# Accurate Inverse Design of Broadband Solar Metamaterial Absorbers via Joint Forward–Inverse Deep Learning

## TL;DR

This paper introduces a deep learning framework that enables efficient design of solar absorbers with high efficiency and broadband performance.

## Contribution

A joint forward–inverse deep learning framework is proposed to reduce ambiguity and improve accuracy in inverse design of solar metamaterials.

## Key findings

- The framework achieved 97.4% average absorptivity across the solar spectrum with polarization insensitivity.
- Outdoor tests showed a peak temperature of 86.3 °C under natural sunlight with 850 W/m2 irradiance.
- Normalized test mean squared errors were 7.2 × 10−5 (inverse) and 6.8 × 10−5 (forward).

## Abstract

The design of broadband, high-efficiency solar absorbers remains challenging due to the complex and ill-posed inverse mapping from the target optical responses to the physical structures in inverse design optimization. To address this, we propose a joint forward–inverse deep learning framework that enables the rapid and accurate optimization of multilayer metamaterial absorbers. This method integrates an inverse network based on a Modified Swin Transformer with a Multilayer Perceptron forward proxy and performs end-to-end training in a consistency-driven cycle. This strategy reduces the one-to-many ambiguity in inverse design and improves the prediction accuracy, with normalized test mean squared errors of 7.2 × 10−5 (inverse) and 6.8 × 10−5 (forward). Using this framework, we optimized an absorber comprising W/SiO2 hyperbolic metamaterial stacks and TiO2/SiO2 anti-reflection coatings, achieving 97.4% average absorptivity across the 400–1750 nm solar spectrum, along with polarization insensitivity and robust wide-angle performance up to 60° incidence. The outdoor solar heating tests showed that the fabricated absorber reaches a peak temperature of 86.3 °C under natural sunlight, with an irradiance peak of about 850 W/m2 at noon. This work shows that combining forward and reverse deep learning provides a powerful and scalable paradigm for accelerating the intelligent design of high-performance solar thermal metamaterials.