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Machine Science Distilling Free-Form Natural Laws from Experimental Data

Machine Science Distilling Free-Form Natural Laws from Experimental Data. Hod Lipson, Cornell University. Lipson & Pollack, Nature 406, 2000. Camera View. Camera. Crossing The Reality Gap. Adapting in simulation. Simulator. Evolve Controller In Simulation. Download. Try it in reality!.

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Machine Science Distilling Free-Form Natural Laws from Experimental Data

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  1. Machine Science Distilling Free-Form Natural Laws from Experimental Data Hod Lipson, Cornell University

  2. Lipson & Pollack, Nature 406, 2000

  3. Camera View Camera

  4. Crossing The Reality Gap Adapting in simulation Simulator Evolve Controller In Simulation Download Try it in reality!

  5. Too many Physical Trials Adapting in reality Evolve Controller In Reality Try it !

  6. “Simulator” Evolve Simulator Evolve Simulators Collect Sensor Data Simulation & Reality Co-Evolution Evolve Controller Evolve Robots Build Try it in reality!

  7. Tilt Sensors Servo Actuators

  8. Emergent Self-Model With Josh Bongard and Victor Zykov, Science 2006

  9. Damage Recovery With Josh Bongard and Victor Zykov, Science 2006

  10. Random Predicted Physical

  11. ? System Identification

  12. Perturbations

  13. Photo: Floris van Breugel

  14. Photo: Floris van Breugel

  15. Structural Damage Diagnosis With Wilkins Aquino

  16. .com With Jeff Clune, Jason Yosinski

  17. f(x)=exsin(|x|) Symbolic Regression What function describes this data? John Koza, 1992

  18. f(x) * – -7 x1 x2 3 sin + Encoding Equations Building Blocks: + - * / sin cos exp log … etc sin(x2) x1*sin(x2) (x1 – 3)*sin(x2) (x1 – 3)*sin(-7 + x2) John Koza, 1992

  19. Models: Expression trees Subject to mutation and selection Experiments: Data-points Subject to mutation and selection {const,+,-,*,/,sin,cos,exp,log,abs} Michael D. Schmidt, Hod Lipson (2006)

  20. Solution Accuracy Coevolved Dataset Entire Dataset

  21. Solution Complexity Entire Dataset Coevolved Dataset

  22. Semi-empirical mass formula Modeling the binding energy of an atomic nucleus Inferred Formula: R2 = 0.99944 Weizsäcker’s Formula: R2 = 0.999915

  23. State Variables Derivatives dx1/dtx2/dt … timex1x2 … 0 3.4 -1.7 … 0.1 3.2 -0.9 … 0.2 3.1 -0.1 … 0.3 2.7 1.2 … … … … … -2.0 8.0 … -1.0 8.0 … -4.0 1.3 … -5.7 1.9 … … … … Systems of Differential Equations • Regress on derivative

  24. Inferring Biological Networks With Michael Schmidt, John Wikswo (Vanderbilt), Jerry Jenkins (CFDRC)

  25. Charles Richter

  26. Ingmar Zanger, John Amend

  27. Wet Data, Unknown System With Michael Schmidt (Cornell) and Gurol Suel (UT Southwestern)

  28. Wet Data, Unknown System With Michael Schmidt (Cornell) and Gurol Suel (UT Southwestern)

  29. Cell #1 Cell #2 Cell #3-60 …

  30. = = Blue Dots = data points, Green Line = regressed fit

  31. Biologist’s Inferred Model: Gurol Suel, et. al., Science 2007 Symbolic Regression Inferred Time-Delay Model:

  32. Withheld Test Set #1 Fit

  33. Withheld Test Set #2 Fit

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