ppt_机器学习_力学.pdf

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PDEs and fundamental laws of physics

Machine learning

Concurrent learning

Molecular modeling

Kinetic model for gas dynamics

Concluding remarks

ʡʡʡᘤᘤᘤᱥᱥᱥᳮᳮᳮɂɂɂ Machine Learning and Physics-based Modeling: How can we construct interpretable and truly reliable physical models using concurrent machine learning? ⎎⎎⎎ᓭᓭᓭ Princeton University Joint work with: Jiequn Han, Han Wang, Linfeng Zhang Roberto Car, Chao Ma, Zheng Ma, Huan Lei, ...... May 14, 2020 1 / 57

Outline Outline 1 PDEs and fundamental laws of physics 2 Machine learning 3 Concurrent learning 4 Molecular modeling 5 Kinetic model for gas dynamics 6 Concluding remarks May 14, 2020 2 / 57

Outline PDEs and fundamental laws of physics 1 PDEs and fundamental laws of physics 2 Machine learning 3 Concurrent learning 4 Molecular modeling 5 Kinetic model for gas dynamics 6 Concluding remarks May 14, 2020 3 / 57

Two main themes of scientiﬁc research PDEs and fundamental laws of physics 9ʠțᳮ Physics: Newton’s laws, Maxwell equations, Quantum mechanics Y3▭_⚪ “Engineering” (industrial) problems: ᑴ⌼ʹᩞᧇȕᶭʹ஺஺஺ May 14, 2020 4 / 57

9ʠțᳮPaul Dirac’s claim (1929) PDEs and fundamental laws of physics ”The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the diﬃculty is only that the exact application of these laws leads to equations much too complicated to be soluble. ” ◀ᦪᱥᳮ⚞9 Pᱥᳮ᪶ᱥᳮᜩᱥᳮ ᜜ᡃA˯N ᑮḄ_⚪᝞ ᓄ, ᩞᧇ, ˯ᱥ, ⚞9Ḅ_⚪[ȑɏ஺ 8`Ḅʖ[ȑᦪɐ8`஺ H= Ḅ6ϛ i∂tΨ = HΨ, Ψ = Ψ(x1, x2,··· , xN) May 14, 2020 5 / 57

ɘ᪵9ʠțᳮ35Y3▭_⚪ PDEs and fundamental laws of physics ᦪǷA ᓄɂ ɏɂ May 14, 2020 6 / 57

ᓄɂ PDEs and fundamental laws of physics ᓄɂḄ⌕ express fundamental physical principles (e.g. conservation laws) obey physical constraints (e.g. symmetries, frame-indiﬀerence, Galilean invariance) (universally) accurate (transferrable): physical parameters can be measured using simple experiments physically meaningful (interpretable) Very successful example: Euler’s equation for gas dynamics (for dense gas) A not very successful example: extended Euler equation for rariﬁed gas (e.g. Grad’s 13-moment equation) Kn = ᑖᙳQᵫ May 14, 2020 7 / 57

ɘ᪵ᓄɂ PDEs and fundamental laws of physics ᱥᳮA generalized hydrodynamics: Onsager Landau: gradient expansion, weakly nonlinear theory successful example: Ericksen-Leslie equation for liquid crystals unsuccessful example: Non-Newtonian ﬂuids ᦪA ᑖ᪆, e.g. PLK (Poincar´e-Lighthill-Kuo) method projection onto principal components truncation (e.g. Lorenz system) May 14, 2020 8 / 57

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