mlsanityData to 14 Oct 2026

History-informed Lagrangian Neural Networks

arXiv 2608.13215 ↗First posted 13 Aug 2026cs.LGcited by 1

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Abstract (arXiv)

Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously. Although physics-guided neural networks like Lagrangian Neural Networks (LNNs) guarantee physical plausibility, they generally require complete state inputs and lack adaptability to changing system parameters. To break these limitations, we introduce History-informed Lagrangian Neural Networks (HiLNN). Grounded in the insight that temporal position sequences implicitly encode underlying dynamics, HiLNN employs a recurrent encoder to extract a latent context from history. This context not only reconstructs the unobserved initial velocity but also adaptively modulates the mass matrix, potential energy, and damping coefficients of a structured Lagrangian system. By leveraging a differentiable RK4 rollout scheme, the entire pipeline is optimized end-to-end under multi-step trajectory supervision and energy-consistency regularization. Empirical evaluations across conservative, dissipative, and heterogeneous variable-parameter systems show that HiLNN delivers superior long-term prediction accuracy and maintains precise energy profiles compared to state-of-the-art baselines. The source code is publicly available at https://github.com/yingtian22/History-informed-LNN.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 18 of its 22 references that are in the map. First posted on arXiv 13 Aug 2026.

Builds on

18 of 22 references.

References · 18

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  5. 2020Lagrangian Neural Networkscited by 398
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  7. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 212
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6 more
  1. 2025Frequency-Aligned Knowledge Distillation for Lightweight Spatiotemporal Forecastingcited by 55
  2. 2022Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separatelycited by 47
  3. 2026Distilling Time Series Foundation Models for Efficient Forecastingcited by 11
  4. 2022Recognition Models to Learn Dynamics from Partial Observations with Neural ODEscited by 8
  5. 2025DDTime: Dataset Distillation with Spectral Alignment and Information Bottleneck for Time-Series Forecastingcited by 7
  6. 2025Floating-Body Hydrodynamic Neural Networkscited by 2

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