machine learning for energy landscapes
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Machine learning for energy landscapes Tristan Bereau Van t Hoff - PowerPoint PPT Presentation

Feb 20, 2023 •347 likes •1.21k views

Machine learning for energy landscapes Tristan Bereau Van t Hoff Institute for Molecular Sciences & Informatics Institute University of Amsterdam Introduction to kernel-based ML Today Incorporation of physical symmetries,

  1. Machine learning for energy landscapes Tristan Bereau Van ’t Hoff Institute for Molecular Sciences & Informatics Institute University of Amsterdam

  2. • Introduction to kernel-based ML Today • Incorporation of physical symmetries, conservation laws Machine learning for energy landscapes Tristan Bereau Van ’t Hoff Institute for Molecular Sciences & Informatics Institute University of Amsterdam

  3. • Introduction to kernel-based ML Today • Incorporation of physical symmetries, conservation laws Machine learning for energy landscapes Tristan Bereau Van ’t Hoff Institute for Molecular Sciences & Informatics Institute University of Amsterdam Supervised ML in chemistry Thursday and materials science Kevin Jablonka Mohamad Moosavi

  4. Molecular dynamics 2

  5. Molecular dynamics F = m a 2

  6. Molecular dynamics F = m a Specify interparticle forces: “force field” 2

  7. Molecular dynamics Numerically integrate particle positions F = m a Specify interparticle forces: “force field” 2

  8. Molecular dynamics Numerically integrate particle positions F = m a Specify interparticle forces: “force field” Wikipedia 2

  9. Molecular dynamics Numerically integrate particle positions F = m a Specify interparticle forces: “force field” Wikipedia fs ps ns s ms s µ 2

  10. Molecular dynamics Numerically integrate particle positions F = m a Specify interparticle forces: “force field” Wikipedia integration time step fs ps ns s ms s µ 2

  11. Molecular dynamics Numerically integrate particle positions F = m a Specify interparticle forces: “force field” Wikipedia integration Timescales of interest time step fs ps ns s ms s µ 2

  12. Molecular dynamics Numerically integrate particle positions F = m a Specify interparticle forces: “force field” Wikipedia integration Timescales of interest time step Emergent complexity fs ps ns s ms s µ 2

  13. Data as the 4 th pillar of science A. Agrawal and A. Choudhary APL Mater. 4 053208 (2016); https://www.bigmax.mpg.de 3

  14. Data science Hardware Machine learning Databases 4

  15. Data science Hardware DeepMind Machine learning Databases Google 4

  16. Links to machine learning Interpolation of a high-dimensional function Potential energy surface Can we build a more accurate PES? Can we easily build an accurate PES? Can we make the numerical integration faster and/or more efficient? … 5

  17. Teaser: let’s fit data points Good Not good 6

  18. Teaser: let’s fit data points Good Not good 6

  19. Teaser: let’s fit data points Good Not good I want to be here 6

  20. Teaser: let’s fit data points Good Not good I want to be here ruthlessly stolen from A. von Lilienfeld 6

  21. Multivariate function approximation Sparse data infer smooth function 7

  22. Multivariate function approximation “inverse problems” Sparse data infer smooth function 7

  23. Multivariate function approximation “inverse problems” Sparse data infer smooth function sparse data ground truth Ê property interpolation property Ê Ê Ê Ê Ê molecular structure descriptor Rupp, International Journal of Quantum Chemistry 115 (2015) 7

  24. Multivariate function approximation “inverse problems” Sparse data infer smooth function Regression : y sparse data prediction of f : ℝ d → ℝ ground truth Ê property interpolation property based on noisy data points Ê Ê D = ( X , y ) = { x n , y n } N Ê Ê n =1 Ê y n = f ( x n ) + ε x molecular structure descriptor What is f ? Rupp, International Journal of Quantum Chemistry 115 (2015) 7

  25. Kernel methods are vintage - needs a representation { - linear algebra Kernel - can be efficient with small data - learns the representation { - complex mathematical Deep learning structure - data hungry 8

  26. � Learning from experience � � � � Inductive (based on examples) � (genera (snake seems like overfitting, � fitting to well, cf. Lecture 2) source: xkcd [7] Visualization of high-dimensional space 9

