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imtoken官方正版|dgm

作者： imtoken官方正版

2024-03-07 18:12:14

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MSDS、UN38.3、DGM、航空运输鉴定报告都是些什么 - 知乎

MSDS、UN38.3、DGM、航空运输鉴定报告都是些什么 - 知乎首发于外贸物流方案切换模式写文章登录/注册MSDS、UN38.3、DGM、航空运输鉴定报告都是些什么物流仔陈小曦航空运输行业销售经理电池，或者带电产品，要空运或者海运，最终的目的是要做一份空运鉴定报告或者海运鉴定报告，那么怎么做这两种报告呢，这就需要先做一份UN38.3检测报告，拿这个报告才能去申请空运鉴定报告、海运鉴定报告。空运鉴定全称为《航空运输条件鉴定报告书》，是根据委托方要求，由我国民航管理当局认可的有资质的专业鉴定公司做出的鉴定。航空货物运输对安全的要求非常高，特别是利用客机机腹舱进行货物运输时，一些被国际航空协会认定为不确定是否给航空运输带有危害的货物，需要在出运前做一份空运鉴定书，来鉴定此货物是否有危险以及危险等级系数。空运鉴定全称：《航空运输条件鉴别报告书》英语：Identification and Classification Report for Air Transport of Goods俗称：空运鉴定或鉴定需要注意海运没有这种鉴定，海运通常需要MSDS，其实MSDS不是检测报告或鉴定报告，也不是认证项目，只是一份侧重安全操作指引的技术性说明书，和《航空运输条件鉴别报告书》（空运鉴定）有根本的区别。MSDS是没有具体的有效期，只要是符合MSDS上的货物，这份报告就是有效的。而空运鉴定报告是由民航管理当局认可的有资质的专业鉴定，有效期一般是当年，过期就失效了。空运鉴定一般只能由本国民航管理当局认可的有资质的专业鉴定公司出具，而且一般需要寄送样品给鉴定公司进行专业检测，然后出具鉴定报告。不方便寄送样品的，就由鉴定公司的专业人员进行现场检测，然后出具鉴定报告。鉴定报告的有效期一般本年度使用，跨年之后，一般要重新做。空运鉴定报告和UN38.3检测认证是什么关系？电池要空运或者海运，最终的目的是要做一份空运鉴定报告或者海运鉴定报告，那么怎么做这两种报告呢，这就需要先做一份UN38.3检测报告，且需要提交测试概要，拿这份完整报告才能去申请空运鉴定报告、海运鉴定报告。UN38.3认证是指在联合国针对危险品运输专门制定的《联合国危险物品运输试验和标准手册》的第3部分38.3款，即要求锂电池运输前，必须要通过高度模拟、高低温循环、振动试验、冲击试验、 55℃外短路、撞击试验、过充电试验、强制放电试验，才能保证锂电池运输安全。PS，这个证书基本出证要1个月左右，厂家最好提前准备。根据IATA 902国际航空运输协议要求，距被测物品表面2.1m处的任意磁场强度应小于0.159A/m(200nT) 才可作普货运输(出普货鉴定) 。凡是物品中含有磁性材料的货物均会在空间产生磁场，需进行磁性货物的安全检测，以保证飞行安全。更多运输鉴定报告请参考之前文章：国际物流运输是最容易出问题的环节，有货出运一定要提前做好出货计划。分享最新国际空海运物流情况及海关新规，以便让客户了解最新国际物流环境，驿传一直在努力！深圳（珠三角）出货，欢迎交流~编辑于 2022-08-09 11:57MSDS鉴定航空运输赞同 1添加评论分享喜欢收藏申请转载文章被以下专栏收录外贸物流方案进出口国际空、海运、快递等物流资讯与操

鉴定北京迪捷姆空运技术开发有限公司

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航空运输条件鉴定

依据国际航空运输协会《危险物品规则》、联合国《试验与标准手册》等，开展航空运输危险品运输条件鉴定业务，涉及的物品包括化工品、磁性物质、机械类设备、电池及含电池的设备等（空运鉴定委托书）

海运运输条件鉴定

依据国际海事组织《国际海运危险货物规则》（IMDG CODE）、联合国《试验与标准手册》等，开展海运危险品运输条件鉴定业务（海运鉴定委托书）

安全技术说明书

依据国际海事组织《国际海运危险货物规则》（IMDG CODE）、国际航空运输协会《危险物品规则》（DGR）、《全球化学品统一分类和标签制度》(GHS)，开展化学品安全数据说明书（MSDS）编制业务（MSDS编制业务委托单）

