# Bayesian Optimization of Partially Known Systems using Hybrid Models

arXiv: https://arxiv.org/abs/2603.11199 · HTML: https://mlsanity.com/paper/2603.11199/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 40 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 13 of 13)

- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Bayesian Optimization of Composite Functions](https://mlsanity.com/paper/1906.01537/) (2019)
- [Bayesian Optimization of Function Networks](https://mlsanity.com/paper/2112.15311/) (2021)
- [COBALT: COnstrained Bayesian optimizAtion of computationaLly expensive grey-box models exploiting derivaTive information](https://mlsanity.com/paper/2105.04114/) (2021)
- [Combining Multi-Fidelity Modelling and Asynchronous Batch Bayesian Optimization](https://mlsanity.com/paper/2211.06149/) (2022)
- [Bayesian optimization as a flexible and efficient design framework for sustainable process systems](https://mlsanity.com/paper/2401.16373/) (2024)
- [Global Optimization of Gaussian processes](https://mlsanity.com/paper/2005.10902/) (2020)
- [Chance Constrained Policy Optimization for Process Control and Optimization](https://mlsanity.com/paper/2008.00030/) (2020)
- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)
- [On the Implementation of a Bayesian Optimization Framework for Interconnected Systems](https://mlsanity.com/paper/2501.00967/) (2025)
- [BONSAI: Structure-exploiting robust Bayesian optimization for networked black-box systems under uncertainty](https://mlsanity.com/paper/2510.03893/) (2025)
- [BOIS: Bayesian Optimization of Interconnected Systems](https://mlsanity.com/paper/2311.11254/) (2023)

## Abstract (arXiv)

Bayesian optimization (BO) has gained attention as an efficient algorithm for black-box optimization of expensive-to-evaluate systems, where the BO algorithm iteratively queries the system and suggests new trials based on a probabilistic model fitted to previous samples. Still, the standard BO loop may require a prohibitively large number of experiments to converge to the optimum, especially for high-dimensional and nonlinear systems. We present a hybrid model-based BO formulation that combines the iterative Bayesian learning of BO with partially known mechanistic physical models. Instead of learning a direct mapping from inputs to the objective, we write all known equations for a physics-based model and infer expressions for variables missing equations using a probabilistic model, in our case, a Gaussian process (GP). The final formulation then includes the GP as a constraint in the hybrid model, thereby allowing other physics-based nonlinear and implicit model constraints. This hybrid model formulation yields a constrained, nonlinear stochastic program, which we discretize using the sample-average approximation. In an in-silico optimization of a single-stage distillation, the hybrid BO model based on mass conservation laws yields significantly better designs than a standard BO loop. Furthermore, the hybrid model converges in as few as one iteration, depending on the initial samples, whereas, the standard BO does not converge within 25 for any of the seeds. Overall, the proposed hybrid BO scheme presents a promising optimization method for partially known systems, leveraging the strengths of both mechanistic modeling and data-driven optimization.