1. experimental apparatus
A self-optimizing
experimental apparatus
Ilka Geisel1, Stefan Jöllenbeck1, Jan Mahnke1,
Kai Cordes2, Wolfgang Ertmer1, Carsten Klempt1
Institut für Quantenoptik, Leibniz Universität Hannover
Institut für Informationsverarbeitung, Leibniz Universität Hannover

2. Optimizing the Experiment
Why don’t we just do it by hand?
[ms]
[ms]
P 1
P 2
P 3
Arbitrary parameter
Ilka Geisel - A self optimizing experimental apparatus

3. Thorough optimization by hand
Number of
Dimensions
Measurements
Time (for 1Hz rep. rate) 1 5
5 s 2 25
25 s 3
125
2 min 4
625
10 min
3 125
52 min 6
15 625
4 h 7
78 125
22 h 8
4,5 days 9
3 weeks 10
4 month 11
1,5 years 12
8 years 9
3 weeks
→ Scales exponentially
with number of dimensions
Ilka Geisel - A self optimizing experimental apparatus

4. What search methods are possible?
Ilka Geisel - A self optimizing experimental apparatus

5. Differential Evolution
Requirements
Optimize multiple correlated experimental parameters
Find the global maximum
Robust regarding fluctuations
Quick search also in high-dimensional parameter space
Differential Evolution
Storn and Price, 1995
Ilka Geisel - A self optimizing experimental apparatus

6. Differential Evolution
Time scales less than quadratically with number of dimensions
Scale and units of the parameters are irrelevant
Uses one target function
Number of atoms
Temperature
Phase Space Density
Position
Any other accessible result
Ilka Geisel - A self optimizing experimental apparatus

7. Evolutionary Algorithms
Generate
first
population
Measure
population
Mutate population and generate trial
vectors
Measure
trial vectors
Compare one on one to choose new population
Ilka Geisel - A self optimizing experimental apparatus

8. Generating the first generation
Dim=2
Current
Detuning P0 x0 y0 P1 y1 x1 P2 y2 x2 P3 y3 x3 P4 y4 x4
# Vectors
= Dim*5 P5 x5 y5 P6 y6 x6 P7 y7 x7 P8 y8 x8 P9 y9 x9
Ilka Geisel - A self optimizing experimental apparatus

9. Measure first population
Cur
rent
Detuning
# Atoms P0 x0 y0
f(P0) P1 y1 x1
f(P1) P2 y2 x2
f(P2) P3 y3 x3
f(P3) P4 y4 x4
f(P4) P5 x5 y5
f(P5) P6 y6 x6
f(P6) P7 y7 x7
f(P7) P8 y8 x8
f(P8) P9 y9 x9
f(P9)
Ilka Geisel - A self optimizing experimental apparatus

10. Ilka Geisel - A self optimizing experimental apparatus
Generate Mutants M0
x'0
y'0 M1
y'1
x'1 M2
y'2
x'2 M3
y'3
x'3 M4
y'4
x'4 M5
x'5
y'5 M6
y'6
x'6 M7
y'7
x'7 M8
y'8
x'8 M9
y'9
x'9
Ilka Geisel - A self optimizing experimental apparatus

11. Create a trial population
yes
Crossover? no T0
x'0 y0
f(T0) T1
y'1 x1
f(T1) T2
y'2
x'2
f(T2) T3 y3
x'3
f(T3) T4
y'4
x'4
f(T4) T5 x5
y'5
f(T5) T6 y6
x'6
f(T6) T7
y'7 x7
f(T7) T8
y'8 x8
f(T8) T9 y9
x'9
f(T9)
Ilka Geisel - A self optimizing experimental apparatus

