用拉普拉斯神经网络解耦外部驱动系统，提升建模精度与泛化能力。
Breaking Free: Decoupling Forced Systems with Laplace Neural Networks
- 基于拉普拉斯变换分解系统内动力、外部输入和初值，实现可解释建模。
- 在8个基准数据集上优于现有方法，尤其对新输入具有更强鲁棒性。
- 适合需要快速适配新输入的场景，如控制器调整与长期预测。
建模外部输入驱动的动力系统在工程、金融和自然科学等领域至关重要。本文提出Laplace-Net，一种解耦的、无需求解器的神经框架，用于学习受迫且具备时延感知能力的系统。该方法基于拉普拉斯变换，将系统内部动力、外部输入和初始值分解为已知理论概念，增强可解释性。由于系统可快速重新训练或微调以适应新激励信号，该框架具有高可迁移性，适用于控制器自适应与长时程预测等场景。在8个基准数据集（涵盖线性、非线性及延迟系统）上的实验表明，该方法在准确性与鲁棒性方面均优于当前最优方法，尤其在处理复杂且未见过的输入时表现更优。
原文摘要 · Abstract (English)
Modelling forced dynamical systems - where an external input drives the system state - is critical across diverse domains such as engineering, finance, and the natural sciences. In this work, we propose Laplace-Net, a decoupled, solver-free neural framework for learning forced and delay-aware systems. It leverages a Laplace transform-based approach to decompose internal dynamics, external inputs, and initial values into established theoretical concepts, enhancing interpretability. Laplace-Net promotes transferability since the system can be rapidly re-trained or fine-tuned for new forcing signals, providing flexibility in applications ranging from controller adaptation to long-horizon forecasting. Experimental results on eight benchmark datasets - including linear, non-linear, and delayed systems - demonstrate the method's improved accuracy and robustness compared to state-of-the-art approaches, particularly in handling complex and previously unseen inputs.
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