Next-Generation Reservoir Computing for Dynamical Inference

Abstract

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.

12 pages, 12 figures; published version

References in corpus (12)

• Recent Advances in Physical Reservoir Computing: A Review
• Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data
• Next Generation Reservoir Computing
• Attractor Reconstruction by Machine Learning
• Reservoir computing with a single time-delay autonomous Boolean node
• Phase-amplitude descriptions of neural oscillator models
• Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem
• Inferring the dynamics of oscillatory systems using recurrent neural networks
• Inferring the phase response curve from observation of a continuously perturbed oscillator
• Inferring oscillator's phase and amplitude response from a scalar signal exploiting test stimulation
• How more data can hurt: Instability and regularization in next-generation reservoir computing
• Limits of Learning Dynamical Systems