DGM和MSDS的区别 - 知乎

DGM和MSDS的区别 - 知乎切换模式写文章登录/注册DGM和MSDS的区别货代是怎样炼成的让世界没有困难的物流不知道是否有货代朋友遇到过这样的情况，在空运化工品过程中，问客户要DGM 时，客户下意识的提供MSDS，却嫌少有人知道DGM。下面INTERMAX来为大家讲解下这两者的区别。MSDS：即物质安全数据单( Material Safety Date Sheet )的英文简写，也常被翻译成化学品安全说明书。它是化学品生产、贸易、销售企业按法律要求向下游客户和公众提供的有关化学品特征的一份综合性法律文件，提供化学品的理化参数、燃爆性能、对健康的危害、安全使用贮存、泄漏处置、急救措施及有关的法律法规等十六项内容。DGM ：DGM鉴定是一份产品安全运输的分析报告，来指导空运的操作。主要是检测空运货物是否为危险品的，在货物装上飞机前先要到DGM公司做鉴定（检测）是否为危险品，对于航空公司来说是个参照，有了DGM鉴定航空公司就可以根据货物的具体情况选择装运方式综上所述，DGM 是空运的唯一报告文件，MSDS 则是海运用的。MSDS和DGM两者应用的场合不同，在化工品运输过程中，需要根据不同的运输方式选择适合的报告。发布于 2022-05-30 10:32化学赞同 1添加评论分享喜欢收藏申请

