Physics Informed Neural Networks (PINNs) have been achieving ever newer feats
of solving complicated PDEs numerically while offering an attractive trade-off
between accuracy and speed of inference. A particularly challenging aspect of
PDEs is that there exist simple PDEs which can evolve into singular solutions
in finite time starting from smooth initial conditions. In recent times some
striking experiments have suggested that PINNs might be good at even detecting
such finite-time blow-ups. In this work, we embark on a program to investigate
this stability of PINNs from a rigorous theoretical viewpoint. Firstly, we
derive generalization bounds for PINNs for Burgers' PDE, in arbitrary
dimensions, under conditions that allow for a finite-time blow-up. Then we
demonstrate via experiments that our bounds are significantly correlated to the
$\ell_2$-distance of the neurally found surrogate from the true blow-up
solution, when computed on sequences of PDEs that are getting increasingly
close to a blow-up.

研究以理论角度验证 PINNs 的稳定性，推导了 Burgers' PDE 通用界限，实验证明界限与由神经网络找到的虚拟爆破解与真实爆破解之间的 L2 距离密切相关。

研究用 PINNs 解决 Burgers' PDE 在有限时间爆炸附近的能力

Investigating the Ability of PINNs To Solve Burgers' PDE Near  Finite-Time BlowUp

Gradient-based optimization is now ubiquitous across graphics, but
unfortunately can not be applied to problems with undefined or zero gradients.
To circumvent this issue, the loss function can be manually replaced by a
"surrogate" that has similar minima but is differentiable. Our proposed
framework, ZeroGrads, automates this process by learning a neural approximation
of the objective function, the surrogate, which in turn can be used to
differentiate through arbitrary black-box graphics pipelines. We train the
surrogate on an actively smoothed version of the objective and encourage
locality, focusing the surrogate's capacity on what matters at the current
training episode. The fitting is performed online, alongside the parameter
optimization, and self-supervised, without pre-computed data or pre-trained
models. As sampling the objective is expensive (it requires a full rendering or
simulator run), we devise an efficient sampling scheme that allows for
tractable run-times and competitive performance at little overhead. We
demonstrate optimizing diverse non-convex, non-differentiable black-box
problems in graphics, such as visibility in rendering, discrete parameter
spaces in procedural modelling or optimal control in physics-driven animation.
In contrast to more traditional algorithms, our approach scales well to higher
dimensions, which we demonstrate on problems with up to 35k interlinked
variables.

使用神经逼近的替代函数来解决具有未定义或零梯度问题的图形优化，适用于渲染、程序建模和物理驱动动画中的非凸、非可微黑盒问题。

零梯度从不给予：学习非可导图形的局部代理损失

Zero Grads Ever Given: Learning Local Surrogate Losses for  Non-Differentiable Graphics

An established way to improve the transferability of black-box evasion
attacks is to craft the adversarial examples on an ensemble-based surrogate to
increase diversity. We argue that transferability is fundamentally related to
uncertainty. Based on a state-of-the-art Bayesian Deep Learning technique, we
propose a new method to efficiently build a surrogate by sampling approximately
from the posterior distribution of neural network weights, which represents the
belief about the value of each parameter. Our extensive experiments on
ImageNet, CIFAR-10 and MNIST show that our approach improves the success rates
of four state-of-the-art attacks significantly (up to 83.2 percentage points),
in both intra-architecture and inter-architecture transferability. On ImageNet,
our approach can reach 94% of success rate while reducing training computations
from 11.6 to 2.4 exaflops, compared to an ensemble of independently trained
DNNs. Our vanilla surrogate achieves 87.5% of the time higher transferability
than three test-time techniques designed for this purpose. Our work
demonstrates that the way to train a surrogate has been overlooked, although it
is an important element of transfer-based attacks. We are, therefore, the first
to review the effectiveness of several training methods in increasing
transferability. We provide new directions to better understand the
transferability phenomenon and offer a simple but strong baseline for future
work.

使用贝叶斯深度学习技术，以神经网络权重的后验分布进行抽样建立一个 surrogate，可以进一步提高黑盒攻击的可转移性，本文探究了提高攻击可转移性的训练方法， 将我们方法的表现与几种已有方法进行了比较，能够在 ImageNet 上获得 94% 的准确率。