A Riemannian Framework for Learning Reduced-order Lagrangian Dynamics

• URL: http://arxiv.org/abs/2410.18868v1
• Date: Thu, 24 Oct 2024 15:53:21 GMT
• Title: A Riemannian Framework for Learning Reduced-order Lagrangian Dynamics
• Authors: Katharina Friedl, Noémie Jaquier, Jens Lundell, Tamim Asfour, Danica Kragic,
• Abstract summary: We propose a novel geometric network architecture to learn physically-consistent reduced-order dynamic parameters. Our approach enables accurate long-term predictions of the high-dimensional dynamics of rigid and deformable systems.
• Score: 18.151022395233152
• License:
• Abstract: By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally increases with the system dimensionality, requiring larger datasets, more complex deep networks, and significant computational effort. We propose a novel geometric network architecture to learn physically-consistent reduced-order dynamic parameters that accurately describe the original high-dimensional system behavior. This is achieved by building on recent advances in model-order reduction and by adopting a Riemannian perspective to jointly learn a structure-preserving latent space and the associated low-dimensional dynamics. Our approach enables accurate long-term predictions of the high-dimensional dynamics of rigid and deformable systems with increased data efficiency by inferring interpretable and physically plausible reduced Lagrangian models.

Related papers

• eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modeling [9.52474299688276]
  We introduce a low-rank structured variational autoencoder framework for nonlinear state-space graphical models. We show that our approach consistently demonstrates the ability to learn a more predictive generative model.
  arXiv  Detail & Related papers  (2024-03-03T02:19:49Z)
• Semi-Supervised Learning of Dynamical Systems with Neural Ordinary Differential Equations: A Teacher-Student Model Approach [10.20098335268973]
  TS-NODE is the first semi-supervised approach to modeling dynamical systems with NODE. We show significant performance improvements over a baseline Neural ODE model on multiple dynamical system modeling tasks.
  arXiv  Detail & Related papers  (2023-10-19T19:17:12Z)
• ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
  This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling. We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
  arXiv  Detail & Related papers  (2023-02-11T21:07:30Z)
• Physics guided neural networks for modelling of non-linear dynamics [0.0]
  This work demonstrates that injection of partially known information at an intermediate layer in a deep neural network can improve model accuracy, reduce model uncertainty, and yield improved convergence during the training. The value of these physics-guided neural networks has been demonstrated by learning the dynamics of a wide variety of nonlinear dynamical systems represented by five well-known equations in nonlinear systems theory.
  arXiv  Detail & Related papers  (2022-05-13T19:06:36Z)
• Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning [9.36739413306697]
  Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. We use deep learning to identify low-dimensional embeddings for high-fidelity dynamical systems.
  arXiv  Detail & Related papers  (2021-11-25T10:09:00Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• Sparse Flows: Pruning Continuous-depth Models [107.98191032466544]
  We show that pruning improves generalization for neural ODEs in generative modeling. We also show that pruning finds minimal and efficient neural ODE representations with up to 98% less parameters compared to the original network, without loss of accuracy.
  arXiv  Detail & Related papers  (2021-06-24T01:40:17Z)
• Continuous-in-Depth Neural Networks [107.47887213490134]
  We first show that ResNets fail to be meaningful dynamical in this richer sense. We then demonstrate that neural network models can learn to represent continuous dynamical systems. We introduce ContinuousNet as a continuous-in-depth generalization of ResNet architectures.
  arXiv  Detail & Related papers  (2020-08-05T22:54:09Z)
• Limited-angle tomographic reconstruction of dense layered objects by dynamical machine learning [68.9515120904028]
  Limited-angle tomography of strongly scattering quasi-transparent objects is a challenging, highly ill-posed problem. Regularizing priors are necessary to reduce artifacts by improving the condition of such problems. We devised a recurrent neural network (RNN) architecture with a novel split-convolutional gated recurrent unit (SC-GRU) as the building block.
  arXiv  Detail & Related papers  (2020-07-21T11:48:22Z)
• Hyperbolic Neural Networks++ [66.16106727715061]
  We generalize the fundamental components of neural networks in a single hyperbolic geometry model, namely, the Poincar'e ball model. Experiments show the superior parameter efficiency of our methods compared to conventional hyperbolic components, and stability and outperformance over their Euclidean counterparts.
  arXiv  Detail & Related papers  (2020-06-15T08:23:20Z)
• Deep learning of contagion dynamics on complex networks [0.0]
  We propose a complementary approach based on deep learning to build effective models of contagion dynamics on networks. By allowing simulations on arbitrary network structures, our approach makes it possible to explore the properties of the learned dynamics beyond the training data. Our results demonstrate how deep learning offers a new and complementary perspective to build effective models of contagion dynamics on networks.
  arXiv  Detail & Related papers  (2020-06-09T17:18:34Z)

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.