Physics-Informed Neural Networks (PINN) for Floating Elastic Plates on Viscoelastic Foundations

This repository contains the official PyTorch implementation and neural network weights for reproducing the Physics-Informed Neural Network (PINN) and Deep Learning surrogate models described in the 2026 paper published in Applied Mathematics and Computation. 

 

📄 Associated Publication

If you find this computational framework useful, please cite the primary research paper: 

Boral, S. (2026). Dynamic response of a floating elastic plate supported on a viscoelastic foundation under moving periodic load: Analytical and neural modelling. Applied Mathematics and Computation, Volume 516, Article 129872. Digital Object Identifier (DOI): https://doi.org/10.1016/j.amc.2025.129872 

bibtex

@article{boral2026dynamic, title={Dynamic response of a floating elastic plate supported on a viscoelastic foundation under moving periodic load: Analytical and neural modelling}, author={Boral, Susam}, journal={Applied Mathematics and Computation}, volume={516}, pages={129872}, year={2026}, publisher={Elsevier}, doi={10.1016/j.amc.2025.129872}, url={https://doi.org/10.1016/j.amc.2025.129872} }

Use code with caution.

📌 Executive Summary & Key AI Keywords

This project fuses Scientific Machine Learning (SciML) with traditional ocean engineering and fluid-structure interactions (FSI). It replaces slow numerical differential equation solvers with rapid, high-accuracy neural network surrogates. 

• Core Methodologies: Physics-Informed Neural Networks (PINNs), Multilayer Perceptrons (MLP), Dispersion Model Mapping, Sine Activation Networks.
• Physical Domain: Hydroelasticity, wave propagation, flexural-gravity waves, moving periodic loads, Kelvin-Voigt/Maxwell viscoelastic foundations.
• Target Applications: Arctic ice sheet-structure interaction, runway designs on floating platforms, offshore engineering, floating airports, and wave energy converter arrays.

📂 Repository Architecture & File Manifest

• 📁 best_sine_pinn_model.pth — Pre-trained network weights for the PINN solver using sine activation functions.
• 📁 trained_dispersion_model.pth — Trained surrogate network mapping the hydroelastic dispersion relationship.
• 📁 X_norm.npy, Y_norm.npy — Standardized validation and testing tensors for benchmark evaluation.
• 📁 pinn_X_norm.npy, pinn_y_norm.npy — Pre-processed spatial-temporal data constraints for physics-based loss functions.

🚀 Execution & Quick Start Guide

Prerequisites & Dependencies

Install the required computational mathematics and machine learning libraries: 

bash

pip install torch numpy matplotlib scipy

Use code with caution.

Loading Pre-trained Models

You can load the neural network models into your PyTorch pipeline directly using the snippet below: 

python

import torch

Load the dispersion relationship neural surrogate

dispersion_model = torch.load('trained_dispersion_model.pth') dispersion_model.eval()

Load the PINN model for floating elastic plate dynamics

pinn_model = torch.load('best_sine_pinn_model.pth') pinn_model.eval()

print("Neural network weights successfully initialized.")

Use code with caution.

📊 Core Scientific Contributions

1. Elimination of Computational Bottlenecks: Shows how neural network surrogates cut down CPU compute times for moving-load wave equations from hours to fractions of a second.
2. Viscoelastic Foundation Mapping: Accurately tracks damping and subgrade drag variations without numerical stability failures.
3. Resonance Boundary Capture: Predicts quasi-resonance structural limits under critical velocities with low mean squared error (MSE).

🤝 Contact and Global Collaboration

Dr. Susam Boral Research Fellow, Trinity College Dublin 📧 Academic Inquiries: susamboral@gmail.com / borals@tcd.ie 🌐 Research Profile: Google Scholar Profile