We consider the problem of predicting gene expressions from DNA sequences. A key challenge of this task is to find the regulatory elements that control gene expressions. Here, we introduce Seq2Exp, a Sequence to Expression network explicitly designed to discover and extract regulatory elements that drive target gene expression, enhancing the accuracy of the gene expression prediction. Our approach captures the causal relationship between epigenomic signals, DNA sequences and their associated regulatory elements. Specifically, we propose to decompose the epigenomic signals and the DNA sequence conditioned on the causal active regulatory elements, and apply an information bottleneck with the Beta distribution to combine their effects while filtering out non-causal components. Our experiments demonstrate that Seq2Exp outperforms existing baselines in gene expression prediction tasks and discovers influential regions compared to commonly used statistical methods for peak detection such as MACS3. The source code is released as part of the AIRS library (https://github.com/divelab/AIRS/).

We consider explainability in equivariant graph neural networks for 3D geometric graphs. While many XAI methods have been developed for analyzing graph neural networks, they predominantly target 2D graph structures. The complex nature of 3D data and the sophisticated architectures of equivariant GNNs present unique challenges. Current XAI techniques either struggle to adapt to equivariant GNNs or fail to effectively handle positional data and evaluate the significance of geometric features adequately. To address these challenges, we introduce a novel method, known as EquiGX, which uses the Deep Taylor decomposition framework to extend the layer-wise relevance propagation rules tailored for spherical equivariant GNNs. Our approach decomposes prediction scores and back-propagates the relevance scores through each layer to the input space. Our decomposition rules provide a detailed explanation of each layer’s contribution to the network’s predictions, thereby enhancing our understanding of how geometric and positional data influence the model’s outputs. Through experiments on both synthetic and real-world datasets, our method demonstrates its capability to identify critical geometric structures and outperform alternative baselines. These results indicate that our method provides significantly enhanced explanations for equivariant GNNs. Our code has been released as part of the AIRS library (https://github.com/divelab/AIRS/).

SO(3)-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate the computation, we develop tensor decomposition networks (TDNs) as a class of approximately equivariant networks whose CG tensor products are replaced by low-rank tensor decompositions, such as the CANDECOMP/PARAFAC (CP) decomposition. With the CP decomposition, we prove (i) a uniform bound on the induced error of SO(3)-equivariance, and (ii) the universality of approximating any equivariant bilinear map. To further reduce the number of parameters, we propose path-weight sharing that ties all multiplicity-space weights across the O(L^3) CG paths into a single shared parameter set without compromising equivariance, where L is the maximum angular degree. The resulting layer acts as a plug-and-play replacement for tensor products in existing networks, and the computational complexity of tensor products is reduced from O(L^6) to O(L^4). We evaluate TDNs on PubChemQCR, a newly curated molecular relaxation dataset containing 105 million DFT-calculated snapshots. We also use existing datasets, including OC20, and OC22. Results show that TDNs achieve competitive performance with dramatic speedup in computations. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

The integration of machine learning (ML) into the physical sciences is reshaping computational paradigms, offering the potential to accelerate demanding simulations such as computational fluid dynamics (CFD). Yet, persistent challenges in accuracy, generalization, and physical consistency hinder the practical deployment of ML models in scientific domains. To address these limitations and systematically benchmark progress, we organized the ML4CFD competition, centered on surrogate modeling for aerodynamic simulations over two-dimensional airfoils. The competition attracted over 240 teams, who were provided with a curated dataset generated via OpenFOAM and evaluated through a multi-criteria framework encompassing predictive accuracy, physical fidelity, computational efficiency, and out-of-distribution generalization. This retrospective analysis reviews the competition outcomes, highlighting several approaches that outperformed baselines under our global evaluation score. Notably, the top entry exceeded the performance of the original OpenFOAM solver on aggregate metrics, illustrating the promise of ML based surrogates to outperform traditional solvers under tailored criteria. However, this does not imply that the winning solution could replace the OpenFOAM solver or that it was overall superior, even for this specific task. Drawing from these results, we analyze the key design principles of top submissions, assess the robustness of our evaluation framework, and offer guidance for future scientific ML challenges.

We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Supervised machine learning approaches have been increasingly used in accelerating electronic structure prediction as surrogates of first-principle computational methods, such as density functional theory (DFT). While numerous quantum chemistry datasets focus on chemical properties and atomic forces, the ability to achieve accurate and efficient prediction of the Hamiltonian matrix is highly desired, as it is the most important and fundamental physical quantity that determines the quantum states of physical systems and chemical properties. In this work, we generate a new Quantum Hamiltonian dataset, named as QH9, to provide precise Hamiltonian matrices for 2,399 molecular dynamics trajectories and 130,831 stable molecular geometries, based on the QM9 dataset. By designing benchmark tasks with various molecules, we show that current machine learning models have the capacity to predict Hamiltonian matrices for arbitrary molecules. Both the QH9 dataset and the baseline models are provided to the community through an open-source benchmark, which can be highly valuable for developing machine learning methods and accelerating molecular and materials design for scientific and technological applications. Our benchmark is publicly available at \url{https://github.com/divelab/AIRS/tree/main/OpenDFT/QHBench}.

Deep learning methods are achieving ever-increasing performance on many artificial intelligence tasks. A major limitation of deep models is that they are not amenable to interpretability. This limitation can be circumvented by developing post hoc techniques to explain predictions, giving rise to the area of explainability. Recently, explainability of deep models on images and texts has achieved significant progress. In the area of graph data, graph neural networks (GNNs) and their explainability are experiencing rapid developments. However, there is neither a unified treatment of GNN explainability methods, nor a standard benchmark and testbed for evaluations. In this survey, we provide a unified and taxonomic view of current GNN explainability methods. Our unified and taxonomic treatments of this subject shed lights on the commonalities and differences of existing methods and set the stage for further methodological developments. To facilitate evaluations, we provide a testbed for GNN explainability, including datasets, common algorithms and evaluation metrics. Furthermore, we conduct comprehensive experiments to compare and analyze the performance of many techniques. Altogether, this work provides a unified methodological treatment of GNN explainability and a standardized testbed for evaluations.

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.

This tutorial is proposed based upon the recently released open-source library Dive into Graphs (DIG) along with hands-on code examples. DIG is a turnkey library that considers four frontiers in graph deep learning, including self-supervised learning of GNNs, 3D GNNs, explainability of GNNs, and graph generation. It provides data interfaces, common algorithms, and evaluation metrics for each direction. It has 255,000+ visitors, 11,000+ installations, and 1,100+ stars within a year and is becoming a robust and dominant ecosystem for graph neural network research. In this tutorial, we will review representative methodologies for these four directions and show hands-on code examples to demonstrate how to effortlessly implement benchmarks using DIG. This tutorial targets a broad audience working on or interested in various research themes. To encourage audience participation, we will promote our tutorial in advance on social media, reading groups, and library contribution community. We anticipate this tutorial would attract more researchers to these interesting and promising topics, leading to a more active community, eventually generating both scientific values and real-world impacts.

We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.

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 turnkey library that provides a unified testbed for higher level, research-oriented graph deep learning 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 is available at https://github.com/divelab/DIG.