深度学习求解偏微分方程系列一：Deep Galerkin Method - 知乎

深度学习求解偏微分方程系列一：Deep Galerkin Method - 知乎首发于Kawayikiwi切换模式写文章登录/注册深度学习求解偏微分方程系列一：Deep Galerkin MethodKawayikiwi 我们接下来将用一个系列的文章，介绍使用神经网络的办法求解偏微分方程。这是本系列的第一篇，介绍Deep Galerkin Method (DGM）。我们首先介绍DGM的理论。最后我们使用Python求解一个热传播方程。1. 简介偏微分方程被广泛地应用到自然科学的各个领域，用于对自然或者社会领域问题的建模，例如热传导方程建模热的传播过程，Black-Scholes建模期权的价格，空间的SIR方程建模疾病的传播等。在复杂的场景下，偏微分方程的解是很难用显示的公式来表示。因此，我们只能求助于数值计算。偏微分方程的数值求解方法一直是非常前沿的研究热点，常用的方法包括有限差分、有限元、有限体等。一般地，这些方法需要使用网格来近似偏微分方程的定义空间。网格越细，那么求解得到的解越精确。但相应地，越细的网格需要更高的计算代价与更大的存储空间。因此，这些方法能在低维度的时候得到很好的对原方程解的近似，但受到维度诅咒，在高维度的情况下，计算代价相当大。所以，在高维度的情况下，我们要求助无网格的办法。据我们所知，目前无网格的思想下主要有两类方法。其中一种是蒙特卡洛方法，在某些情况下，可以使用Feynman-Kac公式，将偏微分方程中的待求函数表示成某种随机过程中的随机变量的数学期望，再通过蒙特卡洛求期望的办法求解偏微分方程。蒙特卡洛法的收敛性依赖于空间中采样的点的个数，采样的点越多，我们能得到越精确的解。但相应地，采样点越多，我们的计算时间越长和存储空间越大，在非常高维的情况下，仍然需要很大的计算量。最近，基于深度学习的方法求解偏微分方程得到了越来越多的关注。我们可以使用神经网络来表示偏微分方程中的待求函数，通过学习神经网络的参数来求得偏微分方程的近似解。相较于有网格的方法，深度学习的方法能使得参数的数量大量地降低，从而有更少的计算消耗。同时，由于目前深度学习框架的普及，使用深度学习求解偏微分方程的编程难度也会比有网格的办法更低。目前，基于深度学习的办法求解偏微分方程已经有了很多的研究。关于深度学习，我们之前写过几篇介绍文章，见《深度学习（Deep Learning）系列一：神经网络简介》，《深度学习（Deep Learning）系列二：随机梯度下降与反向传播》，和《深度学习（Deep Learning）系列三：使用伴随法推导反向传播》。这里，我们将做一个系列的文章来介绍神经网络求解偏微分方程的方法。本篇是本系列的第一篇。我们介绍《DGM: A deep learning algorithm for solving partial differential equations》这篇文章中提出的DGM方法。2. 神经网络回顾这里，我们简要回顾一下深度学习的知识。概况地说，深度学习的方法使用神经网络来表达函数，该函数能表示我们需要完成的某个任务的功能。例如，在猫的图片识别的任务中，深度学习能够生成出一张神经网络，该网络能准确判断出用户提供的图片是否是猫。典型地，神经网络由若干层组成，如图1所示。第一层为输入层（图1中的绿色节点），表示了整个网络的输入变量。最后一层为输出层（图1中的红色节点），表示了网络的处理结果。中间的所有层为隐藏层（图1中的蓝色节点）。每一个层又由若干节点组成。隐藏层的每个节点接受上一层的输出，处理后将结果输出到下一层。因此，图1中的每个神经网络的节点都表示一个处理函数。每个节点表示的处理函数都包含了若干个待确定的参数，一旦我们确定了参数，那么整个神经网络就确定了。确定参数的过程就是“学习”的过程。这个“学习”的过程通常来自于对某个优化问题的求解。一般地，我们可以使用符号u_\theta(x)来表示一个神经网络。为了便于叙述，我们仍然使用猫的图片识别任务来作为例子。我们期望函数u_\theta表达的神经网络能处理图片识别任务。函数u_\theta的参数x表达了神经网络的输入，即猫的图片。参数\theta即为整个神经网络的每个节点的函数的参数的集合。我们的目标就是要确定参数\theta从而确定函数u_\theta，这样，我们就有了能判断给定的图像是否是猫的图片的智能工具。为了达到此目的，我们得训练该神经网络。我们给定一些已经标识好有N个样本点的训练集，\{(x_i, y_i)\}_{i=1}^N，其中x_i表示了第i张图片，y_i表示x_i是否为猫的图片。我们的目标是想要u_\theta(x_i)，即神经网络对图片x_i的判断，与y_i的结果接近。为此，我们需要求解下面的优化问题\min_\theta \frac{1}{N}\sum_{i=1}^N\|u_\theta(x_i)-y_i\|^2。\qquad （2.1） \\学习的过程即为求解(2.1)优化问题的过程。3. DGM 方法从第2节的描述我们可以看出，本质上，神经网络可以看做一个函数，u_\theta。神经网络的输入层为u_\theta的输入，而输出层为u_\theta的输出。因此，我们可以使用u_\theta来近似偏微分方程中的函数，一旦确定\theta，我们就得到了偏微分方程的解。在本文中，我们介绍《DGM: A deep learning algorithm for solving partial differential equations》中的Deep Galerkin Method (DGM）。本节后面的”我们“可以被理解为使用该篇文章的口吻。具体地，我们考虑下列的偏微分方程的求解\begin{cases} \partial_tu(t,x)+\mathcal{L}u(t,x)=0, (t,x)\in [0,T]\times \Omega,\\ u(0,x)=u_0(x), x\in \Omega,\\ u(t,x)=g(t,x), x\in [0, T]\times \partial \Omega, \end{cases}\qquad (3.1) \\其中，u为未知函数，依赖于时间变量t与空间变量x，\partial \Omega为空间\Omega的边界。因此，方程组(3.1)中，给定了函数u的在t=0时刻的初始条件与在空间\Omega的边界条件。我们需要求解函数u在整个空间中的值。为此，我们使用神经网络u_\theta来近似函数u，其中\theta为神经网络的参数。因此，与第2节中介绍的图片识别的任务类似，我们需要训练神经网络，寻找参数\theta。为此，我们要构造类似(2.1)中的优化问题，使得对每一个输入参数(t,x)，u_\theta(t,x)与u(t,x)的值都很接近。因此，我们需要u_\theta尽可能地满足方程组(3.1)。我们定义消耗函数\begin{align*} J(u_\theta)=&\|\partial_tu_\theta+\mathcal{L}u_\theta\|^2_{[0,T]\times\Omega,\nu_1}\\ &+\|u_\theta(t,x)-g(t,x)\|^2_{[0,T]\times\partial\Omega,\nu_2}\\ &+\|u_\theta(0,x)-u_0(x)\|^2_{\Omega,\nu_3}, \end{align*}\qquad (3.2) \\其中，\|f\|^2_{\Omega, \nu}=\int_\Omega f^2\nu dx, \nu为\Omega上的概率密度函数。J(u_\theta)表示了u_\theta对原方程解u的近似误差，如果J(u_\theta)的值很小，那么表示u_\theta大致满足(3.1)中的偏微分方程、初始条件和边界条件。因此，求解偏微分方程(3.1)的解的过程，即为训练神经网络u_\theta的过程，即为求解下列优化问题\min_\theta J(u_\theta)。\qquad （3.3） \\一般情况下，目标函数J(u_\theta)为高维度的非凸函数，且其中包含了高维的积分，直接求解(3.3)是非常困难的。因此，我们使用机器学习中的随机梯度下降方法。具体地，算法的步骤如下：按照概率密度函数\nu_1从 [0,T]\times \Omega中生成样本点(t_n, x_n)。同样地，以\nu_2的概率密度从[0,T]\times\partial\Omega中生成样本点(\tau_n,z_n)，按\nu_3的概率密度从\Omega中生成样本点w_n。记\theta_n为第n步迭代的\theta的值，计算平方根误差G(\theta_n,s_n)，其中s_n为样本点，即s_n=\{(t_n,x_n), (\tau_n, z_n), w_n\}，且\begin{align*} G(\theta_n, s_n)=&\bigg(\partial_tu_{\theta_n}(t_n,x_n)+\mathcal{L}u_{\theta_n}(t_n,x_n)\bigg)^2\\ &+\bigg(u_{\theta_n}(\tau_n,z_n)-g(\tau_n,z_n)\bigg)^2\\ &+\bigg(u_{\theta_n}(0,w_n)-u_0(w_n)\bigg)^2, \end{align*}\qquad (3.4) \\进行梯度下降，更新\theta的值\theta_{n+1}=\theta_n-\alpha_n\nabla_{\theta}G(\theta_n,s_n), \qquad (3.5) \\其中，\alpha_n为下降步长，即也被称为学习率。重复上述步骤直到收敛注：在论文《DGM: A deep learning algorithm for solving partial differential equations》中，为了使得计算更有效率，作者给出了使用蒙特卡洛的方法来近似二阶导数，详情可以参考原文。论文《DGM: A deep learning algorithm for solving partial differential equations》也给出了DGM算法在单隐藏层无限宽度网络的情况下的收敛性证明，感兴趣的读者可以参考原文。 4. Python 求解代码在这一节中，我们介绍使用Pytorch来求解下面的热传导方程\begin{cases} u_t - u_{yy}-u_{yy} = (\pi + 2\pi^2)(\cos(\pi t) + \sin(\pi t))\sin(\pi x)\sin(\pi y)，\ \text{on}\ [0,4]\times [0,1]\times [0,1]，\\ u(0,x,y)=0， \ \text{on}\ [0,1]\times[0,1]\\ u(t,0,y)=u(t,1,y)=0, \ \text{on}\ [0,4]\times[0,1]，\\ u(t,x,0)=u(t,x,1)=0, \ \text{on}\ [0,4]\times[0,1]。 \end{cases} \qquad （4.1) \\很容易验证，(4.1)的分析解为u(t,x,y)=\sin(\pi t)\sin(\pi x)\sin(\pi y)。\qquad (4.2) \\下面，我们介绍使用DGM求解(4.1)的Pytorch代码。源代码主要有四个文件组成：libs.py，net.py, heat.py, train.py, 和main.py。其中，libs.py中主要包含了我们要加载的所有包的引入代码，如下:import torch

