Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domains
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Abstract (arXiv)
Deep learning has achieved great success in modeling dynamical systems, providing data-driven simulators to predict complex phenomena, even without known governing equations. However, existing models have two major limitations: their narrow focus on mechanical systems and their tendency to treat systems as monolithic. These limitations reduce their applicability to dynamical systems in other domains, such as electrical and hydraulic systems, and to coupled systems. To address these limitations, we propose Poisson-Dirac Neural Networks (PoDiNNs), a novel framework based on the Dirac structure that unifies the port-Hamiltonian and Poisson formulations from geometric mechanics. This framework enables a unified representation of various dynamical systems across multiple domains as well as their interactions and degeneracies arising from couplings. Our experiments demonstrate that PoDiNNs offer improved accuracy and interpretability in modeling unknown coupled dynamical systems from data.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 27 of its 48 references that are in the map. First posted on arXiv 15 Oct 2024.
Builds on
27 of 48 references.
References · 27
- 2017Attention Is All You Needcited by 60,361
- 2015Deep Residual Learning for Image Recognitioncited by 52,096
- 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 5,045
- 2018Neural Ordinary Differential Equationscited by 3,779
- 2016Density estimation using Real NVPcited by 2,042
- 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
- 2019Hamiltonian Neural Networkscited by 712
- 2017DGM: A deep learning algorithm for solving partial differential equationscited by 678
- 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 506
- 2016Input Convex Neural Networkscited by 414
- 2020Lagrangian Neural Networkscited by 398
- 2019Symplectic Recurrent Neural Networkscited by 150
15 more
- 2019Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamicscited by 134
- 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 105
- 2019Unconstrained Monotonic Neural Networkscited by 92
- 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 79
- 2021Evolutional Deep Neural Networkcited by 50
- 2020Learning Poisson systems and trajectories of autonomous systems via Poisson neural networkscited by 38
- 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
- 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
- 2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 18
- 2022Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networkscited by 18
- 2020Isometric Transformation Invariant and Equivariant Graph Convolutional Networkscited by 17
- 2022FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantitiescited by 12
- 2022Constants of motion networkcited by 10
- 2020SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systemscited by 6
- 2021KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Losscited by 2
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Citing papers per year: 2026: 1.
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