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Moment Map of SU(n,n)/S(U(n)xU(n))

Figure 72 Moment Map of SU(n,n)/S(U(n)xU(n))

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> Paris-Metz-Valenciennes-Lille-Louvain- Liége-Bruxelles
> Paris-Metz-Valenciennes-Lille-Louvain- Liége-Bruxelles
Wolfgang Pauli Lectures on Physics, Volume 3 “Thermodynamics and the Kinetic Theory of Gases”, 2nd chapter dedicated to the 2"? Law: [...] The second law distinguishes heat from the other forms of energy. It indicates a direction in time and makes apparent that heat is a disordered form of energy. (Pauli 1973)
Wolfgang Pauli Lectures on Physics, Volume 3 “Thermodynamics and the Kinetic Theory of Gases”, 2nd chapter dedicated to the 2"? Law: [...] The second law distinguishes heat from the other forms of energy. It indicates a direction in time and makes apparent that heat is a disordered form of energy. (Pauli 1973)
Figure 1: Comparison of FAdam and Adam performance. (a) Eval loss (log pplx) on 1B LLMs presenting FAdafactor outperforms Adafactor. (b) Average WER on LibriSpeech using 600M Conformer models, presenting FAdam outperforms Adam. (c) FID of ImageNet generation using 100M VQ-VAE models, presenting FAdam outperforms AdamW. (d) Comparison of FIM exponents on a 1B LLM, showing 0.5 (square root) as the optimal choice. Table |: LibriSpeech WERs
Figure 1: Comparison of FAdam and Adam performance. (a) Eval loss (log pplx) on 1B LLMs presenting FAdafactor outperforms Adafactor. (b) Average WER on LibriSpeech using 600M Conformer models, presenting FAdam outperforms Adam. (c) FID of ImageNet generation using 100M VQ-VAE models, presenting FAdam outperforms AdamW. (d) Comparison of FIM exponents on a 1B LLM, showing 0.5 (square root) as the optimal choice. Table |: LibriSpeech WERs
http:/Awww.jmsouriau.com/structure des systemes dynamiques.htm http://www.springer.com/us/book/9780817636951
http:/Awww.jmsouriau.com/structure des systemes dynamiques.htm http://www.springer.com/us/book/9780817636951
F. Barbaresco, Esthétique structurelle des feuilletages symplectiques du mouvement, de la chaleur et de I’information : la quéte romantique de Jean-Marie Souriau de Carthage 4 Massilia ou le triptyque de la Nature des choses (De Rerum Natura) « Esthétisme — Structure - Mouvement », ENS/IRCAM MAMUPHI sem to be published by Spartacus Editor for MAMUPHI anniversary hitps://spartacus-idh.com/ MAMUPHI video: hitps://www.youtube.com/waich?v=dWyWXubGixA MAMUPHI Slides: http://www.entretemps.asso.fr/2022-2023/Barbaresco.pdf https://www.academia.edu/112471996/Structural_aesthetics_of_the_symplectic_foliations_of_movement_heat_and_information_the_romantic_quest_of_Jean ria Souriaqu fram Carthaaqe to Macciliq or the trintvch of the Notiure of thingae De Rarim Natura Aecthatice Striictirea AAgovamaeant
F. Barbaresco, Esthétique structurelle des feuilletages symplectiques du mouvement, de la chaleur et de I’information : la quéte romantique de Jean-Marie Souriau de Carthage 4 Massilia ou le triptyque de la Nature des choses (De Rerum Natura) « Esthétisme — Structure - Mouvement », ENS/IRCAM MAMUPHI sem to be published by Spartacus Editor for MAMUPHI anniversary hitps://spartacus-idh.com/ MAMUPHI video: hitps://www.youtube.com/waich?v=dWyWXubGixA MAMUPHI Slides: http://www.entretemps.asso.fr/2022-2023/Barbaresco.pdf https://www.academia.edu/112471996/Structural_aesthetics_of_the_symplectic_foliations_of_movement_heat_and_information_the_romantic_quest_of_Jean ria Souriaqu fram Carthaaqe to Macciliq or the trintvch of the Notiure of thingae De Rarim Natura Aecthatice Striictirea AAgovamaeant
H.B.G. Casimir, On the Rotation of a Rigid Body in Quantum Mechanics, Doctoral Thesis, Leiden, 1931.
