Dataset and Pre-trained Models for Predicting Antiferroelectric Hysteresis using a Recurrent Multigrid Neural Operator

Multigrid Neural Operator (MgNO) for Antiferroelectric Hysteresis This repository contains the replication dataset, pre-trained models, and evaluation code for predicting hysteresis loops in antiferroelectric materials using a physics-informed recurrent MgNO. The dataset consists of high-fidelity phase-field simulations of polarization dynamics under varying energy barriers. To analyze the data, the gradient energy coefficient $f$ is parameterized using a scalar multiplier $x$ (ranging from 0.5 to 6.0). The simulation data models the polarization dynamics under varying energy barriers. To easily analyze the data, we parameterize the gradient energy coefficient $f$ using a scalar multiplier $x$: $f = x \times \left(1.75 \times 10^7 \, a_c^2 \, \text{J m}^{-3} \right)$. In our dataset, only the multiplier $x$ is varied. The .h5 files are named according to their specific $x$ value (e.g., results_hysteresis_x_4.0000...). For complete details on the underlying phase-field model, the governing thermodynamic equations, and the numerical implementation used to generate this dataset, please refer to our related publication: Dilshod Durdiev & Bai-Xiang Xu. (2026). Computational Materials Science. 10.1016/j.commatsci.2026.114684 The provided MgNO models demonstrate the ability to rapidly predict complex antiferroelectric hysteresis curves at standard resolutions (128x128). Furthermore, the repository includes datasets and inference scripts demonstrating the model's zero-shot generalization capabilities, accurately scaling predictions up to 1024x1024 resolutions without retraining. Structure ├── data/ │ ├── training/ │ └── zeroshot/ │ ├── 256x256/ │ ├── 512x512/ │ └── 1024x1024/ ├── src/ │ ├── data.py │ ├── utils.py │ ├── MgNO.pyc │ └── model.pyc ├── trained_models/ │ ├── model_layer1.pt │ ├── model_layer2.pt │ ├── model_layer3.pt │ ├── model_layer4_MSE.pt │ ├── model_layer4_MSE_h1h2.pt │ └── model_layer4.pt └── evaluate_models.py Pre-trained models We provide several variations of the MgNO model to demonstrate the impact of V-cycle MgNO layers and physics-informed loss functions. model_layer4.pt is the best-performing model trained with our complete physics-informed loss (MSE + H1 + H2 + Energy constraints). model_layer4_MSE.pt is trained as purely data-driven using only MSE. model_layer1.pt through model_layer3.pt are provided for ablation studies on layers. Technical requirement The core model architectures (MgNO.pyc and model.pyc) have been provided as compiled Python bytecode to guarantee exact numerical reproducibility matching the original study. Because of this, you must use Python 3.12 to run this code. Required libraries: pip install torch numpy matplotlib h5py tqdm You can run the full evaluation suite by executing: python evaluate_models.py What the script does: Standard Evaluation (128x128) Iterates through all 6 pre-trained models. Evaluates them across the 22 varying physics parameters ($x = 0.5$ to $6.0$). Calculates the global macroscopic $R^2$ scores. Generates and saves split hysteresis plots in respective replots_hysteresis_<model_name>/ directories. Zero-Shot Generalization Automatically selects the best model (model_layer4.pt). Evaluates it dynamically on the high-resolution datasets (256x256, 512x512, 1024x1024) for $x = 4.0$. Automatically performs spatial interpolation on the network's normalization layers to handle the scale shift. Saves the high-resolution predictions in the replots_zeroshot/ directory.