We present a novel form of Liquid Automata, using this to simulate
autopoiesis, whereby living machines self-organise in the physical realm. This
simulation is based on an earlier Cellular Automaton described by Francisco
Varela. The basis of Liquid Automata is a particle simulation with additional
rules about how particles are transformed on collision with other particles.
Unlike cellular automata, there is no fixed grid or time-step, only particles
moving about and colliding with each other in a continuous space/time.

利用新型液体自动机模拟自我组织的活体机器，基于 Francisco Varela 之前描述的细胞自动机，以粒子模拟为基础，通过粒子与其他粒子碰撞时的转化规则进行模拟，与细胞自动机不同的是，它没有固定的网格或时间步长，只有在连续的时空中粒子的移动和碰撞。

液态自动机中的仿真自产能

Simulated Autopoiesis in Liquid Automata

Learning system dynamics directly from observations is a promising direction
in machine learning due to its potential to significantly enhance our ability
to understand physical systems. However, the dynamics of many real-world
systems are challenging to learn due to the presence of nonlinear potentials
and a number of interactions that scales quadratically with the number of
particles $N$, as in the case of the N-body problem. In this work, we introduce
an approach that transforms a fully-connected interaction graph into a
hierarchical one which reduces the number of edges to $O(N)$. This results in
linear time and space complexity while the pre-computation of the hierarchical
graph requires $O(N\log (N))$ time and $O(N)$ space. Using our approach, we are
able to train models on much larger particle counts, even on a single GPU. We
evaluate how the phase space position accuracy and energy conservation depend
on the number of simulated particles. Our approach retains high accuracy and
efficiency even on large-scale gravitational N-body simulations which are
impossible to run on a single machine if a fully-connected graph is used.
Similar results are also observed when simulating Coulomb interactions.
Furthermore, we make several important observations regarding the performance
of this new hierarchical model, including: i) its accuracy tends to improve
with the number of particles in the simulation and ii) its generalisation to
unseen particle counts is also much better than for models that use all
$O(N^2)$ interactions.

本文提出了一种能够在单个 GPU 上运行高精度大规模 N 粒子动力学模拟的机器学习方法，将完全连接的交互图转换为分层图以减少复杂度和边数。