Abstract Details
Abstracts
Author: Byoungchan Jang
Requested Type: Poster
Submitted: 2025-03-16 12:43:05
Co-authors: R. Colin, M. Landreman
Contact Info:
University of Maryland
3205 Georgia Ave
Washington, DC 20010
USA
Abstract Text:
Stellarator boundary optimization faces a fundamental numerical challenge: extreme disparity between low and high mode amplitudes creates an optimization landscape where direct full-spectrum approaches typically converge to poor local minima. Traditional methods address this through computationally expensive multi-step procedures where optimization begins with low Fourier modes before gradually incorporating higher modes. We present Exponential Spectral Scaling (ESS), a technique that applies a mode-dependent exponential scaling factor to each Fourier mode. Our primary implementation uses the L∞ norm to determine the scaling pattern, creating a square spectral decay profile that effectively reduces the dynamic range of optimization variables from 6-7 orders of magnitude to 2-3. We also explored L₁ and L₂ norms, which create diamond and circular decay patterns respectively, with the L∞ norm providing optimal results for most configurations. This normalization aligns with the natural spectral decay of physically meaningful configurations and enables direct single-step optimization with the full spectrum of boundary Fourier modes. When implemented within scipy's trust region reflection algorithm, ESS consistently achieves convergence to superior minima compared to Jacobian-based approaches, eliminating arbitrary staging decisions while reducing computation time by up to 5x in benchmark cases.
Characterization: 4.0
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