import matplotlib.pyplot as plt

import numpy as np

from torch.autograd import Variable

import torch.nn as nn

import torch.nn.functional as F

import torch.optim as optim

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

from scipy.stats import norm

from matplotlib import cm

神经网络的搭建主要在文件Net.py中。Net.py中包含了Net类，通过给Net的构造函数传递隐藏层的数目与每一层的节点数，就能构造一个神经网络。Net.py的源代码如下:from libs import *

class Net(nn.Module):

# NL: the number of hidden layers

# NN: the number of vertices in each layer

def __init__(self, NL, NN):

super(Net, self).__init__()

self.input_layer = nn.Linear(3, NN)

self.hidden_layers = nn.ModuleList([nn.Linear(NN, NN) for i in range(NL)])

self.output_layer = nn.Linear(NN, 1)

def forward(self, x):

o = self.act(self.input_layer(x))

for i, li in enumerate(self.hidden_layers):

o = self.act(li(o))

out = self.output_layer(o)

return out

def act(self, x):

return x * torch.sigmoid(x)

我们把与方程(4.1)相关的代码放在文件heat.py中。其中包含Heat类，用来计算根据(4.1)得到的神经网络的损失函数。Heat.py的源代码如下：from libs import *

class Heat():

def __init__(self, net, te, xe, ye):

self.net = net

self.te = te

self.xe = xe

self.ye = ye

def sample(self, size=2**8):

te = self.te

xe = self.xe

ye = self.ye

x = torch.cat((torch.rand([size, 1]) * te, torch.rand([size, 1]) * xe, torch.rand([size, 1]) * ye), dim=1)

x_initial = torch.cat((torch.zeros(size, 1), torch.rand([size, 1]) * xe, torch.rand([size, 1]) * ye), dim=1)

x_boundary_left = torch.cat((torch.rand([size, 1]) * te, torch.zeros([size, 1]), torch.rand(size, 1) * ye), dim=1)

x_boundary_right = torch.cat((torch.rand([size, 1]) * te, torch.ones([size, 1]) * xe, torch.rand(size, 1) * ye), dim=1)

x_boundary_up = torch.cat((torch.rand([size, 1]) * te, torch.rand([size, 1]) * xe, torch.ones(size, 1) * ye), dim=1)

x_boundary_down = torch.cat((torch.rand([size, 1]) * te, torch.rand([size, 1]) * xe, torch.zeros(size, 1)), dim=1)

return x, x_initial, x_boundary_left, x_boundary_right, x_boundary_up, x_boundary_down

def loss_func(self, size=2**8):

x, x_initial, x_boundary_left, x_boundary_right, x_boundary_up, x_boundary_down = self.sample(size=size)

x = Variable(x, requires_grad=True)

d = torch.autograd.grad(self.net(x), x, grad_outputs=torch.ones_like(self.net(x)), create_graph=True)

dt = d[0][:, 0].reshape(-1, 1) # transform the vector into a column vector

dx = d[0][:, 1].reshape(-1, 1)

dy = d[0][:, 2].reshape(-1, 1)

