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Register a new userGeometric learning of the conformational dynamics of molecules using dynamic graph neural networks
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We apply a temporal edge prediction model for weighted dynamic graphs to predict time-dependent changes in molecular structure. Each molecule is represented as a complete graph in which each atom is a vertex and all vertex pairs are connected by an edge weighted by the Euclidean distance between atom pairs. We ingest a sequence of complete molecular graphs into a dynamic graph neural network (GNN) to predict the graph at the next time step. Our dynamic GNN predicts atom-to-atom distances with a mean absolute error of 0.017 r{A}, which is considered ``chemically accurate for molecular simulations. We also explored the transferability of a trained network to new molecular systems and found that finetuning with less than 10% of the total trajectory provides a mean absolute error of the same order of magnitude as that when training from scratch on the full molecular trajectory.
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Molecular machine learning bears promise for efficient molecule property prediction and drug discovery. However, due to the limited labeled data and the giant chemical space, machine learning models trained via supervised learning perform poorly in generalization. This greatly limits the applications of machine learning methods for molecular design and discovery. In this work, we present MolCLR: Molecular Contrastive Learning of Representations via Graph Neural Networks (GNNs), a self-supervised learning framework for large unlabeled molecule datasets. Specifically, we first build a molecular graph, where each node represents an atom and each edge represents a chemical bond. A GNN is then used to encode the molecule graph. We propose three novel molecule graph augmentations: atom masking, bond deletion, and subgraph removal. A contrastive estimator is utilized to maximize the agreement of different graph augmentations from the same molecule. Experiments show that molecule representations learned by MolCLR can be transferred to multiple downstream molecular property prediction tasks. Our method thus achieves state-of-the-art performance on many challenging datasets. We also prove the efficiency of our proposed molecule graph augmentations on supervised molecular classification tasks.
Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical model or class of models of the underlying random walks. Reliable inference is made difficult by the inherent stochastic nature of single particle motion, by experimental noise, and by the short duration of most experimental trajectories. Model identification is further complicated by the fact that main physical properties of random walk models are only defined asymptotically, and are thus degenerate for short trajectories. Here, we introduce a new, fast approach to inferring random walk properties based on graph neural networks (GNNs). Our approach consists in associating a vector of features with each observed position, and a sparse graph structure with each observed trajectory. By performing simulation-based supervised learning on this construct [1], we show that we can reliably learn models of random walks and their anomalous exponents. The method can naturally be applied to trajectories of any length. We show its efficiency in analysing various anomalous random walks of biological relevance that were proposed in the AnDi challenge [2]. We explore how information is encoded in the GNN, and we show that it learns relevant physical features of the random walks. We furthermore evaluate its ability to generalize to types of trajectories not seen during training, and we show that the GNN retains high accuracy even with few parameters. We finally discuss the possibility to leverage these networks to analyse experimental data.
Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of AMG algorithms is the selection of the prolongation operator -- a problem-dependent sparse matrix which governs the multiscale hierarchy of the solver and is critical to its efficiency. Over many years, numerous methods have been developed for this task, and yet there is no known single right answer except in very special cases. Here we propose a framework for learning AMG prolongation operators for linear systems with sparse symmetric positive (semi-) definite matrices. We train a single graph neural network to learn a mapping from an entire class of such matrices to prolongation operators, using an efficient unsupervised loss function. Experiments on a broad class of problems demonstrate improved convergence rates compared to classical AMG, demonstrating the potential utility of neural networks for developing sparse system solvers.
Existing graph neural networks (GNNs) largely rely on node embeddings, which represent a node as a vector by its identity, type, or content. However, graphs with unlabeled nodes widely exist in real-world applications (e.g., anonymized social networks). Previous GNNs either assign random labels to nodes (which introduces artefacts to the GNN) or assign one embedding to all nodes (which fails to distinguish one node from another). In this paper, we analyze the limitation of existing approaches in two types of classification tasks, graph classification and node classification. Inspired by our analysis, we propose two techniques, Dynamic Labeling and Preferential Dynamic Labeling, that satisfy desired properties statistically or asymptotically for each type of the task. Experimental results show that we achieve high performance in various graph-related tasks.
The pre-training on the graph neural network model can learn the general features of large-scale networks or networks of the same type by self-supervised methods, which allows the model to work even when node labels are missing. However, the existing pre-training methods do not take network evolution into consideration. This paper proposes a pre-training method on dynamic graph neural networks (PT-DGNN), which uses dynamic attributed graph generation tasks to simultaneously learn the structure, semantics, and evolution features of the graph. The method includes two steps: 1) dynamic sub-graph sampling, and 2) pre-training with dynamic attributed graph generation task. Comparative experiments on three realistic dynamic network datasets show that the proposed method achieves the best results on the link prediction fine-tuning task.
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