One of the most exciting applications of AI is automated scientific discovery
based on previously amassed data, coupled with restrictions provided by the
known physical principles, including symmetries and conservation laws. Such
automated hypothesis creation and verification can assist scientists in
studying complex phenomena, where traditional physical intuition may fail. Of
particular importance are complex dynamic systems where their time evolution is
strongly influenced by varying external parameters. In this paper we develop a
platform based on a generalised Onsager principle to learn macroscopic
dynamical descriptions of arbitrary stochastic dissipative systems directly
from observations of their microscopic trajectories. We focus on systems whose
complexity and sheer sizes render complete microscopic description impractical,
and constructing theoretical macroscopic models requires extensive domain
knowledge or trial-and-error. Our machine learning approach addresses this by
simultaneously constructing reduced thermodynamic coordinates and interpreting
the dynamics on these coordinates. We demonstrate our method by studying
theoretically and validating experimentally, the stretching of long polymer
chains in an externally applied field. Specifically, we learn three
interpretable thermodynamic coordinates and build a dynamical landscape of
polymer stretching, including (1) the identification of stable and transition
states and (2) the control of the stretching rate. We further demonstrate the
universality of our approach by applying it to an unrelated problem in a
different domain: constructing macroscopic dynamics for spatial epidemics,
showing that our method addresses wide scientific and technological
applications.

基于基本的物理原理，特别重要的是对复杂动态系统进行宏观动力学建模，通过学习化简的热力学坐标和在这些坐标上解释动力学来实现。我们通过在聚合物拉伸和空间流行病的研究中验证了这种方法的有效性，表明我们的方法适用于广泛的科学和技术应用。

利用深度学习构建定制热力学

Constructing Custom Thermodynamics Using Deep Learning

In nonlinear voter models the transitions between two states depend in a
nonlinear manner on the frequencies of these states in the neighborhood. We
investigate the role of these nonlinearities on the global outcome of the
dynamics for a homogeneous network where each node is connected to $m=4$
neighbors. The paper unfolds in two directions. We first develop a general
stochastic framework for frequency dependent processes from which we derive the
macroscopic dynamics for key variables, such as global frequencies and
correlations. Explicite expressions for both the mean-field limit and the pair
approximation are obtained. We then apply these equations to determine a phase
diagram in the parameter space that distinguishes between different dynamic
regimes. The pair approximation allows us to identify three regimes for
nonlinear voter models: (i) complete invasion, (ii) random coexistence, and --
most interestingly -- (iii) correlated coexistence. These findings are
contrasted with predictions from the mean-field phase diagram and are confirmed
by extensive computer simulations of the microscopic dynamics.

探究非线性投票模型在频率依赖进程中的作用，得出两个方向的总体动力学模型并应用于确定参数空间中的相位图表，揭示了三种不同的动态模式。