Machine Learning and Optimization Towards Improved Radiative Cooling Paints

Monte Carlo simulations are commonly used to determine the spectral response of particulate coatings, including radiative cooling paints. However, due to the high computational expense of the Monte Carlo method, combined with the large design space of spectrally selective coatings, accelerated simulations are highly desired to answer open questions. For example, many new materials are being utilized for ultra-white radiative cooling paints, but it is unknown if and when a particle size distribution over a single size is beneficial to enhancing solar reflectance. Furthermore, only a limited number of UV-resistant narrow-band absorption particles are utilized in colored radiative cooling paints, but material discovery is difficult due to the lack of available optical properties and limited simulation tools. In this Dissertation, we aim to develop accelerated simulation approaches with machine learning for research and design of spectrally selective particulate coatings, package these approaches in open-source codes that benefit the thermal science community, as well as to utilize these tools to construct new and improved radiative cooling paint designs.

We first demonstrate a general purpose fully connected neural network approach, trained with Monte Carlo simulations, to accurately predict the spectral response of single layer media while dramatically accelerating the computational speed. Monte Carlo simulations are first used to generate a training set with a wide range of optical properties covering dielectrics, semiconductors, and metals. The neural network is validated on a validation set with randomized optical properties, as well as nanoparticle medium examples including barium sulfate, aluminum, and silicon. The error in the spectral response predictions is within 1% which is sufficient for many applications, while the speedup is 1-3 orders of magnitude.

Although the plain neural network is effective for treating single layer particulate media, the curse of dimensionality brings severe challenges for multilayer media due to the struggle in generating enough training data for a plain neural network to properly capture the spectral response. Multilayer media are important for many types of coatings, as well as for biomedical, nuclear, and atmospheric modeling. To address this issue, we demonstrate a Recurrent Neural Network (RNN) trained on Monte Carlo simulations to greatly accelerate and accurately provide spectral response predictions of multi-layer media. The RNN architecture greatly outperforms a plain neural network on the same size dataset by solving the curse of dimensionality, keeping the number of inputs into the network constant for any number of layers. This is demonstrated with three case studies, including multi-layer tissue, radiative cooling paint, and atmospheric clouds, showing 1-2 orders of magnitude acceleration over Monte Carlo simulations while providing significantly less error than a plain neural network.

In order to provide these machine learning accelerated tools to the community, as well as to integrate all the simulation methods required to model particulate media into one convenient package, we developed FOS. FOS, which means light in Greek, is an open-source program for Fast Optical Spectrum calculations of particulate media including Mie theory, Monte Carlo simulations, parallel processing, and our pre-trained machine learning surrogate models. This program can accelerate optimization and high throughput design of optical properties of nanoparticle or nanocomposite media, such as radiative cooling paint and solar heating liquids, allowing for the discovery of new materials and designs. FOS also enables convenient modeling of lunar dust coatings, combustion particulates, and many other particulate systems.

With these tools, we aim to answer an open question regarding optimal particle size for radiative cooling paints. Previous works find that multiple nanoparticle sizes increase solar reflectance compared to a single particle size. In this study, we assess this finding by utilizing FOS to identify the optimum particle size combinations in BaSO4 and TiO2-acrylic radiative cooling paints. We have found that the optimal multiple particle sizes indeed outperform the optimal single size in TiO2 paint, but surprisingly underperform compared to the optimal single size in BaSO4 paint. This is due to the near constant refractive index of BaSO4 across the solar spectrum. Also, different particle size distributions yield similarly high solar reflectance as long as the average particle size is in the neighborhood of 300-600 nm. Considering that it is unfeasible to precisely manufacture a single particle size, we conclude that the true benefits of multiple particle sizes is that they enable cost effective manufacturing while preserving robust high performance.

Moreover, to maximize solar reflectance, radiative cooling paints are often white, however, colored paints are also necessary for aesthetic, anti-glare, and color-coding purposes. Here, we demonstrate single-layer green and blue colored radiative cooling paint with a 26.9 and 13.7 percentage point enhancement, respectively, over commercial paints of a similar color. The enhanced solar reflectance is achieved by increasing the UV and NIR reflectance through a narrow band absorption color pigment, a low absorption binder, and a high volume fraction of BaSO4 pigment. Additionally, accelerated UV weathering tests show this paint retains high UV-resistance. This is attributed to the use of inorganic pigment instead of dyes or organic pigment which are commonly used in colored radiative cooling paints. Field tests further confirm these results with our colored radiative cooling paints showing up to 6.3 °C (11.3 °F) and 3.2 °C (5.8 °F) lower temperatures than the commercial counterparts under direct sunlight. Overall, our work realizes single-layer, scalable, and cost effective colored radiative cooling paints that allow surfaces to stay cooler, thereby reducing energy demand for buildings, vehicles, and outdoor equipment while retaining high UV-resistance.