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Automated medical image segmentation plays a key role in quantitative research and diagnostics. Convolutional neural networks based on the U-Net architecture are the state-of-the-art. A key disadvantage is the hard-coding of the receptive…

Molecular Dynamics (MD) simulation is a powerful tool for understanding the dynamics and structure of matter. Since the resolution of MD is atomic-scale, achieving long time-scale simulations with femtosecond integration is very expensive.…

This paper studies the problem of modeling multi-agent dynamical systems, where agents could interact mutually to influence their behaviors. Recent research predominantly uses geometric graphs to depict these mutual interactions, which are…

The great learning ability of deep learning models facilitates us to comprehend the real physical world, making learning to simulate complicated particle systems a promising endeavour. However, the complex laws of the physical world pose…

We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…

Disease progression modeling aims to characterize and predict how a patient's disease complications worsen over time based on longitudinal electronic health records (EHRs). For diseases such as type 2 diabetes, accurate progression modeling…

Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for…

Graph Neural Networks (GNNs) traditionally employ a message-passing mechanism that resembles diffusion over undirected graphs, which often leads to homogenization of node features and reduced discriminative power in tasks such as node…

Deep generative models have been praised for their ability to learn smooth latent representation of images, text, and audio, which can then be used to generate new, plausible data. However, current generative models are unable to work with…

Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical…

We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…

Graph neural networks (GNNs) have been used extensively for addressing problems in drug design and discovery. Both ligand and target molecules are represented as graphs with node and edge features encoding information about atomic elements…

The dominant paradigm for machine learning on graphs uses Message Passing Graph Neural Networks (MP-GNNs), in which node representations are updated by aggregating information in their local neighborhood. Recently, there have been…

Transformer-based neural operators have emerged as promising surrogate solvers for partial differential equations, by leveraging the effectiveness of Transformers for capturing long-range dependencies and global correlations, profoundly…

Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs…

Graph-based spatio-temporal neural networks are effective to model the spatial dependency among discrete points sampled irregularly from unstructured grids, thanks to the great expressiveness of graph neural networks. However, these models…

Neural operators are becoming the default tools to learn solutions to governing partial differential equations (PDEs) in weather and ocean forecasting applications. Despite early promising achievements, significant challenges remain,…

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…

Graph neural networks (GNNs) leverage message passing mechanisms to learn the topological features of graph data. Traditional GNNs learns node features in a spatial domain unrelated to the topology, which can hardly ensure topological…

Partial differential equations (PDEs) are central to describing complex physical system simulations. Their expensive solution techniques have led to an increased interest in deep neural network based surrogates. However, the practical…