# du/dxdx

dxx = torch.autograd.grad(dx, x, grad_outputs=torch.ones_like(dx), create_graph=True)[0][:, 1].reshape(-1, 1)

# du/dydy

dyy = torch.autograd.grad(dy, x, grad_outputs=torch.ones_like(dy), create_graph=True)[0][:, 2].reshape(-1, 1)

f = np.pi * (torch.cos(np.pi*x[:, 0])) * (torch.sin(np.pi*x[:, 1])) * (torch.sin(np.pi*x[:, 2]))\

+ 2 * np.pi * np.pi * (torch.sin(np.pi*x[:, 0])) * (torch.sin(np.pi*x[:, 1])) * (torch.sin(np.pi*x[:, 2]))

diff_error = (dt - dxx - dyy - f.reshape(-1, 1))**2

# initial condition

init_error = (self.net(x_initial)) ** 2

# boundary condition

bd_left_error = (self.net(x_boundary_left)) ** 2

bd_right_error = (self.net(x_boundary_right)) ** 2

bd_up_error = (self.net(x_boundary_up)) ** 2

bd_down_error = (self.net(x_boundary_down)) ** 2

return torch.mean(diff_error + init_error + bd_left_error + bd_right_error + bd_up_error + bd_down_error)

我们将整个的训练过程放在了train.py中。我们使用Adam算法进行训练，源代码如下:from libs import *

class Train():

def __init__(self, net, heateq, BATCH_SIZE):

self.errors = []

self.BATCH_SIZE = BATCH_SIZE

self.net = net

self.model = heateq

def train(self, epoch, lr):

optimizer = optim.Adam(self.net.parameters(), lr)

avg_loss = 0

for e in range(epoch):

optimizer.zero_grad()

loss = self.model.loss_func(self.BATCH_SIZE)

avg_loss = avg_loss + float(loss.item())

loss.backward()

optimizer.step()

if e % 50 == 49:

loss = avg_loss/50

print("Epoch {} - lr {} - loss: {}".format(e, lr, loss))

avg_loss = 0

error = self.model.loss_func(2**8)

self.errors.append(error.detach())

def get_errors(self):

return self.errors

最后，我们在main.py中，将各个类的功能结合在一起，生成并训练网络，得到结果后，我们画出训练误差的变化以及训练出的函数的绘图，源代码如下:import os

os.chdir(os.path.dirname(os.path.abspath(__file__)))

from libs import *

from train import *

from net import *

from heat import *

net = Net(NL=2, NN=20)

te = 4

xe = 1

ye = 1

heatequation = Heat(net, te, xe, ye)

train = Train(net, heatequation, BATCH_SIZE=2**8)

train.train(epoch=10**5, lr=0.0001)

torch.save(net, 'net_model.pkl')

errors = train.get_errors()

#plot errors

fig = plt.figure()

plt.plot(np.log(errors), '-b', label='Errors')

plt.title('Training Loss', fontsize=10)

path = "./pictures/trainingloss.png"

plt.savefig(path)

plt.close(fig)

# net = torch.load('net_model.pkl')

t_range = np.linspace(0, te, 100, dtype=np.float64)

x_range = np.linspace(0, xe, 100, dtype=np.float64)

y_range = np.linspace(0, ye, 100, dtype=np.float64)

data = np.empty((3, 1))

k = 0

for _t in t_range:

TrueZ = []

Z = []

data[0] = _t

for _x in x_range:

data[1] = _x

for _y in y_range:

data[2] = _y

indata = torch.Tensor(data.reshape(1, -1))

Zdata = net(indata).detach().cpu().numpy()

Z.append(Zdata)

TrueZ.append(np.sin(np.pi*_t)*np.sin(np.pi*_x)*np.sin(np.pi*_y))

_X, _Y = np.meshgrid(x_range, y_range, indexing='ij')

Z_surface = np.reshape(Z, (x_range.shape[0], y_range.shape[0]))

True_Z_surface = np.reshape(TrueZ, (x_range.shape[0], y_range.shape[0]))

# plot the approximated values

fig = plt.figure()

ax = fig.gca(projection='3d')

ax.set_zlim([-1, 1])

ax.plot_surface(_X, _Y, Z_surface, cmap=cm.RdYlBu_r, edgecolor='blue', linewidth=0.0003, antialiased=True)

ax.set_xlabel('x')

ax.set_ylabel('y')

ax.set_zlabel('u')

path = "./pictures/%i.png" % k

plt.savefig(path)

plt.close(fig)

