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 introduced 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 unitary effective spectral radius and zero local Lyapunov exponents, intrinsically operating at the edge of stability. Experiments on synthetic tasks indicate the marked superiority of the proposed approach, compared to standard RC models, in tasks requiring long-term memorization skills. Furthermore, results on real-world time series classification benchmarks point out that EuSN is capable of matching (or even surpassing) the level of accuracy of trainable Recurrent Neural Networks, while allowing up to 100-fold savings in computation time and energy consumption.

翻译：在普通差异方程式的数字解决方案的启发下,我们在本文件中提出了一个名为Euler国家网络(Eusnational Network)的新型储量计算(RC)模型。引入的方法利用前向电离分解和反对称的经常性矩阵设计储油层动态,这些动态既稳定又不因施工而异。我们的数学分析表明,由此形成的模型偏向单一有效光谱半径和零当地Lyapunov Exponents,在稳定边缘自然运行。合成任务实验表明,与标准的RC模型相比,拟议方法在需要长期记忆化技能的任务中具有显著的优势。此外,实时时间序列分类基准的结果表明,Eusnel能够匹配(甚至超过)可培训的元神经网络的准确度,同时允许在计算时间和能源消耗方面实现高达100倍的节约。