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:2607. 20541v1 Announce Type: cross Abstract: We introduce HypNO, a graph-based neural operator for scalar hyperbolic conservation laws.
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.
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:2606. 16273v1 Announce Type: cross Abstract: We introduce, to our knowledge, the first deep generative modeling framework for probability distributions continuously supported on compact metric graphs.
arXiv:2509. 12484v2 Announce Type: replace Abstract: We propose a novel neural network architecture, called Non-Trainable Modification (NTM), for computing Nash equilibria in stochastic differential games (SDGs) on graphs.
arXiv:2606. 19303v1 Announce Type: new Abstract: High-fidelity simulation of spatiotemporal dynamics is computationally prohibitive, necessitating efficient super-resolution techniques to reconstruct high-resolution data from coarse-grained inputs.
arXiv:2511. 10841v3 Announce Type: replace-cross Abstract: Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge.
arXiv:2608. 13827v1 Announce Type: new Abstract: Machine-learned physical surrogate models have become promising alternatives to mesh-based numerical solvers.
arXiv:2607. 20535v1 Announce Type: cross Abstract: Traditional Predictive Digital Twins often remain geometrically rigid, requiring extensive retraining or fine-tuning whenever the underlying physical domain or boundary conditions change.