# plot the exact solution

fig = plt.figure()

ax = fig.gca(projection='3d')

ax.set_zlim([-1, 1])

ax.plot_surface(_X, _Y, True_Z_surface, cmap=cm.RdYlBu_r, edgecolor='blue', linewidth=0.0003, antialiased=True)

ax.set_xlabel('x')

ax.set_ylabel('y')

ax.set_zlabel('u')

path = "./Sol/%i.png" % k

plt.savefig(path)

plt.close(fig)

k = k + 1

在下面的图2中，我们画出了训练过程中的误差的减小与收敛情况（纵轴为误差的自然对数，横轴为训练的epoch值，即时期数目）。在图3中，显示了(4.2)中的函数的分析解，图4显示了神经网络的数值结果。我么可以看出，神经网络对于偏微分方程(4.1)得出了很好的近似结果。感兴趣的朋友可以试着增加层的深度和宽度看是否能得到更好的结果。发布于 2021-03-23 17:50偏微分方程深度学习（Deep Learning）数值优化赞同 634149 条评论分享喜欢收藏申请转载文章被以下专栏收录Kawayikiwi数学与编程知识分享BluehomseGreek Inc.物理信息驱动的深度学习方法本专栏主要追踪物理信息驱动的深度学习研

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"Everything we are is revealed in our playing."

The Complete 1969 Recordings

The complete audio history of one of the most important debut albums of all time presented across 26 discs (20CD/4Blu-Ray/1DVD/1DVD-A).

The complete audio history of one of the most important debut albums of all time presented across 26...

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Music Is Our Friend 3LP set

Limited edition 3LP set on 200gram Super-Heavyweight vinyl. King Crimson’s final US concert in Washington, DC (Sept 2021) and 4 additional tracks from Albany, New York (August 2021) available on vinyl for the first time.

Limited edition 3LP set on 200gram Super-Heavyweight vinyl. King Crimson’s final US concert in Was...

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McDonald and Giles LP

This is the first official release of the album on vinyl in decades and the first time since 1970 that the album has been cut from the original masters.

This is the first official release of the album on vinyl in decades and the first time since 1970 th...

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Robert Fripp Exposures

One of the most comprehensive boxed sets devoted to a single period of an artist’s career, Exposures features the complete collection of Robert Fripp’s studio and live solo material from 1977-1983, covering the period from the first Exposure sessions to the end of The League of Gentlemen and final Frippertronics concerts.

One of the most comprehensive boxed sets devoted to a single period of an artist’s career, Exposur...

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Let The Power Fall CD

Let The Power Fall is the only full album of Frippertronics released during the original vinyl era and within two years of the original tour of shops/offices/restaurants that acted as venues for the concerts.

Let The Power Fall is the only full album of Frippertronics released during the original vinyl era a...

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The Grid/Fripp Leviathan vinyl

A 2021 collaborative album from electronic duo The Grid (aka Richard Norris and Dave Ball) and Robert Fripp, combining Fripp Soundscapes with synth, drums, programming and effects by The Grid.

A 2021 collaborative album from electronic duo The Grid (aka Richard Norris and Dave Ball) and Rober...

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Three Of A Perfect Pair 40th anniversary vinyl

40th anniversary stereo mix by Steven Wilson and Robert Fripp of King Crimson’s dazzling 1984 release, Three Of A Perfect Pair.

On 200g super-heavyweight vinyl for the first time. Mastered by Jason Mitchell at Loud Mastering from original studio masters.

40th anniversary stereo mix by Steven Wilson and Robert Fripp of King Crimson’s dazzling 1984 rele...

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King Crimson At 50 DVD Blu-ray

A two disc Blu-Ray/DVD edition of Toby Amies' superb documentary In The Court Of The Crimson King - King Crimson at 50 including the full documentary film, an edit from an early version of the film, the final performance of Starless from the band’s final concert in Tokyo (in December 2021) and four trailers/shorts.

A two disc Blu-Ray/DVD edition of Toby Amies' superb documentary In The Court Of The Crimson King - ...

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In The Court Of The Crimson King - 3CD Blu-ray

50th anniversary 3CD/Blu-ray edition of King Crimson’s seminal debut

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Let The Power Fall vinyl

Let The Power Fall is the only full album of Frippertronics released during the original vinyl era a...

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In The Court Of The Crimson King - King Crimson At 50 8 disc boxed set

An 8 disc (2Blu-Ray/2DVD/4CD) box set edition of Toby Amies' superb documentary In The Court Of The Crimson King - King Crimson at 50 including the full documentary film, an edit from an early version of the film, live and studio performances from the 50th anniversary tour, and an abundance of additional footage.

An 8 disc (2Blu-Ray/2DVD/4CD) box set edition of Toby Amies' superb documentary In The Court Of The ...

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Earthbound vinyl

Earthbound, originally released in 1972, was one of the earliest (if not the first) “official bootleg” released by a major rock band, consisting of a series of deliberately lo-fi live recordings of King Crimson’s Islands era line-up on tour in the USA.

Earthbound, originally released in 1972, was one of the earliest (if not the first) “official boot...

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Washington Square Church vinyl

Recorded in New York City between July & August 1981, these are perhaps the finest example of Frippertronics in performance.

Recorded in New York City between July & August 1981, these are perhaps the finest example of Frippe...

