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A Bayesian Filtering Approach for Learning Lagrangian Dynamics from Noisy Measurements

arXiv 2606.31137 ↗First posted 30 Jun 2026cs.LG eess.SPcited by 0

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Abstract (arXiv)

This paper proposes a Bayesian filtering-based approach for learning the dynamics of a physical system from partial, noisy measurements. We model the system dynamics using a Lagrangian mechanics formulation. As in Lagrangian neural networks (LNNs), we parameterize the kinetic and potential energies with neural networks. The unknown external forces in the Lagrangian formulation are modeled as white Gaussian noise. The corresponding Euler--Lagrange equations then yield a continuous-time stochastic state-space model (SSM) that describes the system dynamics. The neural network parameters and system states are then jointly learned via a maximum-likelihood method using Gaussian-approximation-based Bayesian filters. The effectiveness of the proposed method is demonstrated on pendulum and Duffing oscillator examples, and its performance is compared with conventional LNNs and with approximate Bayesian filters using known system models.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 11 of its 31 references that are in the map. First posted on arXiv 30 Jun 2026.

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References · 11

  1. 2019Hamiltonian Neural Networkscited by 712
  2. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  3. 2020Lagrangian Neural Networkscited by 398
  4. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 212
  5. 2019Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systemscited by 33
  6. 2021Combining Physics and Deep Learning to learn Continuous-Time Dynamics Modelscited by 20
  7. 2015Computationally Efficient Bayesian Learning of Gaussian Process State Space Modelscited by 18
  8. 2015Sigma-Point Filtering and Smoothing Based Parameter Estimation in Nonlinear Dynamic Systemscited by 6
  9. 2015Nonlinear State Space Model Identification Using a Regularized Basis Function Expansioncited by 2
  10. 2019The Use of Gaussian Processes in System Identificationcited by 2
  11. 2026Integrating Lagrangian Neural Networks into the Dyna Framework for Reinforcement Learningcited by 1

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