Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This paper aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science.

A Latent Diffusion Model for Protein Structure Generation

Proteins are complex biomolecules that perform a variety of crucial functions within living organisms. Designing and generating novel proteins can pave the way for many future synthetic biology applications, including drug discovery. However, it remains a challenging computational task due to the large modeling space of protein structures. In this study, we propose a latent diffusion model that can reduce the complexity of protein modeling while flexibly capturing the distribution of natural protein structures in a condensed latent space. Specifically, we propose an equivariant protein autoencoder that embeds proteins into a latent space and then uses an equivariant diffusion model to learn the distribution of the latent protein representations. Experimental results demonstrate that our method can effectively generate novel protein backbone structures with high designability and efficiency.

A new perspective on building efficient and expressive 3D equivariant graph neural networks

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these networks through a local-to-global analysis lacks today. In this paper, we propose a local hierarchy of 3D isomorphism to evaluate the expressive power of equivariant GNNs and investigate the process of representing global geometric information from local patches. Our work leads to two crucial modules for designing expressive and efficient geometric GNNs; namely local substructure encoding (LSE) and frame transition encoding (FTE). To demonstrate the applicability of our theory, we propose LEFTNet which effectively implements these modules and achieves state-of-the-art performance on both scalar-valued and vector-valued molecular property prediction tasks. We further point out the design space for future developments of equivariant graph neural networks. Our codes are available at \url{https://github.com/yuanqidu/LeftNet}.

Learning Protein Representations via Complete 3D Graph Networks

We consider representation learning for proteins with 3D structures. We build 3D graphs based on protein structures and develop graph networks to learn their representations. Depending on the levels of details that we wish to capture, protein representations can be computed at different levels, \emph{e.g.}, the amino acid, backbone, or all-atom levels. Importantly, there exist hierarchical relations among different levels. In this work, we propose to develop a novel hierarchical graph network, known as ProNet, to capture the relations. Our ProNet is very flexible and can be used to compute protein representations at different levels of granularity. We show that, given a base 3D graph network that is complete, our ProNet representations are also complete at all levels. To close the loop, we develop a complete and efficient 3D graph network to be used as a base model, making our ProNet complete. We conduct experiments on multiple downstream tasks. Results show that ProNet outperforms recent methods on most datasets. In addition, results indicate that different downstream tasks may require representations at different levels. Our code is available as part of the DIG library (\url{https://github.com/divelab/DIG}).

GraphFM: Improving Large-Scale GNN Training via Feature Momentum

Training of graph neural networks (GNNs) for large-scale node classification is challenging. A key difficulty lies in obtaining accurate hidden node representations while avoiding the neighborhood explosion problem. Here, we propose a new technique, named feature momentum (FM), that uses a momentum step to incorporate historical embeddings when updating feature representations. We develop two specific algorithms, known as GraphFM-IB and GraphFM-OB, that consider in-batch and out-of-batch data, respectively. GraphFM-IB applies FM to in-batch sampled data, while GraphFM-OB applies FM to out-of-batch data that are 1-hop neighborhood of in-batch data. We provide a convergence analysis for GraphFM-IB and some theoretical insight for GraphFM-OB. Empirically, we observe that GraphFM-IB can effectively alleviate the neighborhood explosion problem of existing methods. In addition, GraphFM-OB achieves promising performance on multiple large-scale graph datasets.

ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphs

Many real-world data can be modeled as 3D graphs, but learning representations that incorporates 3D information completely and efficiently is challenging. Existing methods either use partial 3D information, or suffer from excessive computational cost. To incorporate 3D information completely and efficiently, we propose a novel message passing scheme that operates within 1-hop neighborhood. Our method guarantees full completeness of 3D information on 3D graphs by achieving global and local completeness. Notably, we propose the important rotation angles to fulfill global completeness. Additionally, we show that our method is orders of magnitude faster than prior methods. We provide rigorous proof of completeness and analysis of time complexity for our methods. As molecules are in essence quantum systems, we build the \underline{com}plete and \underline{e}fficient graph neural network (ComENet) by combing quantum inspired basis functions and the proposed message passing scheme. Experimental results demonstrate the capability and efficiency of ComENet, especially on real-world datasets that are large in both numbers and sizes of graphs. Our code is publicly available as part of the DIG library (\url{https://github.com/divelab/DIG}).