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God Save The Queen/Under Heavy Manners vinyl

Containing one side of Frippertronics and another - featuring David Byrne plus a rhythm section of Busta Jones and Paul Duskin - of what came to be referred to Discotronics, the album provides a fascinating snapshot of Fripp's creative endeavours during the Post-Punk era.

Containing one side of Frippertronics and another - featuring David Byrne plus a rhythm section of B...

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Larks' Tongues In Aspic 2LP 2023 Mixes

Larks' Tongues In Aspic 2LP Edition 2023 Mixes

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Beat 40th anniversary vinyl

40th anniversary stereo mix by Steven Wilson and Robert Fripp of King Crimson’s sparkling 1982 release, Beat.

On 200g super-heavyweight vinyl for the first time. Mastered by Jason Mitchell at Loud Mastering from original studio masters.

40th anniversary stereo mix by Steven Wilson and Robert Fripp of King Crimson’s sparkling 1982 rel...

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Music For Quiet Moments

In May 2020, with much of the world in lockdown and reeling from the consequences of the Covid-19 pandemic, Robert Fripp began uploading the first of 52 individual Soundscapes on his YouTube channel, streaming platforms, and DGMLive.

In May 2020, with much of the world in lockdown and reeling from the consequences of the Covid-19 pa...

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Larks' Tongues In Aspic 2CD 2 Blu-ray

50th Anniversary, Complete Recording Sessions, Dolby Atmos, 2023 Mixes

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Discipline 40th anniversary vinyl

40th anniversary stereo mix by Steven Wilson and Robert Fripp of King Crimson’s innovative 1981 release, Discipline.

On 200g super-heavyweight vinyl for the first time. Mastered by Jason Mitchell at Loud Mastering from original studio masters.

40th anniversary stereo mix by Steven Wilson and Robert Fripp of King Crimson’s innovative 1981 re...

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New Soundscapes added to...

5 shows from 1997 to download

Toyah & Robert's Weekend

Toyah & Robert's Upbeat Moments (Robert from the road in the US, and Toyah from the UK)...

Happy birthday, Michael

KC co-founder 82 today

Fripp & Eno Live in Paris

Fripp & Eno - Live In Paris 28.05.1975 premieres on YouTube this Friday at 11:00 CET....

Stormy on the road

Alex hits the college circuit

David Singleton interviewed

David Singleton has been interviewed by Jeff Moehlis, ahead of the Englishmen Abroad event...

RF's diary from the road

RF diary

New Soundscapes added to...

READ FULL ARTICLE

5 shows from 1997 to download

Toyah & Robert's Weekend

READ FULL ARTICLE

Toyah & Robert's Upbeat Moments (Robert from the road in the US, and...

Happy birthday, Michael

READ FULL ARTICLE

KC co-founder 82 today

Fripp & Eno Live in Paris

READ FULL ARTICLE

Fripp & Eno - Live In Paris 28.05.1975 premieres on YouTube this...

Stormy on the road

READ FULL ARTICLE

Alex hits the college circuit

David Singleton interviewed

READ FULL ARTICLE

David Singleton has been interviewed by Jeff Moehlis, ahead of the...

RF's diary from the road

READ FULL ARTICLE

RF diary

David Singleton's Diary

READ FULL ARTICLE

Robert Fripp and I have now completed the first four speaking engagements of our "Englishmen Abroad" California tour. A travel day/day off in Agourra Hills yesterday, and now...

The Guitar Circle

Robert Fripp's Diary

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23.57

We arrived at Denver International Airport, four hours ahead of flight departure. With only carry-on baggage, we...

On Living

David Singleton's Diary

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My father died yesterday. Certainly not a tragedy, as he was ninety-one. And he had been...

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I see that the Youtube channels have just uploaded the latest in the videos from Robert's...

The Music Business

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10.48

Mobile HQ, Crimson Tourbus, currently at W.42 & 8th. Avenue, NYCNY.

Farewell Hotel...

Liner Notes

Court In On The Act

King Crimson's debut album is featured in this piece about the potential return of the...

On The Vicar

David Singleton's Diary

READ FULL ARTICLE

Inevitable Music

Forgive me for stating the obvious - and repeating what has, no doubt,...

On Fripp

Robert Fripp's Diary

READ FULL ARTICLE

10.18

Bredonborough.

On the afternoon of this day in 1984 my Father, Arthur Henry, flew...

Kicking The Wasps' Nest

Robert Fripp's Diary

READ FULL ARTICLE

20.33

A cold day here in Nashville & its environs.

The first day of winding up the...

The Guitar Circle

Robert Fripp's Diary

READ FULL ARTICLE

23.57

We arrived at Denver International Airport, four hours ahead of flight departure. With only carry-on baggage, we were checked-in and through security in 45 minutes, except for MJK Tour Manager whose passport was on the Crewbus. MJK flew to...

