SEEDS: Structural Error Estimation in Dynamic System Models

了解和预测复杂系统的动力学是包括生物学、流行病、工程学和经济学在内的多个领域的一项关键任务。然而，为真实系统设计足够精确的模型仍然是一项具有挑战性的任务。由于对真实系统中的定量相互作用的了解不足以及来自环境的隐藏输入而导致的结构性模型错误是模型开发的根本障碍。在这个项目中，我们设计了从数据中重建这些模型错误的根本原因的方法和算法，从而促进了模型的系统扩展和改进。我们最近设计了一些新的准则，用于从输出测量中唯一地恢复模型误差信号。基于这一进展，我们的目标是设计更健壮的恢复算法，并证明重建的准确性得到了保证。作为第二个主要研究目标，我们将通过发现不完备模型中缺失的控制方程来研究不完备模型的自动扩展。这些算法将以自由软件的形式提供。

Understanding and predicting the dynamics of complex systems is a key task in diverse areas, including biology, epidemics, engineering and economics. However, devising sufficiently accurate models for real systems remains a challenging task. Structural model errors caused by insufficient knowledge about the quantitative interactions in the real system and hidden inputs from the environment are fundamental obstacles to model development. In this project, we devise methods and algorithms for reconstructing the root cause of these model errors from data, thereby facilitating the systematic extension and improvement of models. We have recently devised some new criteria for the unique recovery of the model error signal from output measurements. Based on this progress, we aim at designing more robust recovery algorithms with proven guarantees for the accuracy of the reconstruction. As a second main research goal, we will investigate the automatic extension of incomplete models by discovering the governing equations missing in this model. These algorithms will be made available as free software.