Lindblad-Inspired Multi-Timescale Reservoir Computing with Separable Rotation and Dissipation

2026-07-27

AI Summary

This work addresses the limitations of conventional reservoir computing, which struggles to independently control signal mixing and memory forgetting while lacking global stability guarantees. Inspired by the Lindblad equation, the authors introduce dissipative dynamics from open quantum systems into classical reservoirs, proposing a multi-timescale damped rotating reservoir. By employing orthogonal modes, the approach explicitly decouples rotation (for mixing) and dissipation (for forgetting). Stability of the echo state network is directly ensured through a tunable decay spectrum, eliminating the need for post-hoc spectral scaling. The method achieves state-of-the-art performance on the NARMA-20 and Lorenz-63 prediction tasks as well as linear memory benchmarks, demonstrating consistently competitive results across multiple standard datasets.

Abstract

Echo-state networks enable efficient temporal learning by fixing the recurrent dynamics and training only a linear readout. However, conventional reservoirs typically accommodate signal mixing, memory retention, and stability within a single random recurrent matrix. Existing structured designs improve topology, norm preservation, leakage, or depth, but generally do not provide separate modal control of reversible mixing and irreversible forgetting together with a direct global stability guarantee. We introduce a classical Lindblad-inspired multi-timescale reservoir that bridges open-system dynamical principles with structured state-space modeling. The recurrent operator is assembled from exactly discretized damped rotational modes, so rotation and decay become independent design variables governing phase mixing and memory loss. Orthogonal mode mixing preserves normality, while the decay spectrum directly determines the echo-state stability margin without post-hoc spectral-radius rescaling. We evaluate the method over ten aligned seeds against standard, leaky, deep, orthogonal, cycle, and next-generation reservoirs, together with a compact trained gated recurrent unit, across linear memory, nonlinear recurrence, chaotic forecasting, delayed logic, and real sensor calibration. Across the benchmark suite, the proposed reservoir achieves the best fixed-reservoir performance on bounded NARMA-20 and the lowest mean error on Lorenz-63, matches the strongest linear-memory result, and remains broadly competitive across broad range of benchmarks. Ablation studies show that rotation increases state diversity, whereas dissipation provides controlled forgetting and improves predictive conditioning. The resulting framework offers an interpretable recurrent architecture in which mixing, memory, and stability are explicit and independently tunable design variables.

Problem

• reservoir computing
• memory retention
• signal mixing
• stability
• dissipation

Innovation

• Lindblad-inspired reservoir
• separable rotation and dissipation
• multi-timescale dynamics
• echo-state stability
• structured state-space modeling