# Density Estimation Based on Mixtures of Gaussians for Perovskite Solar Cells Modeling

## TL;DR

This paper introduces a probabilistic modeling approach using Gaussian Mixture Models to improve the design and optimization of perovskite solar cells.

## Contribution

The novel contribution is a GMM-Assisted Optimization method that improves inverse design of solar cell synthesis conditions.

## Key findings

- GMM-Assisted Optimization achieves an RMSE of 1.52 for predicting target power conversion efficiencies.
- The method outperforms standard random-start optimization by more than halving the RMSE.
- GMMs are shown to be effective for tasks like clustering, regression, and inverse design in perovskite solar cell research.

## Abstract

Accurately modeling
the complex relationships among synthesis parameters,
material compositions, and performance metrics is essential for accelerating
the development of perovskite solar cells (PSCs). In this context,
machine learning (ML) has proven to be a valuable tool. While most
ML applications in PSC research rely on discriminative “black-box”
models, this study adopts a generative approach by modeling the joint
probability density function. We employ Gaussian Mixture Models (GMMs),
a pragmatic and interpretable choice well-suited for the scarce, low-dimensional
tabular data typical of PSC research. This single GMM framework is
evaluated on five distinct tasks: discovering clusters, regression,
generating novel configurations, training on data sets with missing
data and, inverse design of the experimental (synthesis) conditions.
That is, assuming we have the perovskite material composition and
a target PCE, we infer the experimental conditions. For this latter
task we use a novel “GMM-Assisted Optimization” method,
which demonstrates to be more effective than standard random-start
optimization, achieving an RMSE of 1.52 against target PCEs, more
than halving the 3.32 RMSE of the baseline. These findings highlight
the power of probabilistic modeling for data-driven discovery in PSC
research.