H.B.G. Casimir, On the Rotation of a Rigid Body in Quantum Mechanics, Doctoral Thesis, Leiden, 1931.
Link with Souriau development
Link with Souriau development
de Saxcé, G. Euler-Poincaré equation for Lie groups with non null symplectic cohomology. Application to the mechanics. In GSI 2019. LNCS; Nielsen, F., Barbaresco, F., Eds.; Springer: Berlin, Germany, 2019; Volume 11712
de Saxcé, G. Euler-Poincaré equation for Lie groups with non null symplectic cohomology. Application to the mechanics. In GSI 2019. LNCS; Nielsen, F., Barbaresco, F., Eds.; Springer: Berlin, Germany, 2019; Volume 11712
> First principle: Energy conservation
> First principle: Energy conservation
2nd Principle Entrooy production
2nd Principle Entrooy production
Dissipative part of Metriplectic Model
Dissipative part of Metriplectic Model
Sergei Petrovich Novikov Andre Haefliger
Sergei Petrovich Novikov Andre Haefliger
: La thermodynamique a habitué de longue date la physique ma- sible est une telle forme complétement intégrable. Ce point
: La thermodynamique a habitué de longue date la physique ma- sible est une telle forme complétement intégrable. Ce point
> The gradient system (8) is always linearizable. The induced flow on an open subset of the Riemannian Statistical Manifold such that there exists a potential function satisfying (@) converges to equilibrium points exponentially. OV (0) dn n— oth «w—ln n \r and (0) Ww __4h—_—n nt) — op 'n())
> The gradient system (8) is always linearizable. The induced flow on an open subset of the Riemannian Statistical Manifold such that there exists a potential function satisfying (@) converges to equilibrium points exponentially. OV (0) dn n— oth «w—ln n \r and (0) Ww __4h—_—n nt) — op 'n())
ttos://www.cnrsatcreate.cnrs.fr/descartes
ttos://www.cnrsatcreate.cnrs.fr/descartes
Fig.2 Double thermoelastic pendulum. A single pendulum with exter- nal perturbations is learned, and the coupling between both systems is achieved via the port-metriplectic framework We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy, non-negative entropy production), we modify accordingly the port-Hamiltonian formalism so as to achieve a port-metriplectic one. We show that the constructed networks are able to learn the physics of complex systems by parts, thus alleviating the burden associated to the experimental characterization and posterior learning process of this kind of systems. Predictions can be done, however, at the scale of the complete system. Examples are shown on the performance of the proposed technique.
Fig.2 Double thermoelastic pendulum. A single pendulum with exter- nal perturbations is learned, and the coupling between both systems is achieved via the port-metriplectic framework We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy, non-negative entropy production), we modify accordingly the port-Hamiltonian formalism so as to achieve a port-metriplectic one. We show that the constructed networks are able to learn the physics of complex systems by parts, thus alleviating the burden associated to the experimental characterization and posterior learning process of this kind of systems. Predictions can be done, however, at the scale of the complete system. Examples are shown on the performance of the proposed technique.
Web Site: htips://sites. google.com/view/calistaworkshop2024paris/nome Videos: https://www.youtube.com/@CalistaWorkshopParis2024
Web Site: htips://sites. google.com/view/calistaworkshop2024paris/nome Videos: https://www.youtube.com/@CalistaWorkshopParis2024
Related topics:
ThermodynamicsRepresentation TheoryLie GroupsSymplectic geometryNon-equilibrium thermodynamicsphysics-informed neural networks
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