We present an active learning algorithm for learning dynamics that leverages
side information by explicitly incorporating prior domain knowledge into the
sampling process. Our proposed algorithm guides the exploration toward regions
that demonstrate high empirical discrepancy between the observed data and an
imperfect prior model of the dynamics derived from side information. Through
numerical experiments, we demonstrate that this strategy explores regions of
high discrepancy and accelerates learning while simultaneously reducing model
uncertainty. We rigorously prove that our active learning algorithm yields a
consistent estimate of the underlying dynamics by providing an explicit rate of
convergence for the maximum predictive variance. We demonstrate the efficacy of
our approach on an under-actuated pendulum system and on the half-cheetah
MuJoCo environment.

我们提出了一种主动学习算法，通过将先验领域知识明确纳入采样过程，利用副信息来学习动态。通过数值实验，我们证明了该策略探索了高差异区域，加速了学习过程同时降低了模型不确定性。我们还通过提供最大预测方差的收敛速度的明确速率，严格证明了我们的主动学习算法给出了底层动态的一致估计。我们在一个欠驱动的摆系统和半猎豹 MuJoCo 环境上展示了我们方法的有效性。

利用先验领域知识在采样过程中主动学习动力学

Active Learning of Dynamics Using Prior Domain Knowledge in the Sampling  Process

We present a framework designed to learn the underlying dynamics between two
images observed at consecutive time steps. The complex nature of image data and
the lack of temporal information pose significant challenges in capturing the
unique evolving patterns. Our proposed method focuses on estimating the
intermediary stages of image evolution, allowing for interpretability through
latent dynamics while preserving spatial correlations with the image. By
incorporating a latent variable that follows a physical model expressed in
partial differential equations (PDEs), our approach ensures the
interpretability of the learned model and provides insight into corresponding
image dynamics. We demonstrate the robustness and effectiveness of our learning
framework through a series of numerical tests using geoscientific imagery data.

我们提出了一个框架，旨在学习两个连续时间步骤中观察到的图像之间的基本动态。通过估计图像演化的中间阶段，我们的方法关注在保持图像的空间相关性的同时提供可解释性，并通过偏微分方程中表示的物理模型引入潜在动态学变量，确保了所学模型的可解释性并提供了相应图像动态的洞察力。通过对地球科学图像数据进行一系列数值测试，我们证明了我们学习框架的鲁棒性和有效性。

通过物理潜变空间学习中间图像动态

Learning In-between Imagery Dynamics via Physical Latent Spaces

Adding interpretability to multivariate methods creates a powerful synergy
for exploring complex physical systems with higher order correlations while
bringing about a degree of clarity in the underlying dynamics of the system.

为多元方法添加可解释性，提升探索具有高阶相关性的复杂物理系统的能力，同时在系统的基本动态方面带来一定程度的清晰度。

物理学中的可解释机器学习

Interpretable machine learning in Physics

Continuous deep learning architectures have recently re-emerged as Neural
Ordinary Differential Equations (Neural ODEs). This infinite-depth approach
theoretically bridges the gap between deep learning and dynamical systems,
offering a novel perspective. However, deciphering the inner working of these
models is still an open challenge, as most applications apply them as generic
black-box modules. In this work we "open the box", further developing the
continuous-depth formulation with the aim of clarifying the influence of
several design choices on the underlying dynamics.

本文通过进一步开发连续深度神经微分方程模型，以期澄清几种设计选择对其底层动态的影响，进而解密其内部运作方式。