12. Ilka Geisel - A self optimizing experimental apparatus
Compare one on one
Population
Generation 1
Trial vectors
Generation 1
Population
Generation 2 P0
f(P0) T0
f(T0) T0
f(T0) P1
f(P1) T1
f(T1) T1
f(T1) P2
f(P2) T2
f(T2) T2
f(T2) P3
f(P3) T3
f(T3) P3
f(P3) P4
f(P4) T4
f(T4) P4
f(P4) P5
f(P5) T5
f(T5) T5
f(T5) P6
f(P6) T6
f(T6) P6
f(P6) P7
f(P7) T7
f(T7) P7
f(P7) P8
f(P8) T8
f(T8) T8
f(T8) P9
f(P9) T9
f(T9) P9
f(P9)
Ilka Geisel - A self optimizing experimental apparatus

13. Visualization in 9 Dimensions
2 Currents [-140,140] A
1 Detuning [-90,0] MHz
3 Currents [0,140] A
1 Current [-140,0] A
2 Currents [-140,140] A
Blue: Trial Vectors,
Orange: Population Vectors
Ilka Geisel - A self optimizing experimental apparatus

14. Visualization in 9 Dimensions
2 Currents [-140,140] A
1 Detuning [-90,0] MHz
3 Currents [0,140] A
1 Current [-140,0] A
2 Currents [-140,140] A
Blue: Trial Vectors,
Orange: Population Vectors
Ilka Geisel - A self optimizing experimental apparatus

15. Optimization in the experiment
Ilka Geisel - A self optimizing experimental apparatus

16. Optimizing a MOT in 9 Dimensions
Average of Population
Average of Trials
Ilka Geisel - A self optimizing experimental apparatus

17. Ilka Geisel - A self optimizing experimental apparatus
Human vs. DE
Ilka Geisel - A self optimizing experimental apparatus

18. Ilka Geisel - A self optimizing experimental apparatus
Add-ons
Hard boundaries
Force mutants inside boundaries
Different approaches show different behavior
Elite
Use only upper X% as parent vectors
Consider speed against accuracy
Finite Lifetime
If a trial vector survived X times, redo the measurement
Slows but helps consider experimental noise
Ilka Geisel - A self optimizing experimental apparatus

19. Ilka Geisel - A self optimizing experimental apparatus
Summary
Little computing power required
Easy implementation (i.e. into LabView)
Finds the global optimum
We optimized up to 13 parameters
Better than human
Thank you for your attention!
Ilka Geisel - A self optimizing experimental apparatus

20. Ilka Geisel - A self optimizing experimental apparatus
Pseudo Code
// initialize…
do // generate a trial population
{ for (i=0; i<Np; i++) // r0!=r1!=r2!=i
{ do r0=floor(rand(0,1)*Np); while (r0==i);
do r1=floor(rand(0,1)*Np); while (r1==i or r1==r0);
do r2=floor(rand(0,1)*Np); while (r2==i or r2==r1 or r2==r1);
jrand=floor(D*rand(0,1));
for (j=0; j<D; j++) // generate one trial vector
{ if (rand(0,1) <=Cr or j==jrand) // use mutant
{ tj,i = pj,ro+F*(pj,r1-p,r2); // check for out of bounds? }
else
{ tj,i=pj,i; // use old population
// select the population of the next generation
for (i=0; i<Np; i++)
{ if ( f(ti) >= f(pi)) pi=ti;
} while (termination criterion not met);
Ilka Geisel - A self optimizing experimental apparatus

21. Optimizing a Trap in 5 Dimensions
Ilka Geisel - A self optimizing experimental apparatus

22. What we optimized so far
Dimensions
Samples per Generation
Generations
Before
After
MOT 9
9*10 = 90
417
1,69*1010
2,05*1010
MOT II 12
12*10 = 120
330
6,27*108
7,3*108
Molasses 2
2*10 = 20 15
8,15*108
Optical pumping 7
7*5 = 35 50
1,24*109
Magnetic trap
1,75*109
Ilka Geisel

23. How does that compare? Number of Dimensions Measurements
Number of Measurements with DE 2 25
300 7
78 125
1 750 9
37 530 12
39 600
Ilka Geisel