SEEDS: Structural Error Estimation in Dynamic System Models

理解和预测复杂系统的动力学是生物学、流行病、工程学和经济学等不同领域的一项关键任务。然而，为真实的系统设计足够精确的模型仍然是一项具有挑战性的任务。结构模型的错误所造成的知识不足的定量相互作用在真实的系统和隐藏的输入从环境中的模型开发的根本障碍。在这个项目中，我们设计的方法和算法，从数据中重建这些模型错误的根本原因，从而促进系统的扩展和模型的改进。我们最近设计了一些新的标准，从输出测量的模型误差信号的唯一恢复。基于这一进展，我们的目标是设计更强大的恢复算法，证明保证重建的准确性。作为第二个主要的研究目标，我们将研究自动扩展不完整的模型，发现在这个模型中丢失的控制方程。这些算法将作为自由软件提供。

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.