Graph Neural Networks

Background Diffusion models are rapidly advancing the field of 3D molecular generation, offering new tools for applications in drug discovery and materials science. These models generate realistic molecular structures by iteratively refining noisy inputs, capturing the intricate spatial relationships crucial to molecular properties. The aim of this project is to explore Equivariant Neural Diffusion (END), an innovative 3D molecular generation model that preserves equivariance to Euclidean transformations. END stands out for its learnable forward process, parameterized in a time- and data-dependent manner, ensuring robust equivariance to rigid transformations. The project will involve extending the capabilities of END, benchmarking its performance on standard molecular generation datasets, and refining its generative accuracy and scalability to enhance its utility in molecular modeling applications. ...

Background Graph Neural Networks (GNNs) have become powerful tools for modeling molecular systems, with applications in drug discovery and materials science. Equivariant GNNs, which preserve symmetries like rotations and translations, are especially well-suited for molecular modeling as they ensure that the model’s output changes consistently with the molecular structure’s orientation. This capability enhances accuracy and generalization, making them valuable for tasks such as drug discovery and material design. However, challenges remain around their robustness, generalization, and uncertainty quantification (UQ) capabilities. Reliable UQ is crucial for scientific applications, where predictions need to be interpretable and uncertainties well-calibrated. ...

Background Geometric Algebra (GA) provides a unified mathematical framework for representing and manipulating geometric entities and transformations in arbitrary dimensions. Its ability to elegantly encode rotations, reflections, and other symmetries makes it an ideal tool for advancing geometric deep learning. While current Graph Neural Networks (GNNs) have made significant strides in processing molecular data, they often rely on specialized techniques to handle equivariance and fail to fully leverage the expressive power of GA. ...