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 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 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 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.

翻译：长期以来，推导简化模型的闭式解析表达式并审慎选择导致这些模型的闭合项，一直是研究基于主体模型（ABM）中相变与噪声诱导相变的首选策略。本文提出一种数据驱动框架，通过比传统闭式模型更少的变量，精确定位ABM平均场极限下的相变点。为此，我们采用流形学习算法扩散映射（Diffusion Maps）识别一组简约的数据驱动隐变量，并证明它们与ABM期望的理论序参量存在一一对应关系。随后利用深度学习框架获得数据驱动坐标的共形重参数化，在示例中这种重参数化便于在这些坐标下识别单个参数相关的常微分方程（ODE）。我们通过受数值积分方案（前向欧拉法）启发的残差神经网络识别该ODE，接着利用经奇对称变换强化的识别ODE构建展示相变的分岔图。