Thomas Bailie

Thomas Bailie, Yun Sing Koh, Karthik Mukkavilli

Graphs model latent variable relationships in many real-world systems, and Message Passing Neural Networks (MPNNs) are widely used to learn such structures for downstream tasks. While edge-based MPNNs effectively capture local interactions, their expressive power is theoretically bounded, limiting the discovery of higher-order relationships. We introduce the Higher-Order Graph Attention (HoGA) module, which constructs a k-order attention matrix by sampling subgraphs to maximize diversity among feature vectors. Unlike existing higher-order attention methods that greedily resample similar k-order relationships, HoGA targets diverse modalities in higher-order topology, reducing redundancy and expanding the range of captured substructures. Applied to two single-hop attention models, HoGA achieves at least a 5% accuracy gain on all benchmark node classification datasets and outperforms recent baselines on six of eight datasets. Code is available at https://github.com/TB862/Higher_Order.

Thomas Bailie, Yun Sing Koh, S. Karthik Mukkavilli et al.

Graphical forecasting models learn the structure of time series data via projecting onto a graph, with recent techniques capturing spatial-temporal associations between variables via edge weights. Hierarchical variants offer a distinct advantage by analysing the time series across multiple resolutions, making them particularly effective in tasks like global weather forecasting, where low-resolution variable interactions are significant. A critical challenge in hierarchical models is information loss during forward or backward passes through the hierarchy. We propose the Hierarchical Graph Flow (HiGFlow) network, which introduces a memory buffer variable of dynamic size to store previously seen information across variable resolutions. We theoretically show two key results: HiGFlow reduces smoothness when mapping onto new feature spaces in the hierarchy and non-strictly enhances the utility of message-passing by improving Weisfeiler-Lehman (WL) expressivity. Empirical results demonstrate that HiGFlow outperforms state-of-the-art baselines, including transformer models, by at least an average of 6.1% in MAE and 6.2% in RMSE. Code is available at https://github.com/TB862/ HiGFlow.git.

Thomas Bailie, S. Karthik Mukkavilli, Varvara Vetrova et al.

Climate events arise from intricate, multivariate dynamics governed by global-scale drivers, profoundly impacting food, energy, and infrastructure. Yet, accurate weather prediction remains elusive due to physical processes unfolding across diverse spatio-temporal scales, which fixed-resolution methods cannot capture. Hierarchical Graph Neural Networks (HGNNs) offer a multiscale representation, but nonlinear downward mappings often erase global trends, weakening the integration of physics into forecasts. We introduce HiFlowCast and its ensemble variant HiAntFlow, HGNNs that embed physics within a multiscale prediction framework. Two innovations underpin their design: a Latent-Memory-Retention mechanism that preserves global trends during downward traversal, and a Latent-to-Physics branch that integrates PDE solution fields across diverse scales. Our Flow models cut errors by over 5% at 13-day lead times and by 5-8% under 1st and 99th quantile extremes, improving reliability for rare events. Leveraging pretrained model weights, they converge within a single epoch, reducing training cost and their carbon footprint. Such efficiency is vital as the growing scale of machine learning challenges sustainability and limits research accessibility. Code and model weights are in the supplementary materials.