On Living

David Singleton's Diary

READ FULL ARTICLE

My father died yesterday. Certainly not a tragedy, as he was ninety-one. And he had been in great pain with cancer for the last few weeks, so probably a blessed release. But still a sad, and major event in my life. I am now an orphan!

Last year, at the time of his ninetieth birthday, I wrote a diary where I described my entire life as a voyage around my father. And it remains true that he was my...

On Music

David Singleton's Diary

READ FULL ARTICLE

I see that the Youtube channels have just uploaded the latest in the videos from Robert's and my...

The Music Business

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10.48

Mobile HQ, Crimson Tourbus, currently at W.42 & 8th. Avenue, NYCNY.

Farewell Hotel Designer!...

Liner Notes

Court In On The Act

READ FULL ARTICLE

King Crimson's debut album is featured in this piece about the potential return of the album sleeve,...

On The Vicar

David Singleton's Diary

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Inevitable Music

Forgive me for stating the obvious - and repeating what has, no doubt, been written many times before in these pages. Probably even by me. But I was struck this morning by the absolute absurdity of the music industry. Not the machinations, dodgy contracts, and double dealing. But by the underlying principle - namely ownership of music.

The absurdity struck me, with an astonishing clarity, almost like the proverbial lightning bolt, while playing Bach’s Prelude No1 in C major....

On Fripp

Robert Fripp's Diary

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10.18

Bredonborough.

On the afternoon of this day in 1984 my Father, Arthur Henry, flew from this world while being held by my Mother. Fortunately, I had returned to Wimborne the day before (from the first two Guitar Craft courses).

Several weeks later, while staying with my Sister in San Francisco, I had a vivid dream from which I woke. Feeling that this dream was...

Kicking The Wasps' Nest

Robert Fripp's Diary

READ FULL ARTICLE

20.33

A cold day here in Nashville & its environs.

The first day of winding up the Crimson Beast of Terror in preparation for unleashing it on the world. Apparently, the English magazine Classic Rock, in their review of TPTB, suggests we should call it a day. This is the simple arrogance of a reviewer not yet quite grown out of believing their own reviews. Yet not quite...

DGM Universe

David Singleton's Diary

READ FULL ARTICLE

Robert Fripp and I have now completed the first four speaking engagements of our "Englishmen Abroad" California tour. A travel day/day off in Agourra Hills yesterday, and...

Crimson Commentaries

Robert Fripp's Diary

READ FULL ARTICLE

12.59

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[1708.07469] DGM: A deep learning algorithm for solving partial differential equations

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Quantitative Finance > Mathematical Finance

arXiv:1708.07469 (q-fin)

[Submitted on 24 Aug 2017 (v1), last revised 5 Sep 2018 (this version, v5)]

Title:DGM: A deep learning algorithm for solving partial differential equations

Authors:Justin Sirignano, Konstantinos Spiliopoulos Download a PDF of the paper titled DGM: A deep learning algorithm for solving partial differential equations, by Justin Sirignano and Konstantinos Spiliopoulos

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Abstract:High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial condition, and boundary conditions. Our algorithm is meshfree, which is key since meshes become infeasible in higher dimensions. Instead of forming a mesh, the neural network is trained on batches of randomly sampled time and space points. The algorithm is tested on a class of high-dimensional free boundary PDEs, which we are able to accurately solve in up to $200$ dimensions. The algorithm is also tested on a high-dimensional Hamilton-Jacobi-Bellman PDE and Burgers' equation. The deep learning algorithm approximates the general solution to the Burgers' equation for a continuum of different boundary conditions and physical conditions (which can be viewed as a high-dimensional space). We call the algorithm a "Deep Galerkin Method (DGM)" since it is similar in spirit to Galerkin methods, with the solution approximated by a neural network instead of a linear combination of basis functions. In addition, we prove a theorem regarding the approximation power of neural networks for a class of quasilinear parabolic PDEs.

Comments:

Deep learning, machine learning, partial differential equations

Subjects:

Mathematical Finance (q-fin.MF); Numerical Analysis (math.NA); Computational Finance (q-fin.CP); Machine Learning (stat.ML)

Cite as:

arXiv:1708.07469 [q-fin.MF]

(or

arXiv:1708.07469v5 [q-fin.MF] for this version)

https://doi.org/10.48550/arXiv.1708.07469

Focus to learn more

arXiv-issued DOI via DataCite

Related DOI:

https://doi.org/10.1016/j.jcp.2018.08.029

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DOI(s) linking to related resources

Submission history From: Konstantinos Spiliopoulos [view email] [v1]

Thu, 24 Aug 2017 15:50:24 UTC (10 KB)

[v2]

Tue, 5 Dec 2017 13:56:45 UTC (2,452 KB)

[v3]

Sat, 16 Dec 2017 19:19:32 UTC (2,452 KB)

[v4]

Fri, 27 Jul 2018 18:16:30 UTC (5,503 KB)

[v5]

Wed, 5 Sep 2018 19:39:17 UTC (5,498 KB)

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