History-informed Lagrangian Neural Networks

2026-08-13

AI Summary

Accurately predicting the long-term evolution of mechanical systems from position-only observations requires simultaneously inferring latent velocities and unknown physical parameters—a challenge that existing physics-informed models struggle with due to their reliance on full state information and limited adaptability to parameter variations. This work proposes HiLNN, the first Lagrangian neural network framework that integrates historical trajectory context via a recurrent encoder to adaptively reconstruct initial velocities and modulate the mass matrix, potential energy, and damping coefficients. Coupled with differentiable RK4 integration, HiLNN enables end-to-end training and achieves superior performance across conservative, dissipative, and time-varying parameter systems, delivering both high-precision long-horizon predictions and strict energy consistency.

Abstract

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.

Problem

• long-horizon forecasting
• position-only observations
• hidden velocities
• system parameter adaptation
• mechanical systems

Innovation

• History-informed Lagrangian Neural Networks
• position-only forecasting
• adaptive Lagrangian dynamics
• recurrent context encoding
• energy-consistent learning