# Bayesian Optimisation under State-Preservation Constraints

arXiv: https://arxiv.org/abs/2610.12150 · HTML: https://mlsanity.com/paper/2610.12150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 44 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 1 of 1)

- [We Still Don't Understand High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2512.00170/) (2025)

## Abstract (arXiv)

In many engineering design problems, the objective and constraints depend on the state: the solution of a PDE determined by the design parameters. We consider improving a design while holding selected state observables near trusted values, which we call state preservation constraints. Constrained Bayesian optimisation handles these with a learnt feasibility model, but struggles with this problem's highly anisotropic feasible set. Our central idea is to pre-compute the set of controls whose linearised constraint response stays within tolerance, thereby pulling back the state-space constraint into design space. This linearisation defines an ellipsoid from which we can efficiently draw a large number of well-spread candidates. The underlying linear response map is refined online, and the ellipsoid is rebuilt accordingly. We demonstrate the method end-to-end on our key application - Tokamak divertor optimisation under plasma-boundary preservation.