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.
Tianshuo Zhang, Xianglei Xing, Wenzhe Zhai et al.· 0 citations
Accurate footprint image segmentation is challenging in forensic applications because fine anatomical structures, weak boundaries, and background interference can degrade segmentation performance. This study presents a task-oriented generative adversarial network (GAN)-based framework for forensic footprint image segmentation. Channel Prior Convolutional Attention (CPCA) modules are integrated into the decoder stages of the generator to recalibrate fused encoder–decoder features and preserve fine details in the toe, arch, and heel regions. In addition, a dual-branch discriminator processes image–mask pairs at the original and downsampled scales, providing complementary constraints on local boundary details and global footprint morphology. The framework is trained with a least-squares adversarial loss and a binary cross-entropy (BCE)–Dice segmentation loss. Experiments on the self-collected aFoot_2025 dataset show that the proposed framework achieves an IoU of 0.9448 and a Dice coefficient of 0.9713, outperforming the evaluated baseline and attention-based alternatives. Under the evaluated synthetic Gaussian-noise settings, the proposed method retained relatively stable segmentation performance. Furthermore, an exploratory footprint-based height-prediction analysis showed modestly lower prediction errors than the baseline GAN. These findings indicate that, under the controlled acquisition conditions of the aFoot_2025 dataset, CPCA-based feature calibration and dual-scale discrimination may improve segmentation-mask quality and provide a possible benefit for subsequent anthropometric analysis.