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

5. Lipson & Pollack, Nature 406, 2000

10. Camera View

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

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

14. Simulation & Reality Evolve Controller “Simulator” Try it in reality! Build Collect Sensor DataEvolve Simulator Evolve Simulators Evolve Robots

15. Servo Actuators Tilt Sensors

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

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

20. Random Predicted Physical

22. System Identification ?

23. Perturbations

24. Photo: Floris van Breugel

26. Structural Damage Diagnosis With Wilkins Aquino

27. . com With Jeff Clune, Jason Yosinski

28. Symbolic Regression f(x)=e x sin(|x|) What function describes this data? John Koza, 1992

29. Encoding Equations * sin – x1x1 3 f(x)f(x) + x2x2 -7 Building Blocks: + - * / sin cos exp log … etc sin(x 2 ) x 1 *sin(x 2 ) (x 1 – 3)*sin(x 2 ) (x 1 – 3)*sin(-7 + x 2 ) John Koza, 1992

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

31. Solution Accuracy Entire Dataset Coevolved Dataset

32. Solution Complexity Entire Dataset Coevolved Dataset

35. Semi-empirical mass formula Modeling the binding energy of an atomic nucleus R 2 = 0.999915 Weizsäcker’s Formula: R 2 = 0.99944 Inferred Formula:

37. Systems of Differential Equations Regress on derivative timex 1 x 2 … 03.4-1.7… 0.13.2-0.9… 0.23.1-0.1… 0.32.71.2… ………… State Variables dx 1 /dtx 2 /dt … -2.08.0… -1.08.0… -4.01.3… -5.71.9… ……… Derivatives

38. Original Equations Inferred Equations Inferring Biological Networks With Michael Schmidt, John Wikswo (Vanderbilt), Jerry Jenkins (CFDRC)

41. Charles Richter

43. Ingmar Zanger, John Amend

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

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

46. Cell #1 Cell #2 Cell #3-60 …

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

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

49. Withheld Test Set #1 Fit

50. Withheld Test Set #2 Fit

51. Withheld Test Set #3 Fit

52. Looking For Invariants

53. Data Mining

55. 42 42+x-x 42+1/(1000+x 2 ) ?

56. From Data: x y… 0.12.3 0.24.5 0.39.7 0.45.1 0.53.3 0.61.0 ……… δxδx δyδy δyδy δxδx,, … Calculate partial derivatives Numerically: δfδf δxδx δfδf δyδy From Equation: δx’δx’ δy’δy’ δy’δy’ δx’δx’,, … Calculate predicted partial derivatives Symbolically:

57. x y x 3 + x – y 2 – 1.5 = 0x 2 + y 2 – 16 = 0x 2 + y 2 + z 2 – 1 = 0 x y x z Homework CircleElliptic CurveSphere

59. Linear Oscillator Coefficients may have different scales and offsets each run

60. Pendulum H L

61. Double Linear Oscillator would be plus for Lagrangian

68. xyz z=f(x,y) ? dy/dt=f(x,y) ? f(x,y,z)=0 ?

69. Run…

70. xyz z=f(x,y) ? dy/dt=f(x,y) ? f(x,y,z)=0 ? I feel lucky

73. Von Thomas Hermanowski, Dr. Andreas Rick, Dr. Jochen Weber

74. Particle Accelerators angle Distortion Correction (GE X-Ray Detectors) 5x Resolution Improvement Jay Schuren

76. Concluding Remarks Correlation is enough. Faced with massive data, [the Scientific Method] is becoming obsolete. We can stop looking for models. “ ” Chris Anderson Wired 16.07 The data deluge accelerates our ability to hypothesize, model, and test.

77. Theoretical physicists are not yet obsolete, but scientists have taken steps toward replacing themselves

78. I am worried that we have enjoyed a brief window in human history where we could actually understand things, but that period may be coming to an end. -- Steve Strogatz The end of insight