Variational Integrator Graph Networks for Learning Energy Conserving Dynamical Systems

• URL: http://arxiv.org/abs/2004.13688v2
• Date: Fri, 16 Jul 2021 16:06:53 GMT
• Title: Variational Integrator Graph Networks for Learning Energy Conserving Dynamical Systems
• Authors: Shaan Desai, Marios Mattheakis and Stephen Roberts
• Abstract summary: Recent advances show that neural networks embedded with physics-informed priors significantly outperform vanilla neural networks in learning. We propose a novel method that unifies the strengths of existing approaches by combining an energy constraint, high-order variational, symplectic variational and graph neural networks.
• Score: 1.2522889958051286
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent advances show that neural networks embedded with physics-informed priors significantly outperform vanilla neural networks in learning and predicting the long term dynamics of complex physical systems from noisy data. Despite this success, there has only been a limited study on how to optimally combine physics priors to improve predictive performance. To tackle this problem we unpack and generalize recent innovations into individual inductive bias segments. As such, we are able to systematically investigate all possible combinations of inductive biases of which existing methods are a natural subset. Using this framework we introduce Variational Integrator Graph Networks - a novel method that unifies the strengths of existing approaches by combining an energy constraint, high-order symplectic variational integrators, and graph neural networks. We demonstrate, across an extensive ablation, that the proposed unifying framework outperforms existing methods, for data-efficient learning and in predictive accuracy, across both single and many-body problems studied in recent literature. We empirically show that the improvements arise because high order variational integrators combined with a potential energy constraint induce coupled learning of generalized position and momentum updates which can be formalized via the Partitioned Runge-Kutta method.

Related papers

• Deep Learning Through A Telescoping Lens: A Simple Model Provides Empirical Insights On Grokking, Gradient Boosting & Beyond [61.18736646013446]
  In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network. Across three case studies, we illustrate how it can be applied to derive new empirical insights on a diverse range of prominent phenomena.
  arXiv  Detail & Related papers  (2024-10-31T22:54:34Z)
• Dynamic Post-Hoc Neural Ensemblers [55.15643209328513]
  In this study, we explore employing neural networks as ensemble methods. Motivated by the risk of learning low-diversity ensembles, we propose regularizing the model by randomly dropping base model predictions. We demonstrate this approach lower bounds the diversity within the ensemble, reducing overfitting and improving generalization capabilities.
  arXiv  Detail & Related papers  (2024-10-06T15:25:39Z)
• Demolition and Reinforcement of Memories in Spin-Glass-like Neural Networks [0.0]
  The aim of this thesis is to understand the effectiveness of Unlearning in both associative memory models and generative models. The selection of structured data enables an associative memory model to retrieve concepts as attractors of a neural dynamics with considerable basins of attraction. A novel regularization technique for Boltzmann Machines is presented, proving to outperform previously developed methods in learning hidden probability distributions from data-sets.
  arXiv  Detail & Related papers  (2024-03-04T23:12:42Z)
• Learning Latent Dynamics via Invariant Decomposition and (Spatio-)Temporal Transformers [0.6767885381740952]
  We propose a method for learning dynamical systems from high-dimensional empirical data. We focus on the setting in which data are available from multiple different instances of a system. We study behaviour through simple theoretical analyses and extensive experiments on synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-06-21T07:52:07Z)
• Newton-Cotes Graph Neural Networks: On the Time Evolution of Dynamic Systems [49.50674348130157]
  We propose a new approach to predict the integration based on several velocity estimations with Newton-Cotes formulas. Experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-05-24T02:23:00Z)
• 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)
• Stretched and measured neural predictions of complex network dynamics [2.1024950052120417]
  Data-driven approximations of differential equations present a promising alternative to traditional methods for uncovering a model of dynamical systems. A recently employed machine learning tool for studying dynamics is neural networks, which can be used for data-driven solution finding or discovery of differential equations. We show that extending the model's generalizability beyond traditional statistical learning theory limits is feasible.
  arXiv  Detail & Related papers  (2023-01-12T09:44:59Z)
• EINNs: Epidemiologically-Informed Neural Networks [75.34199997857341]
  We introduce a new class of physics-informed neural networks-EINN-crafted for epidemic forecasting. We investigate how to leverage both the theoretical flexibility provided by mechanistic models as well as the data-driven expressability afforded by AI models.
  arXiv  Detail & Related papers  (2022-02-21T18:59:03Z)
• Gradient Starvation: A Learning Proclivity in Neural Networks [97.02382916372594]
  Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks.
  arXiv  Detail & Related papers  (2020-11-18T18:52:08Z)
• 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)
• Physics-based polynomial neural networks for one-shot learning of dynamical systems from one or a few samples [0.0]
  The paper describes practical results on both a simple pendulum and one of the largest worldwide X-ray source. It is demonstrated in practice that the proposed approach allows recovering complex physics from noisy, limited, and partial observations.
  arXiv  Detail & Related papers  (2020-05-24T09:27:10Z)

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.