Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systems
- URL: http://arxiv.org/abs/2209.10740v2
- Date: Sat, 15 Jun 2024 13:23:00 GMT
- Title: Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systems
- Authors: Suresh Bishnoi, Ravinder Bhattoo, Sayan Ranu, N. M. Anoop Krishnan,
- Abstract summary: We present a graph based neural ODE, GNODE, to learn the time evolution of dynamical systems.
We show that, similar to LNN and HNN, encoding the constraints explicitly can significantly improve the training efficiency and performance of GNODE.
We demonstrate that inducing these biases can enhance the performance of model by orders of magnitude in terms of both energy violation and rollout error.
- Score: 19.634451472032733
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Neural networks with physics based inductive biases such as Lagrangian neural networks (LNN), and Hamiltonian neural networks (HNN) learn the dynamics of physical systems by encoding strong inductive biases. Alternatively, Neural ODEs with appropriate inductive biases have also been shown to give similar performances. However, these models, when applied to particle based systems, are transductive in nature and hence, do not generalize to large system sizes. In this paper, we present a graph based neural ODE, GNODE, to learn the time evolution of dynamical systems. Further, we carefully analyse the role of different inductive biases on the performance of GNODE. We show that, similar to LNN and HNN, encoding the constraints explicitly can significantly improve the training efficiency and performance of GNODE significantly. Our experiments also assess the value of additional inductive biases, such as Newtons third law, on the final performance of the model. We demonstrate that inducing these biases can enhance the performance of model by orders of magnitude in terms of both energy violation and rollout error. Interestingly, we observe that the GNODE trained with the most effective inductive biases, namely MCGNODE, outperforms the graph versions of LNN and HNN, namely, Lagrangian graph networks (LGN) and Hamiltonian graph networks (HGN) in terms of energy violation error by approx 4 orders of magnitude for a pendulum system, and approx 2 orders of magnitude for spring systems. These results suggest that competitive performances with energy conserving neural networks can be obtained for NODE based systems by inducing appropriate inductive biases.
Related papers
- Graph Neural Reaction Diffusion Models [14.164952387868341]
We propose a novel family of Reaction GNNs based on neural RD systems.
We discuss the theoretical properties of our RDGNN, its implementation, and show that it improves or offers competitive performance to state-of-the-art methods.
arXiv Detail & Related papers (2024-06-16T09:46:58Z) - Label Deconvolution for Node Representation Learning on Large-scale
Attributed Graphs against Learning Bias [75.44877675117749]
We propose an efficient label regularization technique, namely Label Deconvolution (LD), to alleviate the learning bias by a novel and highly scalable approximation to the inverse mapping of GNNs.
Experiments demonstrate LD significantly outperforms state-of-the-art methods on Open Graph datasets Benchmark.
arXiv Detail & Related papers (2023-09-26T13:09:43Z) - SEGNO: Generalizing Equivariant Graph Neural Networks with Physical
Inductive Biases [66.61789780666727]
We show how the second-order continuity can be incorporated into GNNs while maintaining the equivariant property.
We also offer theoretical insights into SEGNO, highlighting that it can learn a unique trajectory between adjacent states.
Our model yields a significant improvement over the state-of-the-art baselines.
arXiv Detail & Related papers (2023-08-25T07:15:58Z) - Graph Neural Network-Inspired Kernels for Gaussian Processes in
Semi-Supervised Learning [4.644263115284322]
Graph neural networks (GNNs) emerged recently as a promising class of models for graph-structured data in semi-supervised learning.
We introduce this inductive bias into GPs to improve their predictive performance for graph-structured data.
We show that these graph-based kernels lead to competitive classification and regression performance, as well as advantages in time, compared with the respective GNNs.
arXiv Detail & Related papers (2023-02-12T01:07:56Z) - Unravelling the Performance of Physics-informed Graph Neural Networks
for Dynamical Systems [5.787429262238507]
We evaluate the performance of graph neural networks (GNNs) and their variants with explicit constraints and different architectures.
Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance.
All the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.
arXiv Detail & Related papers (2022-11-10T12:29:30Z) - Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a
Polynomial Net Study [55.12108376616355]
The study on NTK has been devoted to typical neural network architectures, but is incomplete for neural networks with Hadamard products (NNs-Hp)
In this work, we derive the finite-width-K formulation for a special class of NNs-Hp, i.e., neural networks.
We prove their equivalence to the kernel regression predictor with the associated NTK, which expands the application scope of NTK.
arXiv Detail & Related papers (2022-09-16T06:36:06Z) - Momentum Diminishes the Effect of Spectral Bias in Physics-Informed
Neural Networks [72.09574528342732]
Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs)
They often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias.
In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under gradient descent with momentum (SGDM)
arXiv Detail & Related papers (2022-06-29T19:03:10Z) - Deconstructing the Inductive Biases of Hamiltonian Neural Networks [41.37309202965647]
Physics-inspired neural networks (NNs) dramatically outperform other learned dynamics models by leveraging strong inductive biases.
We show that, contrary to conventional wisdom, the improved generalization of HNNs is the result of modeling acceleration directly.
We show that by relaxing the inductive biases of these models, we can match or exceed performance on energy-conserving systems while dramatically improving performance on practical, non-conservative systems.
arXiv Detail & Related papers (2022-02-10T05:05:38Z) - Continuous-Depth Neural Models for Dynamic Graph Prediction [16.89981677708299]
We introduce the framework of continuous-depth graph neural networks (GNNs)
Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs.
Results prove the effectiveness of the proposed models across applications, such as traffic forecasting or prediction in genetic regulatory networks.
arXiv Detail & Related papers (2021-06-22T07:30:35Z) - The Surprising Power of Graph Neural Networks with Random Node
Initialization [54.4101931234922]
Graph neural networks (GNNs) are effective models for representation learning on relational data.
Standard GNNs are limited in their expressive power, as they cannot distinguish beyond the capability of the Weisfeiler-Leman graph isomorphism.
In this work, we analyze the expressive power of GNNs with random node (RNI)
We prove that these models are universal, a first such result for GNNs not relying on computationally demanding higher-order properties.
arXiv Detail & Related papers (2020-10-02T19:53:05Z) - Binarized Graph Neural Network [65.20589262811677]
We develop a binarized graph neural network to learn the binary representations of the nodes with binary network parameters.
Our proposed method can be seamlessly integrated into the existing GNN-based embedding approaches.
Experiments indicate that the proposed binarized graph neural network, namely BGN, is orders of magnitude more efficient in terms of both time and space.
arXiv Detail & Related papers (2020-04-19T09:43:14Z)
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.