Objective Bayesian Model Selection for Multiphase Decomposition of Solid-State NMR Free Induction Decay Signals in Paper (Cellulose) Samples: A Differential Evolution and BIC-Based Framework

Decomposition of free induction decay (FID) signals from solid-state nuclear magnetic resonance (NMR) methods such as Solid Echo and Magic-Sandwich Echo (MSE) is a standard route to the phase composition of semicrystalline polymers and cellulose-based materials, including paper. In conventional practice this decomposition is subjective: the operator xes the number of phases and supplies initial guesses for local optimization algorithms such as LevenbergMarquardt, which invites over tting whenever super uous mathematical components are introduced merely to reduce the residual tting error at the expense of physical interpretability. We present an automated computational framework that removes this subjectivity by combining a global stochastic optimizer (di erential evolution) with the Bayesian Information Criterion (BIC) to give a statistically rigorous basis for choosing the dimensionality of a multiphase physical model. The algorithm is validated on a Solid Echo FID measured on a paper sample, and is shown to recover a physically consistent two-phase decomposition a rigid, dipolar-coupled crystalline cellulose fraction and a mobile amorphous fraction purely from the statistical evidence in the data. An open-source, interactive software implementation of the method is described.