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Physics-informed neural operators offer a powerful framework for learning solution operators of partial differential equations (PDEs) by combining data and physics losses. However, these physics losses rely on derivatives. Computing these…

Autoregressive neural PDE surrogates predict future states by repeatedly applying a learned one-step operator. This is a simple and widely used method, but small one-step errors can accumulate during long rollouts. The resulting drift often…

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is…

With recent advances in sensing technologies, a myriad of spatio-temporal data has been generated and recorded in smart cities. Forecasting the evolution patterns of spatio-temporal data is an important yet demanding aspect of urban…

As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…

Biological spiking neurons with intrinsic dynamics underlie the powerful representation and learning capabilities of the brain for processing multimodal information in complex environments. Despite recent tremendous progress in spiking…

Whilst spectral Graph Neural Networks (GNNs) are theoretically well-founded in the spectral domain, their practical reliance on polynomial approximation implies a profound linkage to the spatial domain. As previous studies rarely examine…

Mechanics-related problems often present unique challenges in achieving accurate geometric and physical representations, particularly for non-uniform structures. Graph neural networks (GNNs) have emerged as a promising tool to tackle these…

Graph neural networks (GNNs) have achieved impressive impressions for graph-related tasks. However, most GNNs are primarily studied under the cases of signal domain with supervised training, which requires abundant task-specific labels and…

Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals or handcrafted stencils), leading to limited applicability.…

Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world…

Spherical deep learning has been widely applied to a broad range of real-world problems. Existing approaches often face challenges in balancing strong spherical geometric inductive biases with the need to model real-world heterogeneity. To…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on…

Graph Neural Networks (GNNs) have shown impressive performance in graph representation learning, but they face challenges in capturing long-range dependencies due to their limited expressive power. To address this, Graph Transformers (GTs)…

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…

Modeling the complex three-dimensional (3D) dynamics of relational systems is an important problem in the natural sciences, with applications ranging from molecular simulations to particle mechanics. Machine learning methods have achieved…

Graph Neural Networks have gained huge interest in the past few years. These powerful algorithms expanded deep learning models to non-Euclidean space and were able to achieve state of art performance in various applications including…

Neural operators have emerged as powerful tools for learning mappings between function spaces, enabling efficient solutions to partial differential equations across varying inputs and domains. Despite the success, existing methods often…

In the era of big data, there has been a surge in the availability of data containing rich spatial and temporal information, offering valuable insights into dynamic systems and processes for applications such as weather forecasting, natural…