Diffusion model generates glass and silicon structures to order from target properties

The work

Technical · from the record

The authors built AMDEN, a diffusion model whose score function is an equivariant graph neural network, to generate atomic structures of amorphous materials conditioned on target properties, with a ghost-atom mechanism that lets the density of the output be set. It was trained on simulated datasets made for the study: 9,027 multi-element glass samples, three amorphous silicon sets of 10,000 samples each with different thermal histories, and amorphous silica cells of 80 to 250 atoms. Conditioning on Young's modulus and lithium content, the generated lithium concentrations stayed within a few percent of the target while the generated moduli fell short of it; requenching the generated compositions by molecular dynamics gave moduli that correlated more closely with the targets, locating the discrepancy in the generated atomic structures. Standard denoising reproduced structures sampled from the melt but not the lower-energy structures obtained by slow quenching, so the authors added a variant that predicts a noise energy and performs Hamiltonian Monte Carlo steps between denoising steps; with this variant the radial distribution functions, potential energies and generated Young's moduli moved closer to the reference values.

How AI was used

Each sample was represented as a fixed cell with atomic positions and one-hot element embeddings, and a score function was trained on a stochastic-differential-equation diffusion process using a variance-exploding noise schedule for positions and a variance-preserving cosine schedule for element embeddings, with the loss being the mean squared error between predicted and injected noise. The score function is an equivariant graph neural network of four layers with a 6.5 Å cutoff radius, eight vector channels and a hidden dimension of 128 for self-attention, taking interatomic distances under periodic boundary conditions as edge features and element embeddings, diffusion time and linear embeddings of the conditioning properties as node features. Generation solved the reverse-time SDE by the Euler–Maruyama method over 200 steps with classifier-free guidance, and a ghost-atom mechanism assigned part of a fixed atom count to a dummy element class, removed afterwards, so that a target density could be imposed. A second variant output a scalar noise energy per atom, from which the score was obtained by automatic differentiation, and interleaved one Hamiltonian Monte Carlo step on that energy before each denoising step for diffusion times up to 0.5, run with 2000 diffusion steps. Training and reference data came from classical molecular dynamics melt-quench workflows in LAMMPS and ASE using the BMP-shrm, Stillinger-Weber and Tersoff potentials, with elastic moduli from finite differences of the stress tensor, lithium concentration and average ring size used as conditioning values; generated samples were filtered for stoichiometric balance and compared with reference and requenched simulations.