Navigating Small Datasets with Machine Learning: Gaussian Process Modeling for Colloidal Gelation.

Area of Science:

• Materials Science
• Chemical Engineering
• Computational Science

Background:

• Machine learning methods often require large datasets, posing challenges for scientific disciplines with limited data.
• Gaussian Processes (GPs) are powerful probabilistic models adept at handling small datasets and providing uncertainty quantification.

Purpose of the Study:

• To develop a data-driven framework using GPs for modeling and inference in scenarios with limited experimental data.
• To explore the application of single-output and multi-output GPs for mapping synthesis parameters to colloidal sol-gel transition characteristics.
• To establish a Bayesian framework for inverse problems, enabling the discovery of synthesis pathways for desired material properties.

Main Methods:

• Utilized Gaussian Processes (GPs) with single-output and multi-output structures to model the relationship between synthesis parameters and gelation characteristics.
• Implemented a Bayesian framework integrating GP models with Markov Chain Monte Carlo (MCMC) sampling to solve inverse problems.
• Applied the methodology to the spontaneous colloidal sol-gel transition as a case study.

Main Results:

• Both single-output and multi-output GP structures successfully modeled the input-output relationships quantitatively.
• Multi-output GPs demonstrated superior uncertainty calibration by simultaneously learning correlations between different output variables.
• The Bayesian GP framework successfully identified multiple synthesis pathways for achieving specific material properties.

Conclusions:

• The proposed GP-based framework offers a robust methodology for data-constrained modeling in materials science.
• This approach is particularly valuable for material design in the colloidal domain and other fields facing data limitations.
• The framework facilitates the discovery of novel synthesis routes by effectively handling uncertainty and inverse problems.