Neural Cellular Automata (NCA) are a powerful combination of machine learning
and mechanistic modelling. We train NCA to learn complex dynamics from time
series of images and PDE trajectories. Our method is designed to identify
underlying local rules that govern large scale dynamic emergent behaviours.
Previous work on NCA focuses on learning rules that give stationary emergent
structures. We extend NCA to capture both transient and stable structures
within the same system, as well as learning rules that capture the dynamics of
Turing pattern formation in nonlinear Partial Differential Equations (PDEs). We
demonstrate that NCA can generalise very well beyond their PDE training data,
we show how to constrain NCA to respect given symmetries, and we explore the
effects of associated hyperparameters on model performance and stability. Being
able to learn arbitrary dynamics gives NCA great potential as a data driven
modelling framework, especially for modelling biological pattern formation.

神经元元胞自动机（NCA）结合了机器学习和机械建模的强大能力。我们通过对图像时间序列和 PDE 轨迹进行训练，使 NCA 学习复杂动态。我们的方法旨在识别支配大规模动态出现行为的潜在局部规则。我们将 NCA 扩展到在同一系统中捕捉瞬态和稳定结构，以及学习捕捉非线性偏微分方程（PDE）中图灵模式形成的规则。我们展示了 NCA 在 PDE 训练数据之外的广泛推广能力，演示了如何限制 NCA 以尊重给定的对称性，并探索了相关超参数对模型性能和稳定性的影响。能够学习任意动态使得 NCA 成为一种具有很大潜力的数据驱动的建模框架，尤其适用于生物模式形成建模。

用神经元细胞自动机学习时空模式

Learning spatio-temporal patterns with Neural Cellular Automata

We introduce a new formulation of the Hidden Parameter Markov Decision
Process (HiP-MDP), a framework for modeling families of related tasks using
low-dimensional latent embeddings. Our new framework correctly models the joint
uncertainty in the latent parameters and the state space. We also replace the
original Gaussian Process-based model with a Bayesian Neural Network, enabling
more scalable inference. Thus, we expand the scope of the HiP-MDP to
applications with higher dimensions and more complex dynamics.

我们引入了一个新的 HiP-MDP 隐藏参数马尔可夫决策过程的处理方式，它能够通过低维度的潜在嵌入来建模相关任务的家族。我们采用贝叶斯神经网络来替换原模型中的高斯过程，从而使推理更具可扩展性，我们正确地模拟了潜在参数和状态空间中的联合不确定性，并扩大了 HiP-MDP 的应用范围，可以应用于维度更高且具有更复杂动态的问题。

基于隐含参数马尔可夫决策过程的强健高效迁移学习

Robust and Efficient Transfer Learning with Hidden-Parameter Markov  Decision Processes

Learning the parameters of a (potentially partially observable) random field
model is intractable in general. Instead of focussing on a single optimal
parameter value we propose to treat parameters as dynamical quantities. We
introduce an algorithm to generate complex dynamics for parameters and (both
visible and hidden) state vectors. We show that under certain conditions
averages computed over trajectories of the proposed dynamical system converge
to averages computed over the data. Our "herding dynamics" does not require
expensive operations such as exponentiation and is fully deterministic.

本文提出了一种基于复杂的、确定性算法的参数优化方法，称之为 'herding dynamics'，该方法在处理随机场模型上表现良好。