Thermodynamics-informed graph neural networks

• URL: http://arxiv.org/abs/2203.01874v1
• Date: Thu, 3 Mar 2022 17:30:44 GMT
• Title: Thermodynamics-informed graph neural networks
• Authors: Quercus Hern\'andez, Alberto Bad\'ias, Francisco Chinesta, El\'ias Cueto
• Abstract summary: We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting integration scheme. The first is achieved with Graph Neural Networks, which induces a non-Euclidean geometrical prior and permutation invariant node and edge update functions. The second bias is forced by learning the GENERIC structure of the problem, an extension of the Hamiltonian formalism, to model more general non-conservative dynamics.
• Score: 0.09332987715848712
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we present a deep learning method to predict the time evolution of dissipative dynamical systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting integration scheme. The first is achieved with Graph Neural Networks, which induces a non-Euclidean geometrical prior and permutation invariant node and edge update functions. The second bias is forced by learning the GENERIC structure of the problem, an extension of the Hamiltonian formalism, to model more general non-conservative dynamics. Several examples are provided in both Eulerian and Lagrangian description in the context of fluid and solid mechanics respectively.

Related papers

• Injecting Hamiltonian Architectural Bias into Deep Graph Networks for Long-Range Propagation [55.227976642410766]
  dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning. Motivated by this, we introduce (port-)Hamiltonian Deep Graph Networks. We reconcile under a single theoretical and practical framework both non-dissipative long-range propagation and non-conservative behaviors.
  arXiv  Detail & Related papers  (2024-05-27T13:36:50Z)
• Graph neural networks informed locally by thermodynamics [3.495246564946556]
  Thermodynamics-informed neural networks employ inductive biases for enforcement of thermodynamics. A metriplectic evolution of the system is assumed, which provides excellent results. A local version of the metriplectic biases has been developed, which avoids the aforementioned matrix assembly. We apply this framework for examples in the fields of solid and fluid mechanics.
  arXiv  Detail & Related papers  (2024-05-21T12:57:10Z)
• Advective Diffusion Transformers for Topological Generalization in Graph Learning [69.2894350228753]
  We show how graph diffusion equations extrapolate and generalize in the presence of varying graph topologies. We propose a novel graph encoder backbone, Advective Diffusion Transformer (ADiT), inspired by advective graph diffusion equations.
  arXiv  Detail & Related papers  (2023-10-10T08:40:47Z)
• 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)
• Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics [97.38308257547186]
  Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and material models. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. We introduce a new framework termed "Neural Constitutive Laws" (NCLaw) which utilizes a network architecture that strictly guarantees standard priors.
  arXiv  Detail & Related papers  (2023-04-27T17:42:24Z)
• E($3$) Equivariant Graph Neural Networks for Particle-Based Fluid Mechanics [2.1401663582288144]
  We demonstrate that equivariant graph neural networks have the potential to learn more accurate dynamic-interaction models. We benchmark two well-studied fluid flow systems, namely the 3D decaying Taylor-Green vortex and the 3D reverse Poiseuille flow.
  arXiv  Detail & Related papers  (2023-03-31T21:56:35Z)
• Geometric Knowledge Distillation: Topology Compression for Graph Neural Networks [80.8446673089281]
  We study a new paradigm of knowledge transfer that aims at encoding graph topological information into graph neural networks (GNNs) We propose Neural Heat Kernel (NHK) to encapsulate the geometric property of the underlying manifold concerning the architecture of GNNs. A fundamental and principled solution is derived by aligning NHKs on teacher and student models, dubbed as Geometric Knowledge Distillation.
  arXiv  Detail & Related papers  (2022-10-24T08:01:58Z)
• Equivariant Graph Mechanics Networks with Constraints [83.38709956935095]
  We propose Graph Mechanics Network (GMN) which is efficient, equivariant and constraint-aware. GMN represents, by generalized coordinates, the forward kinematics information (positions and velocities) of a structural object. Extensive experiments support the advantages of GMN compared to the state-of-the-art GNNs in terms of prediction accuracy, constraint satisfaction and data efficiency.
  arXiv  Detail & Related papers  (2022-03-12T14:22:14Z)

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.