Learnijoy
ResearchAI ResearchAI Engineering & DevTools

Bayesian Filtering Learns Lagrangian Dynamics from Noisy Data

Kundan Kumar, Shreya Das, Simo S\"arkk\"a· July 1, 2026 View original

Summary

This paper introduces a Bayesian filtering method to learn physical system dynamics from noisy, partial measurements, modeling unknown external forces as Gaussian noise within a Lagrangian mechanics framework. It uses neural networks to parameterize kinetic and potential energies, jointly learning parameters and states via maximum-likelihood with Gaussian-approximation filters.

Researchers have developed a new approach for understanding the underlying physics of systems, even when the available data is incomplete and contains errors. Their method leverages Bayesian filtering, a technique for estimating unknown variables, to infer the Lagrangian dynamics of a physical system. This involves representing the system's kinetic and potential energies using neural networks, similar to Lagrangian neural networks, but crucially, it treats unmodeled external forces as random noise. This framework transforms the problem into a continuous-time stochastic state-space model. The neural network parameters and the system's actual states are then learned simultaneously using a maximum-likelihood estimation process, enhanced by Gaussian-approximation-based Bayesian filters. The effectiveness of this novel technique has been demonstrated through simulations involving classic physics problems like pendulums and Duffing oscillators, showing improved performance compared to traditional Lagrangian neural networks and other approximate Bayesian filters.

Why it matters

Professionals in robotics, control systems, and predictive maintenance can use this to build more robust and accurate models of complex physical systems, even with imperfect sensor data.

How to implement this in your domain

  1. 1Evaluate existing sensor data pipelines for noise characteristics and data completeness.
  2. 2Explore integrating Bayesian filtering techniques into current system identification or digital twin initiatives.
  3. 3Pilot the use of neural networks to parameterize energy functions for specific physical assets.
  4. 4Develop validation metrics to compare the accuracy of learned dynamics against traditional modeling approaches.

Who benefits

RoboticsAerospaceManufacturingAutomotiveEnergy

Key takeaways

  • A new Bayesian filtering method learns physical system dynamics from noisy, partial data.
  • It models unknown external forces as white Gaussian noise within a Lagrangian framework.
  • Neural networks parameterize kinetic and potential energies, with joint learning of parameters and states.
  • The approach shows improved performance over conventional Lagrangian neural networks in simulations.

Original post by Kundan Kumar, Shreya Das, Simo S\"arkk\"a

"arXiv:2606.31137v1 Announce Type: new Abstract: 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…"

View on X

Originally posted by Kundan Kumar, Shreya Das, Simo S\"arkk\"a on X · view source

Want to go deeper?

Turn these trends into skills with Learnijoy's hands-on AI & tech courses.

Explore courses

More in AI Research

AI ResearchAI Engineering & DevTools

Optimizers Control LLM Emergent Misalignment Severity

This research reveals that the choice of optimizer significantly influences the severity of emergent misalignment (EM) in large language models, often more so than model size. It introduces spectral regularization as a method to mitigate EM, particularly for prone adaptive optimizers like Adam and Lion.

Jason R. Brown, Patrick Leask, Lev McKinneyJul 1, 2026
AI Engineering & DevToolsAI Research

Measuring Neural Network Robustness to Input Noise

This paper investigates neural network robustness to random input noise, proposing a simple and efficient black-box measure that provides a high-probability upper bound on the mean squared error. It also introduces "robustness curves" for analyzing robustness within and across datasets.

Mark Levene, Martyn HarrisJul 1, 2026
AI ResearchAI Engineering & DevTools

SDEs for Generative ML: A Variational Introduction

This paper offers a self-contained introduction to stochastic differential equations (SDEs) for generative machine learning, covering their probabilistic framework, the Fokker-Planck equation, and the variational lower bound (ELBO). It discusses how diffusion models, score matching, and flow matching can be viewed as specific parameterizations of a general variational approach.

Ole Winther, Paul Jeha, Sander Dieleman, Andriy Mnih, Manfred Opper, Andrea DittadiJul 1, 2026