6on$ Control$ Noise$ Measures$involving$noise$
Resin Transfer Moulding
Parametric filling
Data assimilation & Online calibration Data assimilation 8 < k ident = argmin : EX e=1 9 PX = (I num ( e,t j,k) I exp ( e,t j )) 2 ; j=1 & Levenberg-Marquardt Addressing noise: (i) Kalmann filters (ii) Bayes within a probabilistic framework
Calibrated model
Modeling the ignorance Without correction With divergence model
System Modelling
Hybrid Twin in nuclear installation operations
Conclusions Smart-Data: quelle, où et quand? MODELE Data-Driven DONNEES deviation model: modeling the ignorance
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