Fig. 1. (a) Illustration of artificial neural network (ANN) architecture for image recognition implemented by photonic units, including optical input encoding parts, optical interference units, optical nonlinear units, and photodetectors. (b) Demonstration of a programmable Mach–Zehnder interferometer consisting of directional couplers and thermo-optical phase shifters.

Fig. 2. Heat map of classification accuracy in the MNIST dataset with the imprecise ONN chip. (a) Classification performance between phase shift error σ and per MZI loss α. (b) Effects of phase shift error σ and extinction ratio E. (c) Impacts of phase shift error σ and photodetection noise σD on the final achieved network performance.

Fig. 3. Training flow of the ONN with parameter imprecisions using the genetic algorithm. Two major stages are involved and illustrated, including gradient training of the ideal ONN and genetic training in the imprecise chips.

Fig. 4. Training curves of the ideal ONN using gradient descent algorithm in (a) Iris and (b) MNIST datasets, including loss curve as well as accuracies in training and test datasets. (c) Maximum accuracy in each generation at the GA training stage considering imprecise optical components. The optimal individual can have 91.4% and 82.7% accuracy in Iris and MNIST datasets, respectively. (d) Accuracy distribution with and without GA training in Iris and MNIST datasets. (e) Comparisons of training curves between the two-step training method and the only GA training method in Iris and MNIST datasets. (f) Standard deviations of accuracy distributions in Iris and MNIST datasets with different numbers of layers and different layer widths.

Fig. 5. (a) Accuracy training curves in the MNIST dataset during the GA training stage in the condition of typical error ranges {σall∈[0.04,0.05],α∈[0.05,0.1],E∈[13,15],σD∈[0.04,0.05]} and experimentally measured low error ranges {σall∈[0.004,0.005],α∈[0.04,0.05],E∈[20,23],σD∈[0.0009,0.0011]}. (b) Accuracy distribution of imprecise chips in two error range cases.

Fig. 6. (a) Accuracy training curves in the GA training stage in different compensated phase shift ranges {Δξ}. (b) Effects of compensated phase shift ranges {Δξ} on the accuracy distribution in imprecise chips.

Fig. 7. (a) Accuracy training curves in the GA training stage using different numbers of imprecise chips M. (b) Effects of the number of imprecise chips M on accuracy distribution.

Fig. 8. (a) Accuracy training curves in the GA training stage in the condition of different populations. (b) Effects of different populations in evolution on the accuracy distribution in imprecise chips.

Fig. 9. (a) Accuracy training curves in three heuristic algorithms with the accuracy converging to a particular value. (b) Accuracy distribution of three algorithms in the same imprecise chips.