Using evolutionary algorithms to design antennas with greater sensitivity to ultrahigh energy neutrinos

The Genetically Evolved NEutrino Telescopes for Improved Sensitivity project seeks to optimize detectors in physics for science outcomes in high-dimensional parameter spaces. In this project, we designed an antenna using a genetic algorithm with a science outcome directly as the sole figure of merit. This paper presents initial results on the improvement of an antenna design for in-ice neutrino detectors using the current Askaryan Radio Array (ARA) experiment as a baseline. By optimizing for the effective volume using the evolved antenna design in ARA, we improve upon ARA’s simulated sensitivity to ultrahigh energy neutrinos by 11%, despite using limited parameters in this initial investigation. Future improvements will continue to increase the computational efficiency of the genetic algorithm and the complexity and fitness of the antenna designs. This work lays the foundation for continued research and development of methods to increase the sensitivity of detectors in physics and other fields in parameter spaces of high dimensionality.

Figure 1

A schematic of an asymmetric bicone antenna. The lengths ($L_1$, $L_2$), inner radii ($r_1$, $r_2$), opening angles (${\theta }_1$, ${\theta }_2$), and separation distance ($s$) fully define the geometry. In the results presented here, the separation distance was held constant, and the other six parameters were varied.

Figure 2

A diagram of the GENETIS work flow used to evolve antennas. The boxes on the far left and right give the beginning and end of the loop. The two central boxes represent the fitness calculation and the bottom two boxes represent the creation of the next generation.

Figure 3

Initial results of GA. Each distribution represents the entire range of scores in the generation, while width indicates the density of scores. The current ARA Bicone Fitness is shown as the horizontal dotted line.

Figure 4

Evolution of the six antenna parameters optimized so far, showing trends toward preferred features (bright yellow being most fit).

Figure 5

Model of the best antenna design, individual 8, evolved in generation 23. This bicone is shown on its side here, with the top side on the left. Other individuals are not shown because they are not visually distinguishable from this one.

Figure 6

SPICE schematic of the matching circuit.

Figure 7

Fitness scores using gain vs realized gain with a matching circuit (blue circles) and without (red crosses).

Figure 8

Antenna fitness score using perfect matching minus antenna fitness score using realized gain for unmatched (red/dots) and matched (blue/circles) antennas.

Figure 9

Antenna gain [Eq. (1)] for the evolved bicone (purple dashed line) and the ARA bicone (black dotted line) from XFdtd. Angles are measured from the positive vertical direction. See Appendix pp3 for gain patterns for frequencies from 500 MHz to 1 GHz.

Figure 10

Histograms of the number of detected neutrinos (left) and radio frequency (RF) signals (right) by each bicone for $3\times {10}^7$ simulated events. These angles denote the direction in which the event is seen by the detector, making them defined the same as the angles in Fig. 9. A RF angle of $\cos {\theta }_{\mathrm{RF}}>0$ would mean that the signal is the incident from the above horizontal.

Figure 11

A down-going neutrino interacting in the ice below the antenna, creating a particle cascade that produces Askaryan radiation that is viewed by the antenna.

Figure 12

Smith chart example matching load $Z_L$ to source $Z_0$ [68].

Figure 13

Overlapping bar plot of results from running the test GA with various combinations of generative operator ratios. The labels on the $x$ axis indicate the percent of individuals formed through reproduction (“R”) and crossover (“C”), with the remainder coming from injection. The results are arranged in descending order of performance as measured by the average maximum score (purple/crosses) of ten runs using the labeled set of ratios. Note that the zero has been suppressed on this plot. While there is no guarantee that the maximum score of a run is close to 100, no individual run in this test produced a maximum fitness score below 92.

Figure 14

Overlapping bar chart showing the performance of the test GA for different population sizes. For this study the fitness score was adjusted to range from 0 to 1.

Figure 15

Gain patterns for the evolved and ARA bicones at 500–800 MHz.

Figure 16

Gain patterns for the evolved and ARA bicones at 900 and 1000 MHz.

Figure 17

Results of the GA for the symmetric evolution.

Figure 18

A parallel coordinate plot of the genes in the symmetric evolution.