arXiv:2607. 05167v1 Announce Type: new Abstract: Many real-world systems are organized as networks where spatio-temporal dynamics unfold along connections and not discretely between nodes.
arXiv:2608. 07161v1 Announce Type: cross Abstract: Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive.
arXiv:2508. 18173v2 Announce Type: replace Abstract: The discovery of symbolic governing equations is a central goal in science; yet, it remains challenging particularly for graph dynamical systems, where the network topology further shapes the system behavior.
arXiv:2606. 19138v1 Announce Type: new Abstract: Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori.
arXiv:2602.22293v2 Announce Type: replace Abstract: Accurate river prediction is essential for water, food and energy security, yet remains challenging across entire river networks. Machine learning...
arXiv:2607. 20541v1 Announce Type: cross Abstract: We introduce HypNO, a graph-based neural operator for scalar hyperbolic conservation laws.
arXiv:2608.27883v1 Announce Type: new Abstract: Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical sta...
arXiv:2605. 21247v3 Announce Type: replace Abstract: Graph Neural Networks (GNNs) have emerged as a cornerstone of deep learning, with most existing methods rooted in graph signal processing and diffusion equations to model message passing.
DeltaGNN introduces an information flow control mechanism that uses a new connectivity measure, the information flow score, to mitigate over‑smoothing and over‑squashing in Graph Neural Networks. This approach enables linear computational and memory overhead while effectively capturing both short‑range and long‑range node interactions. Experiments on ten diverse real‑world datasets demonstrate superior performance with limited computational complexity.
arXiv:2608. 09031v1 Announce Type: new Abstract: Graph neural networks typically propagate information through repeated message-passing layers, coupling the distance over which information travels with the number of nonlinear transformations applied.
arXiv:2509.06154v3 Announce Type: replace Abstract: Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings bet...
arXiv:2608.29892v1 Announce Type: new Abstract: Learning solution operators for partial differential equations (PDEs) on irregular and geometry-dependent domains remains a central challenge in scient...
The paper explores how information propagates in Deep Graph Networks (DGNs) for both static and dynamic graphs, treating DGNs as dynamical systems. It presents new architectures that better preserve long‑term node dependencies and learn complex spatio‑temporal patterns from irregular, sparsely sampled dynamic graphs. The work combines theoretical analysis with empirical results to demonstrate the effectiveness of these designs.