逼近质量作用系统中多稳态与多稳定性的参数区域

中文摘要 AI 辅助

在化学反应网络分析中，识别支持多稳态和多稳定性的动力学参数与守恒量仍然具有挑战性。结构理论提供了存在性与排除性结果，但并不总能给出相应参数区域的显式、可解释的描述。我们提出了一个计算与机器学习框架，用于发现和刻画质量作用系统中具有多稳态和多稳定性数值证据的参数区域。我们将这些数值检测到的行为称为近似多稳态和近似多稳定性。该框架结合了拉丁超立方采样、自适应采样和可解释的替代建模。逻辑回归和神经网络替代模型分别在累积的检测标签上训练，并独立地引导后续采样朝向具有高近似多稳态或多稳定性分数的区域。边界细化针对检测到与未检测到的数值类别之间的过渡。然后使用白金汉π群与CN2规则归纳法，获得检测到的参数区域的可解释经验描述。示例网络产生的规则与已知的多稳态条件一致，而Schlögl模型展示了多稳态检测的自适应富集。在混合组氨酸激酶模型和顺序双磷酸化循环中，在相等的采样预算下，自适应采样相对于全局采样显著增加了检测到多稳定性的参数-总量对的数量。该框架通过提供高效的、参数解析的多稳态与多稳定性区域的发现和刻画，补充了分析性化学反应网络理论。

英文摘要

Identifying kinetic parameters and conserved quantities that support multistationarity and multistability remains challenging in chemical reaction network analysis. Structural theory provides existence and exclusion results, but does not always yield explicit, interpretable descriptions of the corresponding parameter regimes. We present a computational and machine-learning framework for discovering and characterizing parameter regimes with numerical evidence of multistationarity and multistability in mass-action systems. We refer to these numerically detected behaviors as approximate multistationarity and approximate multistability. The framework combines Latin hypercube sampling, adaptive sampling, and interpretable surrogate modeling. Logistic-regression and neural-network surrogates are trained separately on accumulated detection labels and independently guide later sampling toward regions with high scores for approximate multistationarity or multistability. Boundary refinement targets transitions between detected and undetected numerical classes. Buckingham--Pi groups are then used with CN2 rule induction to obtain interpretable empirical descriptions of detected regimes. Illustrative networks yield rules consistent with known multistationarity conditions, while the Schlögl model demonstrates adaptive enrichment of multistationarity detections. In the hybrid histidine kinase model and the sequential dual phosphorylation cycle, adaptive sampling substantially increased the number of parameter - total pairs with detected multistability relative to global sampling under equal sampling budgets. The framework complements analytical chemical reaction network theory by providing efficient, parameter-resolved discovery and characterization of multistationary and multistable regimes.

发表机构

• Institute of Mathematical Sciences, University of the Philippines Los Baños（菲律宾大学洛斯巴尼奥斯分校数学科学研究所）
• Data Science Program, College of Science, University of the Philippines Diliman（菲律宾大学迪利曼分校理学院数据科学项目）
• Institute of Mathematics, University of the Philippines Diliman（菲律宾大学迪利曼分校数学研究所）

机构由 AI 辅助整理，请以论文原文为准。