The discovery of partial differential equations (PDEs) from datasets has
attracted increased attention. However, the discovery of governing equations
from sparse data with high noise is still very challenging due to the
difficulty of derivatives computation and the disturbance of noise. Moreover,
the selection principles for the candidate library to meet physical laws need
to be further studied. The invariance is one of the fundamental laws for
governing equations. In this study, we propose an invariance constrained deep
learning network (ICNet) for the discovery of PDEs. Considering that temporal
and spatial translation invariance (Galilean invariance) is a fundamental
property of physical laws, we filter the candidates that cannot meet the
requirement of the Galilean transformations. Subsequently, we embedded the
fixed and possible terms into the loss function of neural network,
significantly countering the effect of sparse data with high noise. Then, by
filtering out redundant terms without fixing learnable parameters during the
training process, the governing equations discovered by the ICNet method can
effectively approximate the real governing equations. We select the 2D Burgers
equation, the equation of 2D channel flow over an obstacle, and the equation of
3D intracranial aneurysm as examples to verify the superiority of the ICNet for
fluid mechanics. Furthermore, we extend similar invariance methods to the
discovery of wave equation (Lorentz Invariance) and verify it through Single
and Coupled Klein-Gordon equation. The results show that the ICNet method with
physical constraints exhibits excellent performance in governing equations
discovery from sparse and noisy data.

基于物理约束的深度学习网络 (ICNet) 可以有效地从稀疏且有噪声的数据中发现偏微分方程的控制方程。

一种受不变性约束的深度学习网络用于 PDE 发现

An invariance constrained deep learning network for PDE discovery

In this work, we present ARDIAS, a web-based application that aims to provide
researchers with a full suite of discovery and collaboration tools. ARDIAS
currently allows searching for authors and articles by name and gaining
insights into the research topics of a particular researcher. With the aid of
AI-based tools, ARDIAS aims to recommend potential collaborators and topics to
researchers. In the near future, we aim to add tools that allow researchers to
communicate with each other and start new projects.

本文介绍了基于 Web 的应用程序 ARDIAS，旨在为研究人员提供全套的发现和合作工具，包括搜索作者和文章、通过 AI 工具推荐潜在的合作者和专题、以及允许研究人员相互沟通并开展新项目等。

ARDIAS: 智能增强的研究管理、发现和咨询系统

ARDIAS: AI-Enhanced Research Management, Discovery, and Advisory System

This paper addresses the problem of automatically localizing dominant objects
as spatio-temporal tubes in a noisy collection of videos with minimal or even
no supervision. We formulate the problem as a combination of two complementary
processes: discovery and tracking. The first one establishes correspondences
between prominent regions across videos, and the second one associates
successive similar object regions within the same video. Interestingly, our
algorithm also discovers the implicit topology of frames associated with
instances of the same object class across different videos, a role normally
left to supervisory information in the form of class labels in conventional
image and video understanding methods. Indeed, as demonstrated by our
experiments, our method can handle video collections featuring multiple object
classes, and substantially outperforms the state of the art in colocalization,
even though it tackles a broader problem with much less supervision.

本研究提出一种结合发现和跟踪两个过程的算法，用于自动定位包含在视频集合中的物体，并能发现跨不同视频的物体实例之间的隐含拓扑关系，实验表明该算法在多目标定位方面表现优异

视频集合中的无监督目标发现和跟踪

Unsupervised Object Discovery and Tracking in Video Collections

I postulate that human or other intelligent agents function or should
function as follows. They store all sensory observations as they come - the
data is holy. At any time, given some agent's current coding capabilities, part
of the data is compressible by a short and hopefully fast program / description
/ explanation / world model. In the agent's subjective eyes, such data is more
regular and more "beautiful" than other data. It is well-known that knowledge
of regularity and repeatability may improve the agent's ability to plan actions
leading to external rewards. In absence of such rewards, however, known beauty
is boring. Then "interestingness" becomes the first derivative of subjective
beauty: as the learning agent improves its compression algorithm, formerly
apparently random data parts become subjectively more regular and beautiful.
Such progress in compressibility is measured and maximized by the curiosity
drive: create action sequences that extend the observation history and yield
previously unknown / unpredictable but quickly learnable algorithmic
regularity. We discuss how all of the above can be naturally implemented on
computers, through an extension of passive unsupervised learning to the case of
active data selection: we reward a general reinforcement learner (with access
to the adaptive compressor) for actions that improve the subjective
compressibility of the growing data. An unusually large breakthrough in
compressibility deserves the name "discovery". The "creativity" of artists,
dancers, musicians, pure mathematicians can be viewed as a by-product of this
principle. Several qualitative examples support this hypothesis.

通过奖励能够改善日益增大的数据的主观压缩性的普通增强学习程序的行动，可以自然而然地在计算机上实现所有上述内容，并且艺术家、舞者、音乐家、纯数学家的 “创造性” 可以被视为这一原则的副产品。