Time-temperature superposition from multi-temperature chirp rheometry of thermorheologically simple materials via physics-informed Gaussian processes

Abstract

Inferring constitutive laws from transient response data is a central inverse problem in soft condensed-matter physics, particularly when the relevant relaxation spectrum extends beyond the time window of a single experiment. Time-temperature superposition (TTS) constrains this problem for thermorheologically simple materials in the linear viscoelastic regime by allowing temperature to rescale the characteristic relaxation time without changing the underlying shape of the relaxation spectrum. We incorporate this constraint into a physics-informed machine-learning framework for time-resolved mechanical spectroscopy via chirp rheometry. We encode compact fractional viscoelastic models as causal convolutional features derived from the Boltzmann superposition principle, and we jointly fit multi-temperature chirp records using sparse variational Gaussian process regression. The model infers horizontal shift factors, constitutive parameters, and an observational-noise scale directly from time-domain stress-strain signals measured in the linear viscoelastic regime, without first extracting frequency-domain spectra or manually shifting separate curves. For synthetic Fractional Maxwell data, the method recovers the generating constitutive law from a prescribed model library and latent shifts over stress-noise levels from 3% to 25%. Applied to a DGEBA-IPDA epoxy dataset spanning the glass-transition regime, the pooled likelihood distinguishes competing fractional rheology models using the Bayesian information criterion. These results recast TTS master-curve construction as probabilistic inference over latent time rescaling and linear viscoelasticity, while also identifying limitations, such as homoscedastic noise and weakly informative spectral regimes.