Kavli Affiliate: Tim H. Taminiau
| First 5 Authors: Abigail N. Poteshman, Abigail N. Poteshman, , ,
| Summary:
High-throughput characterization often requires estimating parameters and
model dimension from experimental data of limited quantity and quality. Such
data may result in an ill-posed inverse problem, where multiple sets of
parameters and model dimensions are consistent with available data. This
ill-posed regime may render traditional machine learning and deterministic
methods unreliable or intractable, particularly in high-dimensional, nonlinear,
and mixed continuous and discrete parameter spaces. To address these
challenges, we present a Bayesian framework that hybridizes several Markov
chain Monte Carlo (MCMC) sampling techniques to estimate both parameters and
model dimension from sparse, noisy data. By integrating sampling for mixed
continuous and discrete parameter spaces, reversible-jump MCMC to estimate
model dimension, and parallel tempering to accelerate exploration of complex
posteriors, our approach enables principled parameter estimation and model
selection in data-limited regimes. We apply our framework to a specific
ill-posed problem in quantum information science: recovering the locations and
hyperfine couplings of nuclear spins surrounding a spin-defect in a
semiconductor from sparse, noisy coherence data. We show that a hybridized MCMC
method can recover meaningful posterior distributions over physical parameters
using an order of magnitude less data than existing approaches, and we validate
our results on experimental measurements. More generally, our work provides a
flexible, extensible strategy for solving a broad class of ill-posed inverse
problems under realistic experimental constraints.
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