GOOD: A Graph Out-of-Distribution Benchmark

Out-of-distribution (OOD) learning deals with scenarios in which training and test data follow different distributions. Although general OOD problems have been intensively studied in machine learning, graph OOD is only an emerging area of research. Currently, there lacks a systematic benchmark tailored to graph OOD method evaluation. In this work, we aim at developing an OOD benchmark, known as GOOD, for graphs specifically. We explicitly make distinctions between covariate and concept shifts and design data splits that accurately reflect different shifts. We consider both graph and node prediction tasks as there are key differences when designing shifts. Overall, GOOD contains 8 datasets with 14 domain selections. When combined with covariate, concept, and no shifts, we obtain 42 different splits. We provide performance results on 7 commonly used baseline methods with 10 random runs. This results in 294 dataset-model combinations in total. Our results show significant performance gaps between in-distribution and OOD settings. Our results also shed light on different performance trends between covariate and concept shifts by different methods. Our GOOD benchmark is a growing project and expects to expand in both quantity and variety of resources as the area develops. The GOOD benchmark can be accessed via $\href{https://github.com/divelab/GOOD/}{\text{https://github.com/divelab/GOOD/}}$.

Fast Quantum Property Prediction via Deeper 2D and 3D Graph Networks

Molecular property prediction is gaining increasing attention due to its diverse applications. One task of particular interests and importance is to predict quantum chemical properties without 3D equilibrium structures. This is practically favorable since obtaining 3D equilibrium structures requires extremely expensive calculations. In this work, we design a deep graph neural network to predict quantum properties by directly learning from 2D molecular graphs. In addition, we propose a 3D graph neural network to learn from low-cost conformer sets, which can be obtained with open-source tools using an affordable budget. We employ our methods to participate in the 2021 KDD Cup on OGB Large-Scale Challenge (OGB-LSC), which aims to predict the HOMO-LUMO energy gap of molecules. Final evaluation results reveal that we are one of the winners with a mean absolute error of 0.1235 on the holdout test set. Our implementation is available as part of the MoleculeX package (https://github.com/divelab/MoleculeX).

DIG: A Turnkey Library for Diving into Graph Deep Learning Research

Although there exist several libraries for deep learning on graphs, they are aiming at implementing basic operations for graph deep learning. In the research community, implementing and benchmarking various advanced tasks are still painful and time-consuming with existing libraries. To facilitate graph deep learning research, we introduce DIG: Dive into Graphs, a research-oriented library that integrates unified and extensible implementations of common graph deep learning algorithms for several advanced tasks. Currently, we consider graph generation, self-supervised learning on graphs, explainability of graph neural networks, and deep learning on 3D graphs. For each direction, we provide unified implementations of data interfaces, common algorithms, and evaluation metrics. Altogether, DIG is an extensible, open-source, and turnkey library for researchers to develop new methods and effortlessly compare with common baselines using widely used datasets and evaluation metrics. Source code and documentations are available at https://github.com/divelab/DIG/.

Spherical Message Passing for 3D Graph Networks

We consider representation learning from 3D graphs in which each node is associated with a spatial position in 3D. This is an under explored area of research, and a principled framework is currently lacking. In this work, we propose a generic framework, known as the 3D graph network (3DGN), to provide a unified interface at different levels of granularity for 3D graphs. Built on 3DGN, we propose the spherical message passing (SMP) as a novel and specific scheme for realizing the 3DGN framework in the spherical coordinate system (SCS). We conduct formal analyses and show that the relative location of each node in 3D graphs is uniquely defined in the SMP scheme. Thus, our SMP represents a complete and accurate architecture for learning from 3D graphs in the SCS. We derive physically-based representations of geometric information and propose the SphereNet for learning representations of 3D graphs. We show that existing 3D deep models can be viewed as special cases of the SphereNet. Experimental results demonstrate that the use of complete and accurate 3D information in 3DGN and SphereNet leads to significant performance improvements in prediction tasks.