Neural Enhancement of Schapery-Prony Viscoelastic Model

Abstract

Offshore renewable energy deployment faces a fundamental materials challenge: synthetic fibre mooring lines offer an 8-fold weight reduction and tension reduction compared to steel chains, yet their certification requires predicting 20-year operational behaviour from necessarily limited experimental observations. Current approaches employ polynomial functions to represent stress-dependent material behaviour within established viscoelastic frameworks. Still, these rigid mathematical forms constrain material characterisation by forcing complex behaviour into predetermined equations rather than discovering true material physics. This research develops a neural-physics integration framework that replaces polynomial constraints with adaptive neural networks whilst preserving established Schapery-Prony physics principles. The core innovation employs functional decomposition, where neural networks learn stress-dependent nonlinearity functions (g0, g1, g2), while the proven Schapery-Prony framework handles temporal evolution, enabling the discovery of true material behaviour rather than mathematical fitting to predetermined forms.

A systematic five-phase methodology guides development from baseline optimisation through operational validation. Phase 1 employs 13-dimensional Latin Hypercube Sampling across neural architecture, training protocols, and physics parameters. Phase 2 sensitivity analysis identifies optimal methodological choices: Percentage Difference loss functions for scale-invariant learning, Multiple-Steps loading patterns for comprehensive material exercising, and enhanced relaxation spectra for improved temporal coverage. Phase 3 capability testing reveals model limitations through progressive validation scenarios. Phase 4 diagnostic analysis identifies physics model resolution as the primary constraint, leading to targeted improvement from 10 to 14 relaxation terms that address slow relaxation modes critical for long-term accuracy. Phase 5 validates robustness under realistic marine loading using industry-standard JONSWAP wave spectra. The implementation employs a shared-head neural architecture with shared backbone layers (3 layers, 96 neurons) feeding specialised heads (2 layers, 128 neurons each) for individual nonlinearity function learning. Two-stage training coordinates neural network and physics parameter optimisation through differential learning rates whilst maintaining physical consistency. The twin experiment methodology leverages validated HDPE material parameters to generate unlimited synthetic training data spanning stress ranges and loading patterns that are impossible to achieve through physical experimentation alone.Results demonstrate that the neural enhancement approach enables reliable material characterisation from limited experimental data. Temporal validation achieves 85-95% accuracy across 128-fold duration scaling, enabling decades-long predictions from short-term training data, following established principles for temporal extrapolation in physics-inspired neural networks. Marine validation under realistic JONSWAP loading conditions achieves 5.7-13.2% error across diverse sea states spanning significant wave heights 1.5-7.0m and peak periods 8-15s, demonstrating robustness comparable to validated approaches for viscoelastic modelling under complex loading conditions. The diagnostic insight that physics model completeness rather than neural network architectural sophistication determines model capability guides efficient improvement strategies applicable across computational materials science domains. The validated framework transforms synthetic fibre characterisation from an experimental constraint to a predictive capability, while establishing reproducible principles for neural physics integration across materials science applications that require improved understanding from limited observations. This enables accelerated deployment of offshore renewable energy systems whilst preserving the physical foundations necessary for reliable engineering applications.

Keywords: Neural-physics integration, Synthetic fibre characterisation, Nonlinear viscoelasticity, Schapery theory, Materials discovery, Offshore renewable energy, Computational materials science