The aim of this paper is to present a novel general framework for the identification of possibly interconnected systems, while preserving their physical properties and providing accuracy in multi-step prediction. An analytical and recursive algorithm for the gradient computation of the multi-step loss function based on backpropagation is introduced, providing physical and structural insight directly into the learning algorithm. As a case study, the proposed approach is tested for estimating the inertia matrix of a space debris starting from state observations.

翻译：本文旨在提出一个新颖的通用框架，用于辨识可能相互关联的系统，同时保持其物理属性并在多步预测中提供准确性。本文引入了一种基于反向传播的解析递归算法，用于计算多步损失函数的梯度，从而将物理与结构洞察直接融入学习算法中。作为案例研究，所提方法被测试用于从状态观测中估计空间碎片的惯性矩阵。