Inspired by the numerical solution of ordinary differential equations, in
this paper we propose a novel Reservoir Computing (RC) model, called the Euler
State Network (EuSN). The presented approach makes use of forward Euler
discretization and antisymmetric recurrent matrices to design reservoir
dynamics that are both stable and non-dissipative by construction.
Our mathematical analysis shows that the resulting model is biased towards a
unitary effective spectral radius and zero local Lyapunov exponents,
intrinsically operating near to the edge of stability. Experiments on long-term
memory tasks show the clear superiority of the proposed approach over standard
RC models in problems requiring effective propagation of input information over
multiple time-steps. Furthermore, results on time-series classification
benchmarks indicate that EuSN is able to match (or even exceed) the accuracy of
trainable Recurrent Neural Networks, while retaining the training efficiency of
the RC family, resulting in up to $\approx$ 490-fold savings in computation
time and $\approx$ 1750-fold savings in energy consumption.

以数值解求解普通微分方程为灵感，本文提出了一种新颖的储层计算模型，名为欧拉状态网络（EuSN）。该方法使用向前欧拉离散化和反对称循环矩阵来设计储层动力学，这些动力学是通过构造稳定且无耗散的方式实现的。我们的数学分析表明，所得模型偏向于具有单位的有效谱半径和零的局部李雅普诺夫指数，本质上在稳定边缘附近运行。长期记忆任务的实验结果表明，所提出的方法在需要有效传播多个时间步骤的输入信息的问题上优于标准的 RC 模型。此外，时间序列分类基准测试结果表明，EuSN 能够达到（甚至超过）可训练循环神经网络的准确率，同时保留 RC 家族的训练效率，导致计算时间约为 490 倍的节省和能源消耗约为 1750 倍的节省。