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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：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： 从深度学习到智能空间组学：原理、方法与应用
深度学习 黑箱模型 计算实验
2023/4/18
深度学习作为一种黑箱模型，是通过大量计算实验得到的，其数学原理逐渐引起研究者的广泛关注，同时在各科学领域得到广泛应用。该报告将从两种不同的角度简要介绍深度学习的数学理解与认识：一、从多层卷积稀疏编码模型的编码初始化和字典矩阵设计的角度，建立跨连神经网络与多层卷积稀疏编码模型的等价联系；二、提出深度残差神经网络是在Wasserstein空间学习测地曲线的理论。最后，将简要介绍深度学习如何赋能空间组学...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Barron Type Spaces in Neural Network Approximation
神经网络 巴伦类型空间 经典函数空间
2023/4/13
We shall discuss various Barron type spaces arising from neural networks. The relations among these spaces will be clarified, and we shall also establish the relationship between Barron type spaces an...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Deep neural network approximation to inverse conductivity problems for elliptic equations
椭圆方程 反电导率 深度神经网络
2023/4/14
The focus of this talk is on the numerical methods used to identify parameters in partial differential equations. Typically, an optimization approach is used to solve this class of inverse problems, w...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：神经网络算子学习中的结构化损失函数与表征
神经网络 算子学习 结构化损失 函数与表征
2023/4/19
偏微分方程在许多学科和工程应用中扮演着重要的角色，例如物理系统的建模，计算化学，流体力学和数值天气预报等。基于偏微分方程对系统未来的演化进行预测往往需要依赖数值解法。传统数值解法在遇到高维问题，复杂边界，参数变化时，将会遇到计算效率不高，结果不可复用等问题。另一方面，深度神经网络在高维问题建模中展现了巨大优势，其中使用深度神经网络进行算子的逼近和学习成为学术研究热点。本报告将介绍我们在将算子学习应...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Implicit biases of optimization algorithms for neural networks and their effects on generalization
神经网络 优化算法 隐式偏差 泛化的影响
2023/4/26
Modern neural networks are usually over-parameterized—the number of parameters exceeds the number of training data. In this case the loss functions tend to have many (or even infinite) global minima, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Condensation in deep learning
深度学习 凝结 神经网络
2023/4/28
Why do neural networks (NN) that look so complex usually generalize well? To understand this problem, we find some simple implicit regularizations during training NNs. The first is the frequency princ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions
守恒量 两阶段物理信息 神经网络方法 局部波解
2023/5/5
With the advantages of fast calculating speed and high precision, the physics-informed neural network method opens up a new approach for numerically solving nonlinear partial differential equations. B...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Failure-informed adaptive sampling for PINNs
PINN 故障知情 自适应 采样
2023/5/8
Physics-informed neural networks (PINNs) have emerged as an effective technique for solving PDEs in a wide range of domains. Recent research has demonstrated, however, that the performance of PINNs ca...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Calculation of high-order harmonic generation of atoms and molecules by combining time series prediction and neural networks
时间序列预测 神经网络计算 原子分子 高阶谐波生成
2023/5/9
High-order harmonic generation (HHG) from the interaction of ultra-intense laser pulses with atoms is an important tabletop short-wave coherent light source. Accurate quantum simulations of it present...