Evangelou Nikolaos, Giovanis Dimitris G, Kevrekidis George A, Pavliotis Grigorios A, Kevrekidis Ioannis G
Department of Chemical and Biomolecular Engineering, <a href="https://ror.org/00za53h95">Johns Hopkins University</a>, 3400 North Charles Street, Baltimore, Maryland 21218, USA.
Department of Applied Mathematics and Statistics, <a href="https://ror.org/00za53h95">Johns Hopkins University</a>, 3400 North Charles Street, Baltimore, Maryland 21218, USA.
Phys Rev E. 2024 Jul;110(1-1):014121. doi: 10.1103/PhysRevE.110.014121.
Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM-the Desai-Zwanzig model-in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ordinary differential equation (ODE) in these coordinates. We identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE-enabled through an odd symmetry transformation-to construct the bifurcation diagram exhibiting the phase transition.
推导降阶模型的闭式解析表达式，并明智地选择通向这些表达式的封闭条件，长期以来一直是研究基于代理模型（ABM）的相位和噪声诱导转变的首选策略。在本文中，我们提出了一个数据驱动框架，该框架在平均场极限下，使用比传统闭式模型更少的变量来确定ABM（德赛 - 兹万齐格模型）的相变。为此，我们使用流形学习算法扩散映射来识别一组简洁的数据驱动潜在变量，并表明它们与ABM的预期理论序参量一一对应。然后，我们利用深度学习框架对数据驱动坐标进行共形重新参数化，在我们的示例中，这有助于识别这些坐标中的单个参数依赖常微分方程（ODE）。我们通过受数值积分方案（前向欧拉）启发的残差神经网络来识别这个ODE。然后，我们使用通过奇对称变换启用的已识别ODE来构建展示相变的分岔图。
