Generative Models for Materials Science
Part I — Foundations¶
Chapter 1: Basics of Materials Science¶
Crystal structures and symmetry
Thermodynamics and free energy
Free energy landscape
Reaction transition states, energy barriers and mechanisms
Path sampling
Definition, implication and conventional sampling methods.
Chapter 2: Probability and Statistical Modeling¶
Random variables and distributions
Bayesian inference basics
Likelihood, prior, posterior
Chapter 3: Machine Learning Fundamentals¶
Supervised vs unsupervised learning
Representation learning
Overfitting, generalization, and inductive bias
Part II — Representations of Materials¶
Chapter 4: Representing Atomic Structures¶
Graph representations of crystals
Translation, rotation, permutation symmetry
SE(3)/E(3)-equivariant networks
Equivariant deep neural network
Message passing neural networks (MPNNs)
Equivariant transformer
Part III — Core Generative Models¶
Chapter 5: Variational Autoencoders (VAEs)¶
Latent variable models
Amortized inference
Crystal VAEs and compositional design
Trade-offs in latent space interpretability
Refer to [1]
Chapter 6: Generative Adversarial Networks (GANs)¶
Adversarial training principles
Stability issues
CrystalGAN and structure generation
Mode collapse in materials space
Refer to [1]
Chapter 7: Normalizing Flows¶
Invertible transformations
Boltzmann generators
Flow Matching and Transport Models
Optimal transport formulation
Deterministic vs stochastic sampling
Likelihood evaluation
Discrete representations
Flows on categorical variables
Graph flows
Permutation-based invertible mappings
Chapter 8: Diffusion Models¶
Forward noising and reverse denoising
Score-based generative modeling
Sampling efficiency and guidance methods
Langevin Dynamics
Guidance
Chapter 9: Autoregressive Models for Materials¶
Sequence modeling for atomic structures
Limitations for periodic systems
Applications in crystal generation
Part V — Conditional and Inverse Design¶
Chapter 10: Conditional Generation¶
Conditioning on composition, structure, or properties
Inpainting
Guidance
Multi-objective constraints
Chapter 11: Inverse Materials Design¶
Property-to-structure mapping
Bayesian optimization vs generative models
Multi-fidelity design pipelines
Part VI — Applications¶
Chapter 12: Crystal and Solid-State Materials¶
Inorganic crystal generation
Phase diagram generation
Defect, surface, and interface structures
Chapter 13: Molecular and Soft Materials¶
Polymers, MOFs, and organic crystals
Drug-like molecules vs materials design
Chapter 14: Kinetic simulations¶
Free energy landscape and reaction pathway
Reaction network
Kinetic Monte Carlo
Chapter 15: Energy Materials¶
Part VII — Training and Evaluation¶
Chapter 16: Datasets in Materials Science¶
Materials Project, OQMD, NOMAD
Data cleaning and bias issues
Synthetic data generation
Chapter 17: Training Challenges¶
Data scarcity and imbalance
Symmetry enforcement in training
Scalability issues
Chapter 18: Evaluation Metrics¶
Validity, uniqueness, novelty
Physical stability criteria
Property prediction accuracy
Part VIII — Advanced Topics and Frontiers¶
Chapter 19: Multi-Scale Generative Modeling¶
Atomistic to mesoscale coupling
Coarse-graining and backmapping
Chapter 20: Uncertainty Quantification¶
Bayesian deep learning
Calibration of generative outputs
Chapter 21: Active Learning and Closed-Loop Discovery¶
Experiment–model feedback loops
Autonomous materials labs
Chapter 22: Scientific Discovery with Generative Models¶
Hypothesis generation
Discovering new physical laws
Interpretability challenges
Appendices¶
A: Mathematical background (group theory, thermodynamics)
B: Common datasets and benchmarks
C: Software libraries
D: Notation and conventions
References¶
[1] MIT EECS, Fall 2024, Kaiming He:
https://