Nested deep transfer learning for modeling of multilayer thin films

Fig. 1. (a) Schematic illustrating the principle of nested transfer. Left to right: Weights from the previous model are taken after training (box with dashed lines) and used for initialization of the weights of the next model (solid-colored lines between neurons), as the complexity of the output gradually increases. (b) Diagram of a multilayer thin-film structure. The structure has a choice of any of four materials at each layer, with the constraint that no two neighboring layers are the same material. (c) Architecture of the mixed convolutional MDN used for the inverse design. There are initial pairs of convolutional and max pooling layers leading to fully connected layers. The output is split into categorical channels predicting the material choice at each layer and a final MDN channel representing probability distributions of the layer thicknesses.

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Fig. 2. (a) Diagram of a bidirectional RNN used for the forward model. (b) Training curves for nested transfer forward prediction for thin-film structures of increasing complexity (see legends), up to 30 layers. (c) Comparison of requested ground-truth spectrum (blue) and the spectrum predicted by the forward model (orange) for a randomly chosen case in the test data set.

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Fig. 3. (a) Training curves for nested transfer inverse design up to 10 layers. The categorical loss (left panel) refers to the outputs representing the material choices at each layer, while the continuous loss (right panel) refers to the negative log likelihood for the MDN predicting the thickness of each layer. (b) Comparison of requested ground-truth spectrum (blue) and the design suggested by the model for a randomly chosen case in the test data set without postprocessing. The model-suggested design is [ ${Al}_{2} O_{3} - 84 nm$ , ${SiO}_{2} - 85 nm$ , ${Al}_{2} O_{3} - 91 nm$ , ${SiO}_{2} - 90 nm$ , ${Al}_{2} O_{3} - 88 nm$ , ${SiO}_{2} - 90 nm$ , ${Al}_{2} O_{3} - 90 nm$ , ${SiO}_{2} - 88 nm$ , ${TiO}_{2} - 77 nm$ , ${SiO}_{2} - 92 nm$ ]. (c) Comparison between requested ground-truth spectrum (blue) and the spectra of the original design proposed by the inverse model (orange) and of the design after postprocessing (green). The model design after postprocessing is [ ${SiO}_{2} - 95 nm$ , ${Ta}_{2} O_{5} - 78 nm$ , ${SiO}_{2} - 122 nm$ , ${SiO}_{2} - 50 nm$ , ${Al}_{2} O_{3} - 50 nm$ , ${Ta}_{2} O_{5} - 98 nm$ , ${Ta}_{2} O_{5} - 54 nm$ , ${Al}_{2} O_{3} - 119 nm$ , ${TiO}_{2} - 90 nm$ , ${SiO}_{2} - 94 nm$ ].

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Fig. 4. (a) Diagram of thin-film structure used for selective thermal emission. (b) Comparison between requested ground-truth spectrum and spectrum produced by model suggested design for an arbitrary test data set sample. The model-suggested design is [ ${HfO}_{2} - 124 nm$ , ${SiO}_{2} - 130 nm$ , W-10 nm, ${HfO}_{2} - 195 nm$ , ${SiO}_{2} - 119 nm$ , ${HfO}_{2} - 93 nm$ , W-10 nm, ${SiO}_{2} - 196 nm$ , W-20 nm, ${HfO}_{2} - 280 nm$ ]. (c) Comparison of idealized absorptivity spectrum (blue) and spectrum produced by the inverse design model (orange). The red dotted line denotes the transition wavelength $λ_{PV}$ for a PV cell with a bandgap of 0.55 eV. The inset figure shows the blackbody radiation curve at 1000°C (1273 K), with the same $λ_{PV}$ highlighted. The model suggested design is [ ${SiO}_{2} - 90 nm$ , ${HfO}_{2} - 54 nm$ , W-10 nm, ${SiO}_{2} - 251 nm$ , W-10 nm, ${SiO}_{2} - 97 nm$ , ${Al}_{2} O_{3} - 74 nm$ , ${HfO}_{2} - 105 nm$ , W-13 nm, ${SiO}_{2} - 163 nm$ ].