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.

通过降阶模型、数据驱动框架、流形学习算法、深度学习框架和分叉图表，本文提出了一种定位基于代理模型 (ABMs) 的平均场极限相变的方法。

互动智能代理系统中相变鉴别的机器学习方法

Machine Learning for the identification of phase-transitions in  interacting agent-based systems

Scattering of seismic waves can reveal subsurface structures but usually in a
piecemeal way focused on specific target areas. We used a manifold learning
algorithm called "the Sequencer" to simultaneously analyze thousands of
seismograms of waves diffracting along the core-mantle boundary and obtain a
panoptic view of scattering across the Pacific region. In nearly half of the
diffracting waveforms, we detected seismic waves scattered by three-dimensional
structures near the core-mantle boundary. The prevalence of these scattered
arrivals shows that the region hosts pervasive lateral heterogeneity. Our
analysis revealed loud signals due to a plume root beneath Hawaii and a
previously unrecognized ultralow-velocity zone beneath the Marquesas Islands.
These observations illustrate how approaches flexible enough to detect robust
patterns with little to no user supervision can reveal distinctive insights
into the deep Earth.

通过利用 “序列器” 算法对散射的地震波进行协同分析，研究发现太平洋地区具有普遍的侧向异质性，其中包括夏威夷下方的柱根和马克萨斯群岛下方以前未被发现的超低速带。这些观察结果为如何在没有使用者干预的情况下发现深地球的独特洞见，提供了有力的证据。