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This study proposes a novel Graph Convolutional Neural Network with Data-driven Graph Filter (GCNN-DDGF) model that can learn hidden heterogeneous pairwise correlations between stations to predict station-level hourly demand in a large-scale bike-sharing network. Two architectures of the GCNN-DDGF model are explored; GCNNreg-DDGF is a regular GCNN-DDGF model which contains the convolution and feedforward blocks, and GCNNrec-DDGF additionally contains a recurrent block from the Long Short-term Memory neural network architecture to capture temporal dependencies in the bike-sharing demand series. Furthermore, four types of GCNN models are proposed whose adjacency matrices are based on various bike-sharing system data, including Spatial Distance matrix (SD), Demand matrix (DE), Average Trip Duration matrix (ATD), and Demand Correlation matrix (DC). These six types of GCNN models and seven other benchmark models are built and compared on a Citi Bike dataset from New York City which includes 272 stations and over 28 million transactions from 2013 to 2016. Results show that the GCNNrec-DDGF performs the best in terms of the Root Mean Square Error, the Mean Absolute Error and the coefficient of determination (R2), followed by the GCNNreg-DDGF. They outperform the other models. Through a more detailed graph network analysis based on the learned DDGF, insights are obtained on the black box of the GCNN-DDGF model. It is found to capture some information similar to details embedded in the SD, DE and DC matrices. More importantly, it also uncovers hidden heterogeneous pairwise correlations between stations that are not revealed by any of those matrices.
We show experimentally that the accuracy of a trained neural network can be predicted surprisingly well by looking only at its weights, without evaluating it on input data. We motivate this task and introduce a formal setting for it. Even when using simple statistics of the weights, the predictors are able to rank neural networks by their performance with very high accuracy (R2 score more than 0.98). Furthermore, the predictors are able to rank networks trained on different, unobserved datasets and with different architectures. We release a collection of 120k convolutional neural networks trained on four different datasets to encourage further research in this area, with the goal of understanding network training and performance better.
With massive amounts of atomic simulation data available, there is a huge opportunity to develop fast and accurate machine learning models to approximate expensive physics-based calculations. The key quantity to estimate is atomic forces, where the state-of-the-art Graph Neural Networks (GNNs) explicitly enforce basic physical constraints such as rotation-covariance. However, to strictly satisfy the physical constraints, existing models have to make tradeoffs between computational efficiency and model expressiveness. Here we explore an alternative approach. By not imposing explicit physical constraints, we can flexibly design expressive models while maintaining their computational efficiency. Physical constraints are implicitly imposed by training the models using physics-based data augmentation. To evaluate the approach, we carefully design a scalable and expressive GNN model, ForceNet, and apply it to OC20 (Chanussot et al., 2020), an unprecedentedly-large dataset of quantum physics calculations. Our proposed ForceNet is able to predict atomic forces more accurately than state-of-the-art physics-based GNNs while being faster both in training and inference. Overall, our promising and counter-intuitive results open up an exciting avenue for future research.
Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural networks (DNNs) can serve as highly-accurate surrogate models, with the capacity to handle diverse datatypes, offering tremendous speed-ups for prediction and many other downstream tasks. An important use-case for these surrogates is the comparison between simulations and experiments; prediction uncertainty estimates are crucial for making such comparisons meaningful, yet standard DNNs do not provide them. In this work we define the fundamental requirements for a DNN to be useful for scientific applications, and demonstrate a general variational inference approach to equip predictions of scalar and image data from a DNN surrogate model trained on inertial confinement fusion simulations with calibrated Bayesian uncertainties. Critically, these uncertainties are interpretable, meaningful and preserve physics-correlations in the predicted quantities.
Recent works have revealed that infinitely-wide feed-forward or recurrent neural networks of any architecture correspond to Gaussian processes referred to as $mathrm{NNGP}$. While these works have extended the class of neural networks converging to Gaussian processes significantly, however, there has been little focus on broadening the class of stochastic processes that such neural networks converge to. In this work, inspired by the scale mixture of Gaussian random variables, we propose the scale mixture of $mathrm{NNGP}$ for which we introduce a prior distribution on the scale of the last-layer parameters. We show that simply introducing a scale prior on the last-layer parameters can turn infinitely-wide neural networks of any architecture into a richer class of stochastic processes. Especially, with certain scale priors, we obtain heavy-tailed stochastic processes, and we recover Students $t$ processes in the case of inverse gamma priors. We further analyze the distributions of the neural networks initialized with our prior setting and trained with gradient descents and obtain similar results as for $mathrm{NNGP}$. We present a practical posterior-inference algorithm for the scale mixture of $mathrm{NNGP}$ and empirically demonstrate its usefulness on regression and classification tasks.
In this paper, we propose a novel tensor graph convolutional neural network (TGCNN) to conduct convolution on factorizable graphs, for which here two types of problems are focused, one is sequential dynamic graphs and the other is cross-attribute graphs. Especially, we propose a graph preserving layer to memorize salient nodes of those factorized subgraphs, i.e. cross graph convolution and graph pooling. For cross graph convolution, a parameterized Kronecker sum operation is proposed to generate a conjunctive adjacency matrix characterizing the relationship between every pair of nodes across two subgraphs. Taking this operation, then general graph convolution may be efficiently performed followed by the composition of small matrices, which thus reduces high memory and computational burden. Encapsuling sequence graphs into a recursive learning, the dynamics of graphs can be efficiently encoded as well as the spatial layout of graphs. To validate the proposed TGCNN, experiments are conducted on skeleton action datasets as well as matrix completion dataset. The experiment results demonstrate that our method can achieve more competitive performance with the state-of-the-art methods.