用随机非线性投影实现可扩展的动力系统建模，噪声还能当正则化。
Next-Generation Reservoir Computing for Dynamical Inference
- 用时间延迟嵌入输入的伪随机非线性投影，自由控制特征维度。
- 在部分与含噪数据上重建吸引子并估计分岔图，长期预测稳定。
- 小噪声训练提升稳定性，适合数字孪生与代理建模场景。
我们提出一种简单且可扩展的下一代水库计算（NGRC）方法，用于从时间序列数据建模动力系统。该方法采用时间延迟嵌入输入的伪随机非线性投影，使特征空间维度可独立于观测规模选择，为多项式基NGRC提供灵活替代方案。在基准任务中，包括吸引子重构与分岔图估计，均使用部分与含噪测量数据进行验证。结果显示，训练时少量测量噪声可作为有效正则化项，显著提升长期自主预测的稳定性，优于标准回归。所有测试中模型在长时间滚动预测中保持稳定，并能泛化至训练数据之外。该框架支持预测期间对系统状态的显式控制，使其成为代理建模与数字孪生应用的理想候选。
原文摘要 · Abstract (English)
We present a simple and scalable implementation of next-generation reservoir computing (NGRC) for modeling dynamical systems from time-series data. The method uses a pseudorandom nonlinear projection of time-delay embedded inputs, allowing the feature-space dimension to be chosen independently of the observation size and offering a flexible alternative to polynomial-based NGRC projections. We demonstrate the approach on benchmark tasks, including attractor reconstruction and bifurcation diagram estimation, using partial and noisy measurements. We further show that small amounts of measurement noise during training act as an effective regularizer, improving long-term autonomous stability compared to standard regression alone. Across all tests, the models remain stable over long rollouts and generalize beyond the training data. The framework offers explicit control of system state during prediction, and these properties make NGRC a natural candidate for applications such as surrogate modeling and digital-twin applications.
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