Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of dynamical systems formulates this problem as a linear equation system. Here, we explore several simulation-based optimization approaches, which allow much greater freedom in the objective formulation and weaker conditions on the available data. We show that even for relatively small stochastic population models, simultaneous estimation of parameters and structure poses major challenges for optimization procedures. Particularly, we investigate the application of the local stochastic gradient descent method, commonly used for training machine learning models. We demonstrate accurate estimation of models but find that enforcing the inference of parsimonious, interpretable models drastically increases the difficulty. We give an outlook on how this challenge can be overcome.

翻译：从数据中学习机理模型的方法开发正受到越来越多的关注。这一任务不仅涉及参数的精确估计，还需要合适的模型结构。近期关于动态系统发现的研究将该问题表述为一个线性方程组。本文探讨了几种基于模拟的优化方法，这些方法在目标函数构建上允许更大的自由度，并对数据可用性要求更宽松的条件。我们证明，即使对于相对较小的随机种群模型，参数与结构的同步估计也会对优化过程构成重大挑战。特别地，我们研究了常用于训练机器学习模型的局部随机梯度下降方法的应用。我们展示了模型的精确估计能力，但发现强制推断简约、可解释的模型会急剧增加求解难度。本文最后展望了如何克服这一挑战。