Physics-informed AI framework for multiscale design, discovery, and optimization of polymer nanocomposite microstructures using neural operators.

Polymer nanocomposites exhibit highly nonlinear viscoelastic behavior influenced by complex multiscale microstructural interactions between nanofillers and the polymer matrix. Existing data-driven models such as ANN, RNN, GRU, and LightGBM show limitations in capturing spatial-temporal operator dynamics, interfacial energetics, and frequency-dependent mechanical responses. These models often rely on local approximations, struggle with generalization beyond training distributions, and lack the ability to generate optimized microstructures. To address these limitations, this study develops a Hierarchical Neural Operator-Based Multiscale Learning Framework for accurate nonlinear viscoelastic response prediction and microstructure optimization in polymer nanocomposites. The proposed framework aims to establish a physics-aware data-driven pipeline capable of predicting stress-strain behavior, storage modulus G' (Pa), relaxation times τ (s), and glass-transition shift ΔTg​, while simultaneously identifying optimal microstructures. The methodology integrates a Fourier Neural Operator (FNO) surrogate for learning continuous mechanical response operators, a Convolutional Variational Autoencoder (CVAE) for generative microstructure latent representation, and a Physics-Guided Multi-Stage Atom Search Optimization (PG-MS-ASO) module for constrained microstructure design. Python, NumPy, scikit-learn, PyTorch, and Matplotlib form the computational toolset. Key findings indicate strong predictive accuracy, with the hierarchical model achieving RMSE = 0.15, MAE = 0.10, and R² = 0.98, outperforming RNN (R² = 0.92), ANN (R² = 0.91), GRU (R² = 0.97), and SNS-LightGBM (R² = 0.97). Optimized microstructures generated through CVAE + PG-MS-ASO exhibit significant improvements in performance metrics, with ΔTg reaching up to 31 °C and storage modulus (G') exceeding 1.09 × 10