数值代数几何在模型选择中的应用及其在生命科学中的应用
Numerical algebraic geometry for model selection and its application to the life sciences
AI总结：
本文利用数值代数几何方法解决数学模型中的参数估计、验证和选择问题，通过概率一多项式连续方法计算目标函数的所有临界点，并过滤以恢复全局最优解，应用于细胞信号传导、合成生物学和流行病学等领域。
摘要：
从事数学模型研究的人员常常面临参数估计、模型验证和模型选择等相关的挑战问题。这些问题都是优化问题，由于非线性、非凸性和多个局部极值而具有挑战性。此外，当只有部分数据可用时，这些挑战会进一步加剧。本文考虑多项式模型（例如，稳态质量作用化学反应网络）并基于数值代数几何的优化方法描述其分析框架。具体来说，我们使用概率一多项式连续方法计算目标函数的所有临界点，然后过滤以恢复全局极值。我们的方法利用模型与数据之间的几何结构，并在细胞信号传导、合成生物学和流行病学中的示例中展示了其效用。
英文摘要：
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to non-linearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data is available. Here, we consider polynomial models (e.g., mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometric structures relating models and data, and we demonstrate its utility on examples from cell signaling, synthetic biology, and epidemiology.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
