AI for Materials Science: Microstructure Simulation and Prediction Using Fourier Neural Operators

Microstructure evolution plays a critical role in determining the mechanical, thermal, electrical and functional properties of advanced materials. Traditional physics-based simulation methods, including phase-field modelling, help researchers understand processes such as grain growth, phase transformations and the development of complex material structures. However, repeated simulations can be computationally expensive, particularly when exploring multiple material conditions or predicting long-term evolution. This three-day hands-on workshop introduces participants to an integrated workflow combining phase-field simulation concepts with AI-based surrogate modelling using Fourier Neural Operators (FNOs). Participants will explore how microstructure simulation data can be prepared, processed and used to train a neural operator capable of predicting future states of a physical system. Using publicly accessible computational tools, open-source Python libraries and prepared simulation datasets, participants will work through a practical workflow covering microstructure visualization, dataset preparation, FNO model development, prediction and performance evaluation. The workshop is designed around browser-accessible computing wherever possible, without requiring paid software, proprietary datasets or physical laboratory access. Basic familiarity with Python and machine learning concepts is recommended.

To introduce participants to the integration of phase-field modelling and scientific machine learning for microstructure evolution, enabling them to understand physics-based simulation workflows and develop a foundational Fourier Neural Operator surrogate model for predicting future microstructure states using free, publicly accessible computational tools.

• Understand the fundamentals of microstructure evolution, grain growth and phase-field modelling.
• Explore the Allen–Cahn equation and its role in modelling interface-driven evolution.
• Visualize and interpret microstructure simulation data using Python-based tools.
• Prepare simulation datasets for supervised learning, including input-history and future-state construction.
• Understand the principles of neural operators and Fourier Neural Operators.
• Develop a foundational FNO model using PyTorch and the open-source NeuralOperator library.
• Train and evaluate a lightweight model using a prepared simulation dataset.
• Generate future-state predictions and compare them with reference simulation results.
• Understand prediction errors, autoregressive rollout and the limitations of AI-based surrogate models.
• Explore applications of neural operators in computational materials science and materials engineering.

Day 1: Phase-Field Modelling and Microstructure Simulation

• Focus: Understanding the physics and preparing simulation data.
• Introduction to microstructures, grain boundaries, grain growth and phase transformations. Fundamentals of phase-field modelling and the Allen–Cahn equation. Understanding the relationship between governing equations, simulation grids and evolving microstructures. Introduction to numerical simulation outputs and microstructure image sequences. Visualizing microstructure evolution using Python, NumPy and Matplotlib.
• Hands-on Session: Explore a prepared phase-field simulation dataset, visualize microstructure states at different time steps and identify patterns of grain growth and structural evolution.

Day 2: Simulation Data Preparation and Fourier Neural Operators

• Focus: Converting simulation outputs into AI-ready datasets.
• Organizing simulation data into training, validation and test sets. Constructing input-output pairs from previous and future microstructure states. Introduction to scientific machine learning, surrogate models and neural operators. Understanding Fourier transforms, spectral convolution and the basic FNO architecture. Exploring model inputs, outputs, tensor dimensions and training configuration.
• Hands-on Session: Prepare a small simulation dataset, inspect its spatial and temporal dimensions, and configure a lightweight Fourier Neural Operator using PyTorch and the open-source NeuralOperator library.

Day 3: FNO Training, Prediction and Model Evaluation

• Focus: Training an AI surrogate and evaluating its predictions.
• Training a lightweight FNO model using a prepared dataset. Understanding training and validation loss. Evaluating predictions using mean squared error and other appropriate error metrics. Visualizing predicted and reference microstructure states. Introducing autoregressive prediction and the accumulation of prediction errors. Comparing AI surrogate predictions with reference simulation outputs. Discussing generalization, computational limitations and research applications.
• Hands-on Session: Train or fine-tune a compact FNO model, predict a future microstructure state, visualize the result and evaluate its agreement with the reference data.

• Explain the fundamental principles of phase-field modelling and microstructure evolution.
• Interpret simulation outputs representing grain growth and evolving material structures.
• Prepare simulation data for machine learning and construct input-output training pairs.
• Describe how Fourier Neural Operators learn mappings between spatial fields.
• Configure and train a basic FNO model using PyTorch-based tools.
• Generate and visualize future-state microstructure predictions.
• Evaluate model performance using suitable quantitative metrics and visual comparisons.
• Explain the benefits and limitations of surrogate models relative to physics-based simulations.
• Identify potential applications of scientific machine learning in materials research.
• Outline an end-to-end workflow for applying neural operators to a suitable simulation problem.

Undergraduate and Postgraduate Students: Materials Science, Nanotechnology, Metallurgical Engineering, Mechanical Engineering, Computational Physics and related disciplines. PhD Scholars and Research Fellows: Researchers working on microstructure evolution, phase transformations, grain growth and computational materials science. Faculty Members and Academicians: Those interested in physics-based modelling, numerical simulation and AI-assisted materials research. Materials Scientists and Engineers: Professionals exploring computational approaches to materials design, alloy development and microstructure prediction. Scientific Computing and Machine Learning Researchers: Individuals interested in neural operators, surrogate modelling, PDE-based learning and scientific AI. Additive Manufacturing and Materials R&D Professionals: Researchers interested in simulation-assisted materials development and process–structure relationships.