arXiv:2607. 20541v1 Announce Type: cross Abstract: We introduce HypNO, a graph-based neural operator for scalar hyperbolic conservation laws.
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: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. 10389v1 Announce Type: cross Abstract: In recent years, neural networks have significantly advanced numerical solutions of partial differential equations (PDEs).
arXiv:2605. 05488v2 Announce Type: replace Abstract: We propose an architecture that augments the Flux Neural Operator (Flux NO), which combines the classical finite volume method (FVM) with neural operators, with ViT-based context injection.
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...
The paper studies the stability of graph-aware continuous‑time generative models that use a graph filter combined with a learned graph neural network. It derives explicit Wasserstein bounds showing how relative graph perturbations affect the generated distributions, and proposes a principled framework for designing stable graph filters that preserve heat‑diffusion smoothing while improving structural stability. Experiments on synthetic and fMRI data demonstrate that these stable filters enhance robustness and match or surpass the generative quality of a heat‑equation baseline.
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.
The paper introduces a constitutive Markov physics‑informed neural operator (MPNO) designed to stabilize autoregressive predictions for transient‑dynamics PDEs with strong discontinuities. By modeling one‑step evolution as a row‑stochastic propagation operator and embedding material‑interface physics into a non‑negative symmetric adjacency matrix, MPNO guarantees a spectral radius ≤1, preventing exponential error growth. Experiments on Burgers’ equation and concrete‑penetration stress‑field prediction show that MPNO rolls out stably with bounded error, achieving comparable accuracy to the Fourier neural operator while using only a quarter of its parameters and delivering a 10^5× speedup over LS‑DYNA.
arXiv:2607. 15773v1 Announce Type: new Abstract: Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing.
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: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.
TWIG (Time‑Causal Wavelet Operator for Irregular Graphs) is a graph‑native neural operator designed for autoregressive surrogate modeling on static irregular graphs. It transforms each node’s history into causal multiscale temporal features, separating recent changes from slower memory components, and propagates these through graph‑wavelet operator blocks with gated pointwise channel mixing. The architecture is causal by construction, enabling closed‑loop forecasting where predictions are recursively reused as future inputs, and it consistently outperforms non‑time‑causal baselines across three irregular‑domain forecasting problems.