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.

翻译：受常微分方程数值解的启发，本文提出了一种新型储层计算模型，称为欧拉状态网络（EuSN）。该方法利用前向欧拉离散化和反对称循环矩阵设计储层动态，使其在结构上兼具稳定性和无耗散性。数学分析表明，该模型倾向于实现单位有效谱半径和零局部李雅普诺夫指数，本质上在稳定性边界附近运行。在长期记忆任务上的实验显示，当需要跨多个时间步有效传播输入信息时，所提方法明显优于标准储层计算模型。此外，时间序列分类基准测试结果表明，EuSN能够达到（甚至超越）可训练循环神经网络的准确性，同时保留储层计算家族的训练效率，计算时间节省约490倍，能耗节省约1750倍。