PearSAN: A Machine Learning Method for Inverse Design using Pearson Correlated Surrogate Annealing

TL;DR

PearSON Correlated Surrogate Annealing (PearSAN) tackles inverse design in high-dimensional metasurface problems by combining a discretized latent space from a pretrained generator with a surrogate objective trained via a Pearson correlation-based loss (PearSOL). The framework uses variational neural annealing (VCA) to sample latent vectors in a way that is antitonic to the true figure-of-merit (FOM), enabling efficient discovery of high-performance designs without retraining the outer decoder. Empirically, PearSAN outperforms energy-matching surrogates and prior ML-based or topology-optimization methods, achieving a maximum design efficiency around 97% and orders-of-magnitude faster sample generation for TPV emitter metasurface designs. The approach is generalizable to any pretrained discretized latent-space generator and offers substantial speedups and design-quality gains for complex, physics-constrained inverse design tasks, with potential extensions to other energy models and continuous latent spaces.

Abstract

PearSAN is a machine learning-assisted optimization algorithm applicable to inverse design problems with large design spaces, where traditional optimizers struggle. The algorithm leverages the latent space of a generative model for rapid sampling and employs a Pearson correlated surrogate model to predict the figure of merit of the true design metric. As a showcase example, PearSAN is applied to thermophotovoltaic (TPV) metasurface design by matching the working bands between a thermal radiator and a photovoltaic cell. PearSAN can work with any pretrained generative model with a discretized latent space, making it easy to integrate with VQ-VAEs and binary autoencoders. Its novel Pearson correlational loss can be used as both a latent regularization method, similar to batch and layer normalization, and as a surrogate training loss. We compare both to previous energy matching losses, which are shown to enforce poor regularization and performance, even with upgraded affine parameters. PearSAN achieves a state-of-the-art maximum design efficiency of 97%, and is at least an order of magnitude faster than previous methods, with an improved maximum figure-of-merit gain.

Figures (4)

• Figure 1: Thermophotovoltaic system: The TPV system considered in our showcase problem corresponds to the samples $D_{\theta}(\bm{z})$ generated by the pretrained decoder and consists of a thermal emitter and PV cell. The thermal emitter converts thermal energy into photons, and the PV cell generates electricity from these photons within a specific wavelength range (working band: 0.5-$1.7\,\mu\text{m}$, gray area in spectrum subfigure). Each thermal emitter consists of 3 layers: a $120$ nm titanium nitride plasmonic antenna, a $30$ nm silicon nitride spacer, and a $280$ nm titanium nitride back reflector, as shown in the 3D cross-section. Each unit cell is a $280$ nm $\times$$280$ nm square. The topology of the titanium nitride layer determines the shape of the absorption spectrum, whose near-full absorption range ideally falls solely within the working band of the PV cell. The generated thermal emitter design efficiencies are assessed using a regression-model-based Visual Geometry Group Net (VGGNet) during training and via FDTD simulation after sampling.
• Figure 2: PearSAN starts with an initial dataset $Z^{(0)}$. The generated polynomial $h_{\phi^{(\tau)}}(\bm{z})$ is then used in variational neural annealing to train the sampler $q_{\phi^{(\tau)}}(\bm{z})$ by minimizing its free energy $F_{\phi^{(\tau)}}(t)$. The resultant latent vectors $\hat{\bm{z}}$ are then stored in a database. The sampler is then evaluated through the pretrained decoder, which generates real samples $D_{\theta}(\hat{\bm{z}})$. The samples' efficiency is computed using a direct solver, as indicated by the grey area between the ideal and resultant spectra. The efficiency $f(D_{\theta}(\hat{\bm{z}}))$, along with its corresponding sample, are also stored in the database. The Pearson correlation loss is informed through the database, which constitutes an antitonic correlation between $h_{\phi^{(\tau)}}(\bm{z})$ and $f(D_{\theta}(\hat{\bm{z}}))$. The resulting loss value from PearSOL is used to update the surrogate model parameters in the next iteration $\phi^{(\tau + 1)}$, and the process is repeated.
• Figure 3: Retraining performance for PearSOL and EM: (a) Average sampled FOM over 10 retraining iterations, (b) FOM histogram of all decoded vectors from the last iteration, (c) Comparison of FOM between vectors generated by PearSAN and the original dataset (unnormalized VGGNet FOM), (d) Regularization performance of PearSAN versus EM, comparing sampling performance of one binary autoencoder trained with PearSOL vs. one with EM. Bootstrapped confidence intervals are calculated with 10,000 samples agarwal2021deep. We use PearSOL for sampling, but each decoder is separately trained with either an additional PearSOL or EM term.
• Figure 4: Spectra Comparison of different optimization methods PearSAN consistently stays within high values of absorption. NOTE: Sub-figures (a), (b), (c) adapted with permission from kudyshev_machine-learning-assisted_2020 and wilson_machine_2021 respectively.