arXiv subjects

Nick Richardson

Publications and source records attributed to Nick Richardson.

3 recordsLinked to original sources

arXiv2025

Space Group Equivariant Crystal Diffusion

Accelerating inverse design of crystalline materials with generative models has significant implications for a range of technologies. Unlike other atomic systems, 3D crystals are invariant to discrete groups of isometries called the space groups. Crucially, these space group symmetries are known to heavily influence materials properties. We propose SGEquiDiff, a crystal generative model which naturally handles space group constraints with space group invariant likelihoods. SGEquiD-iff consists of an SE(3)-invariant, telescoping discrete sampler of crystal lattices; permutation-invariant, transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space group equivariant diffusion of atomic coordinates. We show that space group equivariant vector fields automatically live in the tangent spaces of the Wyckoff positions. SGEquiDiff achieves state-of-the-art performance on standard benchmark datasets as assessed by quantitative proxy metrics and quantum mechanical calculations. Our code is available at https://github.com/rees-c/sgequidiff.

cond-mat.mtrl-sci↗

arXiv2024

Graph Neural Networks Gone Hogwild

Graph neural networks (GNNs) appear to be powerful tools to learn state representations for agents in distributed, decentralized multi-agent systems, but generate catastrophically incorrect predictions when nodes update asynchronously during inference. This failure under asynchrony effectively excludes these architectures from many potential applications where synchrony is difficult or impossible to enforce, e.g., robotic swarms or sensor networks. In this work we identify "implicitly-defined" GNNs as a class of architectures which is provably robust to asynchronous "hogwild" inference, adapting convergence guarantees from work in asynchronous and distributed optimization. We then propose a novel implicitly-defined GNN architecture, which we call an 'energy GNN'. We show that this architecture outperforms other GNNs from this class on a variety of synthetic tasks inspired by multi-agent systems.

cs.LG↗

arXiv2022

Vitruvion: A Generative Model of Parametric CAD Sketches

Parametric computer-aided design (CAD) tools are the predominant way that engineers specify physical structures, from bicycle pedals to airplanes to printed circuit boards. The key characteristic of parametric CAD is that design intent is encoded not only via geometric primitives, but also by parameterized constraints between the elements. This relational specification can be viewed as the construction of a constraint program, allowing edits to coherently propagate to other parts of the design. Machine learning offers the intriguing possibility of accelerating the design process via generative modeling of these structures, enabling new tools such as autocompletion, constraint inference, and conditional synthesis. In this work, we present such an approach to generative modeling of parametric CAD sketches, which constitute the basic computational building blocks of modern mechanical design. Our model, trained on real-world designs from the SketchGraphs dataset, autoregressively synthesizes sketches as sequences of primitives, with initial coordinates, and constraints that reference back to the sampled primitives. As samples from the model match the constraint graph representation used in standard CAD software, they may be directly imported, solved, and edited according to downstream design tasks. In addition, we condition the model on various contexts, including partial sketches (primers) and images of hand-drawn sketches. Evaluation of the proposed approach demonstrates its ability to synthesize realistic CAD sketches and its potential to aid the mechanical design workflow.

cs.LG↗