Improved Dimensionality Reduction for Inverse Problems in Nuclear Fusion and High-Energy Astrophysics

TL;DR

This paper proposes a hybrid method combining formal verification and advanced dimensionality reduction to improve the physical validity of inverse problem solutions in nuclear fusion and astrophysics.

Contribution

It introduces a novel approach that integrates formal verification with non-linear dimensionality reduction to ensure physically consistent parameter spaces.

Findings

Enhanced parameter space restrictions with mathematical guarantees

Reduced computational complexity in inverse problem solving

Maintained physical and experimental uncertainty considerations

Abstract

Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional parameter scans and large ensembles of simulations to be performed. Such inverse problems typically involve large uncertainties, both in the measurement parameters being inverted and in the underlying physics models themselves. Monte Carlo sampling, when combined with modern non-linear dimensionality reduction techniques such as autoencoders and manifold learning, can be used to reduce the size of the parameter spaces considerably. However, there is no guarantee that the resulting combinations of parameters will be physically valid, or even mathematically consistent. In this position paper, we advocate adopting a hybrid approach that leverages our recent advances in the development of formal verification methods for numerical algorithms, with the goal of constructing parameter space restrictions with provable mathematical and physical correctness properties, whilst nevertheless respecting both experimental uncertainties and uncertainties in the underlying physical processes.