Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data

Zhong, Yaofeng Desmond; Dey, Biswadip; Chakraborty, Amit

doi:10.48550/arxiv.2012.02334

Cited by 4 publications

(5 citation statements)

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“…In all experiments we set the value of T to 60. For more fair comparison across datasets, as proposed in Zhong et al [23]…”

Section: A2 Mean Squared Error Resultsmentioning

confidence: 99%

“…On the other hand, the Lagrangian formulation requires calculating second-order derivatives, which can be computationally expensive and can lead to instabilities in model training. Zhong et al [23] report comparable results with both formulations for training on state space data, however no such comparison exists when it comes to learning from high dimensional observations. Therefore, it is still an open question which, if any, of the two formalisms is better for learning in this latter setting.…”

Section: Systematising Models With Physical Priorsmentioning

confidence: 99%

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Which priors matter? Benchmarking models for learning latent dynamics

Botev¹,

Jaegle²,

Wirnsberger³

et al. 2021

Preprint

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Learning dynamics is at the heart of many important applications of machine learning (ML), such as robotics and autonomous driving. In these settings, ML algorithms typically need to reason about a physical system using high dimensional observations, such as images, without access to the underlying state. Recently, several methods have proposed to integrate priors from classical mechanics into ML models to address the challenge of physical reasoning from images. In this work, we take a sober look at the current capabilities of these models. To this end, we introduce a suite consisting of 17 datasets with visual observations based on physical systems exhibiting a wide range of dynamics. We conduct a thorough and detailed comparison of the major classes of physically inspired methods alongside several strong baselines. While models that incorporate physical priors can often learn latent spaces with desirable properties, our results demonstrate that these methods fail to significantly improve upon standard techniques. Nonetheless, we find that the use of continuous and time-reversible dynamics benefits models of all classes.35th Conference on Neural Information Processing Systems (NeurIPS 2021) Track on Datasets and Benchmarks.

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“…In all experiments we set the value of T to 60. For more fair comparison across datasets, as proposed in Zhong et al [23]…”

Section: A2 Mean Squared Error Resultsmentioning

confidence: 99%

Section: Systematising Models With Physical Priorsmentioning

confidence: 99%

Which priors matter? Benchmarking models for learning latent dynamics

Botev¹,

Jaegle²,

Wirnsberger³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…[72] further introduced a meta-learning approach in HNN to find the structure of the Hamiltonian that can be adapted quickly to a new instance of a physical system. [142] benchmark recent energy-conserving neural network models based on Lagrangian/Hamiltonian dynamics on four different physical systems.…”

Section: Physics-guided Loss Functions and Regularizationmentioning

confidence: 99%

Physics-Guided Deep Learning for Dynamical Systems: A Survey

Wang¹,

Yu²

2021

Preprint

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Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are interpretable but rely on rigid assumptions. And the direct numerical approximation is usually computationally intensive, requiring significant computational resources and expertise. While deep learning (DL) provides novel alternatives for efficiently recognizing complex patterns and emulating nonlinear dynamics, it does not necessarily obey the governing laws of physical systems, nor do they generalize well across different systems. Thus, the study of physics-guided DL emerged and has gained great progress. It aims to take the best from both physics-based modeling and state-of-the-art DL models to better solve scientific problems. In this paper, we provide a structured overview of existing methodologies of integrating prior physical knowledge or physics-based modeling into DL and discuss the emerging opportunities.

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“…Other relevant works attempting to shed light on the link between port-Hamiltonian modeling, energy based methods and optimal/learning control can be found in the excellent survey paper [40] (and references therein), where adaptive and iterative learning approach are discussed. Moreover, [41] provides a comprehensive comparison of different energybased machine learning approaches. In [42] reinforcement learning (RL) techniques are applied to port-Hamiltonian systems.…”

Section: Related Workmentioning

confidence: 99%

Optimal Energy Shaping via Neural Approximators

Massaroli¹,

Poli²,

Califano³

et al. 2021

Preprint

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We introduce optimal energy shaping as an enhancement of classical passivity-based control methods. A promising feature of passivity theory, alongside stability, has traditionally been claimed to be intuitive performance tuning along the execution of a given task. However, a systematic approach to adjust performance within a passive control framework has yet to be developed, as each method relies on few and problemspecific practical insights. Here, we cast the classic energyshaping control design process in an optimal control framework; once a task-dependent performance metric is defined, an optimal solution is systematically obtained through an iterative procedure relying on neural networks and gradient-based optimization. The proposed method is validated on state-regulation tasks.

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Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data

Cited by 4 publications

References 0 publications

Which priors matter? Benchmarking models for learning latent dynamics

Which priors matter? Benchmarking models for learning latent dynamics

Physics-Guided Deep Learning for Dynamical Systems: A Survey

Optimal Energy Shaping via Neural Approximators

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