Problem
Research questions and friction points this paper is trying to address.
Bayesian optimisation
state-preservation constraints
engineering design
anisotropic feasible set
Tokamak divertor optimisation
Bayesian Optimisation under State-Preservation Constraints
🤖 AI Summary
This study addresses the challenge that PDE state constraints in engineering design induce highly anisotropic feasible regions, rendering traditional Bayesian optimization inefficient. To overcome this, we propose linearly mapping state-space constraints into the design space and constructing ellipsoids to generate diverse candidate points while updating surrogate models online. Furthermore, we introduce precomputed control sets and a dynamic ellipsoid reconstruction strategy to effectively mitigate anisotropic sampling bottlenecks. The proposed method is validated end-to-end on tokamak divertor design, where it significantly enhances performance while maintaining plasma boundary states. This work establishes an efficient Bayesian optimization paradigm for engineering design problems governed by complex PDE constraints.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Bayesian Optimisation
State-Preservation Constraints
Ellipsoidal Candidate Sampling
Online Refinement
Tokamak Divertor Optimisation
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