# Uncertainty-Aware Mixed-Variable Machine Learning for Materials Design

arXiv: https://arxiv.org/abs/2207.04994 · HTML: https://mlsanity.com/paper/2207.04994/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 57 references that are in the map.
- First posted on arXiv 11 Jul 2022.

## Builds on (most cited first, 14 of 14)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables](https://mlsanity.com/paper/1910.01688/) (2019)
- [Uncertainty Quantification Using Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2005.10036/) (2020)
- [Uncertainty in Gradient Boosting via Ensembles](https://mlsanity.com/paper/2006.10562/) (2020)
- [Benchmarking the Performance of Bayesian Optimization across Multiple Experimental Materials Science Domains](https://mlsanity.com/paper/2106.01309/) (2021)
- [Challenges in Markov chain Monte Carlo for Bayesian neural networks](https://mlsanity.com/paper/1910.06539/) (2019)
- [Aleatoric and Epistemic Uncertainty with Random Forests](https://mlsanity.com/paper/2001.00893/) (2020)
- [JANUS: Parallel Tempered Genetic Algorithm Guided by Deep Neural Networks for Inverse Molecular Design](https://mlsanity.com/paper/2106.04011/) (2021)
- [A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors](https://mlsanity.com/paper/1806.07504/) (2018)
- [Gryffin: An algorithm for Bayesian optimization of categorical variables informed by expert knowledge](https://mlsanity.com/paper/2003.12127/) (2020)
- [High-Dimensional Materials and Process Optimization using Data-driven Experimental Design with Well-Calibrated Uncertainty Estimates](https://mlsanity.com/paper/1704.07423/) (2017)
- [Scalable Gaussian Processes for Data-Driven Design using Big Data with Categorical Factors](https://mlsanity.com/paper/2106.15356/) (2021)
- [Uncertainty Prediction for Machine Learning Models of Material Properties](https://mlsanity.com/paper/2107.07997/) (2021)

## Built on by (most cited first, 6 of 6)

- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [Rapid Design of Top-Performing Metal-Organic Frameworks with Qualitative Representations of Building Blocks](https://mlsanity.com/paper/2302.09184/) (2023)
- [Towards Reliable Uncertainty Quantification via Deep Ensembles in Multi-output Regression Task](https://mlsanity.com/paper/2303.16210/) (2023)
- [Emerging Microelectronic Materials by Design: Navigating Combinatorial Design Space with Scarce and Dispersed Data](https://mlsanity.com/paper/2412.17283/) (2024)
- [RAG: A Random-Forest-Based Generative Design Framework for Uncertainty-Aware Design of Metamaterials with Complex Functional Response Requirements](https://mlsanity.com/paper/2601.13233/) (2026)
- [LEAP: A closed-loop framework for perovskite precursor additive discovery](https://mlsanity.com/paper/2605.20242/) (2026)

## Abstract (arXiv)

Data-driven design shows the promise of accelerating materials discovery but is challenging due to the prohibitive cost of searching the vast design space of chemistry, structure, and synthesis methods. Bayesian Optimization (BO) employs uncertainty-aware machine learning models to select promising designs to evaluate, hence reducing the cost. However, BO with mixed numerical and categorical variables, which is of particular interest in materials design, has not been well studied. In this work, we survey frequentist and Bayesian approaches to uncertainty quantification of machine learning with mixed variables. We then conduct a systematic comparative study of their performances in BO using a popular representative model from each group, the random forest-based Lolo model (frequentist) and the latent variable Gaussian process model (Bayesian). We examine the efficacy of the two models in the optimization of mathematical functions, as well as properties of structural and functional materials, where we observe performance differences as related to problem dimensionality and complexity. By investigating the machine learning models' predictive and uncertainty estimation capabilities, we provide interpretations of the observed performance differences. Our results provide practical guidance on choosing between frequentist and Bayesian uncertainty-aware machine learning models for mixed-variable BO in materials design.