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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Finite-Time Splash for the free boundary incompressible Navier–Stokes equations (I)
自由边界 不可压缩 Navier-Stokes方程 有限时间飞溅
2023/5/18
In this talk, we consider the incompressible Navier-Stokes equations with free boundary, which has a finite-time splash singularity for a large class of specially prepared initial data. The approach i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：过拟合神经网络的泛化能力
过拟合 神经网络 泛化能力
2023/5/17
我们考虑梯度下降法训练的较宽的深层全连接神经网络的泛化能力。 我们首先将论证在宽度足够大时，对于一维数据，由梯度下降训练的两层神经网络的泛化能力在适当的早停策略下可以达到极小极大率,而由梯度下降训练至过拟合的两层神经网络没有泛化能力。基于这个结果，我们对Benign Overfitting现象提出了一个新的解释。 随后，对于更一般的数据或者高维数据，我们将会简单介绍一下我们组与深层神经网络的泛化能...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Equivariant techniques in Chromatic homotopy theory
色度 同伦理论 等变技术
2023/5/15
Chromatic homotopy theory uses the algebraic geometry of smooth 1-parameter formal groups to separate stable homotopy theory into periodic layers. The 1st layer recovers the image of Adams’ J homomorp...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：关键设备的贮存加速退化试验及数据采集方法
关键设备 贮存加速 退化试验 数据采集
2023/5/12
关键装备延寿项目中，需要对产品在贮存状态下的可靠性水平进行量化考核，因此需要选取一定量的试验样本开展相应的寿命相关试验来获取可靠性信息。本报告中将针对所关注的研究对象中的各类典型产品的失效模式分析、失效判别标准、加速退化试验设置、以及数据采集等一系列相关问题进行介绍，以为后续开展可靠性模型的建立和评估做技术准备。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Isometric embedding and fluid mechanics
等距嵌入 流体力学 理论流体力学
2023/5/10
In this talk, I first discuss isometric embedding from differential geometry and its relation with fluid mechanic equations. Then I will present recent progress and my works on isometric embeddings of...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：高维可压缩Navier-Stokes方程三类平面波形在空间周期扰动下的渐近稳定性
高维可压缩 Navier-Stokes方程 三类平面波形 空间周期扰动 渐近稳定性
2023/5/6
疏散波(rarefaction wave)、激波(shock wave)和涡片波(vortex sheet)是可压缩流体中的三类基本波形，它们分别对应可压缩流体的疏散、压缩和剪切三类不同的物理现象。本次报告将研究对于可压缩Navier-Stokes方程，即考虑流体的粘性效应时，这三类波现象在小扰动下的稳定性。特别地，这里的扰动在空间无穷远处可以周期振荡，这类非局部扰动不仅带来数学上的新困难，也让我...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Hyperbolic minimizing closed orbit and Herman's conjecture
双曲 最小化 闭合轨道 赫尔曼猜想
2023/5/6
We are motivated to study this problem so that the proof of Arnold Diffusion of many degrees of freedom can be significantly simplified.
Researchers often use simulations when designing new algorithms, since testing ideas in the real world can be both costly and risky. But since it’s impossible to capture every detail of a complex syst...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：飞机轨迹的预测算法
飞机轨迹 预测算法 神经网络
2023/5/4
Using knowledge-driven trajectory prediction is difficult to describe complex reasoning processes, and the use of expert prior knowledge can add too many subjective factors to the judgment process, wh...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Optimization problem in remote sensing data processing
遥感 数据处理 优化问题
2023/5/4
In this talk, we will introduce some optimization problem in remote sensing data processing. The high dimensional characteristics of remote sensing data, especially hyperspectral data, will not only l...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：受人启发机器人与对类人人形机器人的思考
机器人 类人人形机器人 人工智能
2023/5/4
普通机器人高性能作业能力是机器人领域核心问题之一，也是其广泛高端应用的主要瓶颈。基于人类整体性能高于单元性能的机理，通过模拟人的神经机制与结构机理，研制受人启发的机器人系统，是在有限本体精度和有限传感精度下实现机器人高性能作业的有效途径。本报告将结合中国科学院自动化研究所机器人理论与应用团队的研究工作，对受人启发机器人研究的初步进展进行简要介绍，以期能够对未来类人人形机器人的研究带来启发。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Babuska Problem in Composite Materials and its Application to Acoustic Resonators
复合材料 巴布斯卡问题 声学谐振器
2023/4/27
A long-standing area of material science has been the study of electrostatic and elastic fields in composite material. In high-contrast composites, when two adjacent inclusions are close to touching, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long-time behavior of Alfven waves in a flowing plasma
阿尔文波 流动 等离子体 长期行为
2023/4/28
In this talk, we consider the long-time behavior of the linearized MHD equations around a steady flowing plasma. We confirm the following physical phenomenon: there will be a generation of a magnetic ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：计算机图形学中的非线性方程求根计算
计算机图形学 非线性方程 求根计算
2023/4/25
计算机图形学中的求交、最近距离计算、碰撞检测等问题，涉及到非线性方程或方程组的求根。首先针对单变量非线性方程的求根计算，提出了一种基于插值的多项式包围盒构造方法，可用于快速排除不含根的小区间。其次，为了简化逼近函数后得到的方程组，采用了有理多项式逼近的思想，改进了相应的收敛阶。最后，将上述思路推广到多变量非线性方程组的求解。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：量子人工智能前沿进展
量子 人工智能 前沿进展
2023/4/23
Quantum artificial intelligence (Quantum AI) is an emergent interdisciplinary field that explores the interplay between artificial intelligence and quantum physics. On the one hand, judiciously design...