Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning

By Michael Lutter, Christian Ritter, Jan Peters. International Conference on Learning Representations, 2019

495 citations recorded by the source corpus.

Deep learning has achieved astonishing results on many tasks with large amounts of data and generalization within the proximity of training data. For many important real-world applications, these requirements are unfeasible and additional prior knowledge on the task domain is required to overcome the resulting problems. In particular, learning physics models for model-based control requires robust extrapolation from fewer samples - often collected online in real-time - and model errors may lead to drastic damages of the system. Directly incorporating physical insight has enabled us to obtain a novel deep model learning approach that extrapolates well while requiring fewer samples. As a first example, we propose Deep Lagrangian Networks (DeLaN) as a deep network structure upon which Lagrangian Mechanics have been imposed. DeLaN can learn the equations of motion of a mechanical system (i.e., system dynamics) with a deep network efficiently while ensuring physical plausibility. The resulting DeLaN network performs very well at robot tracking control. The proposed method did not only outperform previous model learning approaches at learning speed but exhibits substantially improved and more robust extrapolation to novel trajectories and learns online in real-time

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e129e344083b307e005c5342ba49524d9981a420

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In Artificial Intelligence

In Statistical and Nonlinear Physics

Citations in the corpus

Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control (2019, background): “Lutter et al. (2019) and Gupta et al. (2019) leverage Lagrangian mechanics to learn the dynamics of kinematic structures from time-series data of position, velocity, and acceleration.”
Physics-aware Difference Graph Networks for Sparsely-Observed Dynamics (2020, background): “Lutter et al. (2019) introduced deep Lagrangian networks specialized to learn Lagrangian mechanics with learnable parameters.”
Meta Learning via Learned Loss (2019, background): “Here we follow the approach in [15], and attempt to learn the inverse dynamics via a neural network that predicts the inertia matrix Mθ(q).”
SAPIEN: A SimulAted Part-Based Interactive ENvironment (2020, background): “PyBullet [10], a real-time physics engine with Python interface, powers a series of projects focusing on robotics tasks [60, 27].”
Hamiltonian Neural Networks (2019, background): “Many of these works are domain-specific: the authors used domain knowledge about molecular dynamics [31, 38, 8, 28], quantum mechanics [36], or robotics [24] to help their models train faster or generalize.”
Lagrangian Neural Networks (2020, methodology): “DeLaN.”
Informed Machine Learning – A Taxonomy and Survey of Integrating Prior Knowledge into Learning Systems (2019, background): “This is currently tackled by online learning methods [48].”