基于历史信息的拉格朗日神经网络
History-informed Lagrangian Neural Networks
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中文总结 AI 辅助
该研究针对拉格朗日神经网络需完整状态输入、参数适应性差的问题，提出HiLNN，通过循环编码器提取历史上下文调制系统参数，经RK4推演优化，在多类系统上实现更优长时程预测精度与能量保持。
中文摘要 AI 辅助
仅从位置观测值预测力学系统的长时程演化是一项关键且困难的任务，因为必须同时推断隐藏的速度和轨迹特有的物理属性。尽管像拉格朗日神经网络（LNN）这类物理引导的神经网络能保证物理合理性，但它们通常需要完整的状态输入，且缺乏对变化系统参数的适应性。为突破这些局限，我们提出了基于历史信息的拉格朗日神经网络（HiLNN）。基于时间位置序列隐含编码潜在动力学的见解，HiLNN采用循环编码器从历史中提取潜在上下文，该上下文不仅能重构未观测的初始速度，还能自适应调制结构化拉格朗日系统的质量矩阵、势能和阻尼系数。通过利用可微分的RK4推演方案，整个流程在多步轨迹监督和能量一致性正则化下进行端到端优化。对保守系统、耗散系统和异质可变参数系统的实证评估表明，与最先进的基线相比，HiLNN在长时程预测精度上表现更优，且能保持精确的能量曲线。源代码可在此URL公开获取。
英文摘要
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.
发表机构
- College of Intelligent Systems Science and Engineering（智能系统科学与工程学院）
- Harbin Engineering University（哈尔滨工程大学）
机构由 AI 辅助整理，请以论文原文为准。