  27. <latexit sha1_base64="G3h4pfP2Yj/buXVPhz0Vw6uTCrc=">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</latexit> <latexit sha1_base64="G3h4pfP2Yj/buXVPhz0Vw6uTCrc=">ACWHichVFNa9wFJSd7+3XJj328shS2By62CG0zaEQ2kspPaRQN4G1u8ja510RSTbSc2Ex/pM5FEL+Sg7R7vrQJoUOCA0z85A0yislHUXRTRBubG5t7+zu9Z48fb8RX/4IcrayswEaUq7WXOHSpMCFJCi8ri1znCi/yq09L/+IXWidL850WFWaz4wspODkpUm/SiZNajV8/dIO7RF8gBNIsXJSlQZShQWN19sQ0sJyAamTM83BQmrlbE5HP5v4uIU3/wu9bTueTfqDaBStAI9J3JEB63A+6V+n01LUGg0JxZ0bx1FWcMtSaGw7aW1w4qLKz7DsaeGa3RZs2qmhdemUJRWr8MwUr9c6Lh2rmFzn1Sc5q7h95S/Jc3rql4nzXSVDWhEeuDiloBlbCsGabSoiC18IQLK/1dQcy5L4f8Z/R8CfHDJz8myfHodBR/Oxmcfeza2GWv2CEbspi9Y2fsMztnCRPsN7sLtoLt4DYMwp1wbx0Ng27mJfsL4cE9X2yxCQ=</latexit> <latexit sha1_base64="G3h4pfP2Yj/buXVPhz0Vw6uTCrc=">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</latexit> <latexit sha1_base64="G3h4pfP2Yj/buXVPhz0Vw6uTCrc=">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</latexit> Extrapolation in machine learning 35 U LJ ( r ) 30 Training points Prediction 25 20 U LJ ( r ) [ ≤ ] 15 ⇣ � ⌘ 6 � ⌘ 12 ⇣ � 10 U LJ ( r ) = 4 ✏ − r r 5 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0 r [ æ ] 10

  28. <latexit sha1_base64="G3h4pfP2Yj/buXVPhz0Vw6uTCrc=">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</latexit> <latexit sha1_base64="G3h4pfP2Yj/buXVPhz0Vw6uTCrc=">ACWHichVFNa9wFJSd7+3XJj328shS2By62CG0zaEQ2kspPaRQN4G1u8ja510RSTbSc2Ex/pM5FEL+Sg7R7vrQJoUOCA0z85A0yislHUXRTRBubG5t7+zu9Z48fb8RX/4IcrayswEaUq7WXOHSpMCFJCi8ri1znCi/yq09L/+IXWidL850WFWaz4wspODkpUm/SiZNajV8/dIO7RF8gBNIsXJSlQZShQWN19sQ0sJyAamTM83BQmrlbE5HP5v4uIU3/wu9bTueTfqDaBStAI9J3JEB63A+6V+n01LUGg0JxZ0bx1FWcMtSaGw7aW1w4qLKz7DsaeGa3RZs2qmhdemUJRWr8MwUr9c6Lh2rmFzn1Sc5q7h95S/Jc3rql4nzXSVDWhEeuDiloBlbCsGabSoiC18IQLK/1dQcy5L4f8Z/R8CfHDJz8myfHodBR/Oxmcfeza2GWv2CEbspi9Y2fsMztnCRPsN7sLtoLt4DYMwp1wbx0Ng27mJfsL4cE9X2yxCQ=</latexit> <latexit sha1_base64="G3h4pfP2Yj/buXVPhz0Vw6uTCrc=">ACWHichVFNa9wFJSd7+3XJj328shS2By62CG0zaEQ2kspPaRQN4G1u8ja510RSTbSc2Ex/pM5FEL+Sg7R7vrQJoUOCA0z85A0yislHUXRTRBubG5t7+zu9Z48fb8RX/4IcrayswEaUq7WXOHSpMCFJCi8ri1znCi/yq09L/+IXWidL850WFWaz4wspODkpUm/SiZNajV8/dIO7RF8gBNIsXJSlQZShQWN19sQ0sJyAamTM83BQmrlbE5HP5v4uIU3/wu9bTueTfqDaBStAI9J3JEB63A+6V+n01LUGg0JxZ0bx1FWcMtSaGw7aW1w4qLKz7DsaeGa3RZs2qmhdemUJRWr8MwUr9c6Lh2rmFzn1Sc5q7h95S/Jc3rql4nzXSVDWhEeuDiloBlbCsGabSoiC18IQLK/1dQcy5L4f8Z/R8CfHDJz8myfHodBR/Oxmcfeza2GWv2CEbspi9Y2fsMztnCRPsN7sLtoLt4DYMwp1wbx0Ng27mJfsL4cE9X2yxCQ=</latexit> <latexit sha1_base64="G3h4pfP2Yj/buXVPhz0Vw6uTCrc=">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</latexit> Extrapolation in machine learning 35 35 U LJ ( r ) U LJ ( r ) 30 30 Training points Training points Prediction Prediction 25 25 20 20 U LJ ( r ) [ ≤ ] U LJ ( r ) [ ≤ ] 15 15 ⇣ � ⌘ 6 � ⌘ 12 ⇣ � 10 10 U LJ ( r ) = 4 ✏ − r r 5 5 0 0 0 . 2 0 . 2 0 . 4 0 . 4 0 . 6 0 . 6 0 . 8 0 . 8 1 . 0 1 . 0 1 . 2 1 . 2 1 . 4 1 . 4 1 . 6 1 . 6 1 . 8 1 . 8 2 . 0 2 . 0 r [ æ ] r [ æ ] 10

  29. Bayesian inference Prediction { Prior beliefs Sampled data 11

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