[Paper Review] Deflation Techniques for Stellarator Equilibrium and Optimization

Dario Panici, Byoungchan Jang+4 more|arXiv (Cornell University)|Feb 10, 2026

Spacecraft Dynamics and Control0 citations

TL;DR

The paper introduces deflation methods to explore the non-convex, multi-objective stellarator optimization landscape, enabling discovery of distinct equilibria and coil designs from a single initial guess. It demonstrates that deflation yields multiple high-quality, physically distinct solutions in both equilibrium and optimization stages.

ABSTRACT

Stellarator optimization is a multi-objective, non-convex problem characterized by a complex objective landscape containing many local minima. The solution resulting from a single optimization is highly sensitive to factors such as the initial guess, objective weights, and the optimization method employed. However, merely varying these factors does not guarantee that a physically distinct minimum will be found; optimizations often fail to converge to good minima or simply return to the same or very similar local minima despite large-scale parameter scans. This paper presents a novel application of deflation methods to effectively explore this landscape. By modifying the objective function to penalize and "deflate" away already-found solutions, this technique encourages the optimizer towards attractive, distinct new minima while using a single initial guess and optimization setup. We provide a primer on deflation for nonlinear systems and non-convex optimization before applying it to non-axisymmetric equilibrium and stellarator optimization problems. Key results include the discovery of families of global equilibria with similar core characteristics and the convergence to helical core equilibria without prescient initial guesses. Furthermore, we demonstrate that augmenting stage-one stellarator and stage-two coil optimization with deflation constraints readily produces multiple high-quality, distinct solutions, establishing the method's efficacy and ease of use.

Motivation & Objective

• Motivate and address the challenge of discovering physically distinct minima in stellarator optimization.
• Introduce deflation as a method to penalize already-found solutions and encourage new minima.
• Demonstrate the applicability of deflation to non-axisymmetric equilibrium and coil optimization problems.

Proposed method

• Provide a primer on deflation for nonlinear systems and non-convex optimization.
• Apply deflation to non-axisymmetric stellarator equilibrium problems to uncover diverse core characteristics.
• Apply deflation to stage-one stellarator optimization and stage-two coil optimization to generate multiple high-quality, distinct solutions.
• Show that deflation constraints can augment existing optimization pipelines with minimal changes to initial setup.

Experimental results

Research questions

• RQ1 Can deflation systematically drive the optimizer toward new, distinct equilibria in stellarator problems?
• RQ2 Does deflation enable discovery of global- and near-global minima that are not found by standard optimization runs?
• RQ3 How does deflation interact with stage-one equilibrium and stage-two coil optimization in producing multiple viable designs?
• RQ4 What are the characteristics of equilibria found using deflation in terms of core structure and helicity?

Key findings

• Deflation enables discovery of families of global equilibria with similar core characteristics.
• Deflation leads to convergence to helical core equilibria without prescient initial guesses.
• Augmenting stage-one and stage-two optimization with deflation constraints yields multiple high-quality, distinct solutions.
• The method is effective and easy to use within existing optimization workflows.