When do neural ordinary differential equations generalize on complex networks?

• URL: http://arxiv.org/abs/2602.08980v1
• Date: Mon, 09 Feb 2026 18:28:41 GMT
• Title: When do neural ordinary differential equations generalize on complex networks?
• Abstract summary: We study neural ordinary differential equations ($mathtnODE$s) with vector fields following the Barabsi-Barzel form.<n>We find that degree heterogeneity and the type of dynamical system are the primary factors in determining $mathtnODE$s' ability to generalize across graph sizes and properties.
• Score: 0.1710303986316337
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural ordinary differential equations (neural ODEs) can effectively learn dynamical systems from time series data, but their behavior on graph-structured data remains poorly understood, especially when applied to graphs with different size or structure than encountered during training. We study neural ODEs ($\mathtt{nODE}$s) with vector fields following the Barabási-Barzel form, trained on synthetic data from five common dynamical systems on graphs. Using the $\mathbb{S}^1$-model to generate graphs with realistic and tunable structure, we find that degree heterogeneity and the type of dynamical system are the primary factors in determining $\mathtt{nODE}$s' ability to generalize across graph sizes and properties. This extends to $\mathtt{nODE}$s' ability to capture fixed points and maintain performance amid missing data. Average clustering plays a secondary role in determining $\mathtt{nODE}$ performance. Our findings highlight $\mathtt{nODE}$s as a powerful approach to understanding complex systems but underscore challenges emerging from degree heterogeneity and clustering in realistic graphs.

Related papers

• Learning graphs and simplicial complexes from data [26.926502862698168]
  We present a novel method to infer the underlying graph topology from available data. We also identify three-node interactions, referred to in the literature as second-order simplicial complexes (SCs) Experimental results on synthetic and real-world data showcase a superior performance for our approach compared to existing methods.
  arXiv  Detail & Related papers  (2023-12-16T22:02:20Z)
• Latent Graph Inference using Product Manifolds [0.0]
  We generalize the discrete Differentiable Graph Module (dDGM) for latent graph learning. Our novel approach is tested on a wide range of datasets, and outperforms the original dDGM model.
  arXiv  Detail & Related papers  (2022-11-26T22:13:06Z)
• Neural Graphical Models [2.6842860806280058]
  We introduce Neural Graphical Models (NGMs) to represent complex feature dependencies with reasonable computational costs. We capture the dependency structure between the features along with their complex function representations by using a neural network as a multi-task learning framework. NGMs can fit generic graph structures including directed, undirected and mixed-edge graphs as well as support mixed input data types.
  arXiv  Detail & Related papers  (2022-10-02T07:59:51Z)
• Learning Graph Structure from Convolutional Mixtures [119.45320143101381]
  We propose a graph convolutional relationship between the observed and latent graphs, and formulate the graph learning task as a network inverse (deconvolution) problem. In lieu of eigendecomposition-based spectral methods, we unroll and truncate proximal gradient iterations to arrive at a parameterized neural network architecture that we call a Graph Deconvolution Network (GDN) GDNs can learn a distribution of graphs in a supervised fashion, perform link prediction or edge-weight regression tasks by adapting the loss function, and they are inherently inductive.
  arXiv  Detail & Related papers  (2022-05-19T14:08:15Z)
• Effects of Graph Convolutions in Deep Networks [8.937905773981702]
  We present a rigorous theoretical understanding of the effects of graph convolutions in multi-layer networks. We show that a single graph convolution expands the regime of the distance between the means where multi-layer networks can classify the data. We provide both theoretical and empirical insights into the performance of graph convolutions placed in different combinations among the layers of a network.
  arXiv  Detail & Related papers  (2022-04-20T08:24:43Z)
• Graph Kernel Neural Networks [53.91024360329517]
  We propose to use graph kernels, i.e. kernel functions that compute an inner product on graphs, to extend the standard convolution operator to the graph domain. This allows us to define an entirely structural model that does not require computing the embedding of the input graph. Our architecture allows to plug-in any type of graph kernels and has the added benefit of providing some interpretability.
  arXiv  Detail & Related papers  (2021-12-14T14:48:08Z)
• Graph-Time Convolutional Neural Networks [9.137554315375919]
  We represent spatial relationships through product graphs with a first principle graph-time convolutional neural network (GTCNN) We develop a graph-time convolutional filter by following the shift-and-sumtemporal operator to learn higher-level features over the product graph. We develop a zero-pad pooling that preserves the spatial graph while reducing the number of active nodes and the parameters.
  arXiv  Detail & Related papers  (2021-03-02T14:03:44Z)
• Graph Contrastive Learning with Augmentations [109.23158429991298]
  We propose a graph contrastive learning (GraphCL) framework for learning unsupervised representations of graph data. We show that our framework can produce graph representations of similar or better generalizability, transferrability, and robustness compared to state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-10-22T20:13:43Z)
• Structural Landmarking and Interaction Modelling: on Resolution Dilemmas in Graph Classification [50.83222170524406]
  We study the intrinsic difficulty in graph classification under the unified concept of resolution dilemmas'' We propose SLIM'', an inductive neural network model for Structural Landmarking and Interaction Modelling.
  arXiv  Detail & Related papers  (2020-06-29T01:01:42Z)
• Scalable Deep Generative Modeling for Sparse Graphs [105.60961114312686]
  Existing deep neural methods require $Omega(n2)$ complexity by building up the adjacency matrix. We develop a novel autoregressive model, named BiGG, that utilizes this sparsity to avoid generating the full adjacency matrix. During training this autoregressive model can be parallelized with $O(log n)$ synchronization stages.
  arXiv  Detail & Related papers  (2020-06-28T04:37:57Z)
• Multipole Graph Neural Operator for Parametric Partial Differential Equations [57.90284928158383]
  One of the main challenges in using deep learning-based methods for simulating physical systems is formulating physics-based data. We propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.
  arXiv  Detail & Related papers  (2020-06-16T21:56:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.