SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 3, Page 1320-1347, January 2021.
We propose a framework of a reservoir with an inertial manifold, which is a finite-dimensional object that attracts all trajectories. In addition, based on the theoretical results concerning infinite-dimensional dynamical systems, we demonstrate that this reservoir should have some desirable properties called the echo state property and the separation property. By considering the projection of the system onto the inertial manifold, we describe the behavior of the reservoir as a system of finite-dimensional ordinary differential equations called an inertial form. Next, we present a finite-dimensional model that approximates the inertial form. Finally, we propose a temporally discretized model, which is more suitable for computer computation. We give the theoretical proofs of our theorems herein.

中文翻译：

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惯性形式的油藏计算

SIAM Journal on Applied Dynamical Systems，第 20 卷，第 3 期，第 1320-1347 页，2021 年 1 月。
我们提出了一个具有惯性流形的水库框架，这是一个吸引所有轨迹的有限维对象。此外，基于关于无限维动力系统的理论结果，我们证明该储层应该具有一些理想的特性，称为回波状态特性和分离特性。通过考虑系统在惯性流形上的投影，我们将储层的行为描述为称为惯性形式的有限维常微分方程系统。接下来，我们提出了一个近似惯性形式的有限维模型。最后，我们提出了一个更适合计算机计算的时间离散化模型。我们在此给出我们定理的理论证明。