Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for
learning dynamical systems that can be modelled by ordinary differential
equations. In this paper, we extend the method to partial differential
equations. The resulting model is comprised of up to three neural networks,
modelling terms representing conservation, dissipation and external forces, and
discrete convolution operators that can either be learned or be prior
knowledge. We demonstrate numerically the superior performance of PHNN compared
to a baseline model that models the full dynamics by a single neural network.
Moreover, since the PHNN model consists of three parts with different physical
interpretations, these can be studied separately to gain insight into the
system, and the learned model is applicable also if external forces are removed
or changed.

本文将伪哈密顿神经网络方法扩展到偏微分方程，生成包含三个神经网络的模型，分别模拟代表守恒、耗散和外力的项，并包括可学习的离散卷积算子，数值结果表明 PHNN 的卓越性能。此外，由于 PHNN 模型由三个有不同物理解释的部分组成，反演时可以分别研究每个部分，具有良好的泛化能力。

利用赝哈密顿神经网络学习偏微分方程

Pseudo-Hamiltonian neural networks for learning partial differential  equations

We characterize the behavior of quantum correlations under the influence of
local noisy channels. Intuition suggests that such noise should be detrimental
for quantumness. When considering qubit systems, we show for which channel this
is indeed the case: the amount of quantum correlations can only decrease under
the action of unital channels. However, non-unital channels (e.g. such as
dissipation) can create quantum correlations for some initially classical
state. Furthermore, for higher-dimensional systems even unital channels may
increase the amount of quantum correlations. Thus, counterintuitively, local
decoherence can generate quantum correlations.

本文研究了在局部噪声通道的影响下，量子相关性的行为特征，并且发现对于 qubit 系统来说，只有处于联合状态通道的噪声才会对量子性产生负面影响。但是对于一些初始状态为经典态的系统，非联合通道（如耗散通道）可以产生一些量子相关性。此外，对于高维系统，甚至联合通道也可能增加量子相关性，表明局部的非相干性竟然可以产生量子相关性。

局部噪声下的量子相关性行为

Behavior of Quantum Correlations under Local Noise

We propose a novel dynamical method for beating decoherence and dissipation
in open quantum systems. We demonstrate the possibility of filtering out the
effects of unwanted (not necessarily known) system-environment interactions and
show that the noise-suppression procedure can be combined with the capability
of retaining control over the effective dynamical evolution of the open quantum
system. Implications for quantum information processing are discussed.

提出了一种用于控制开放式量子系统的新型动力学方法，可以过滤掉不需要的系统 - 环境相互作用的影响并结合保持开放式量子系统的有效动力学演化控制。该方法在实现量子信息处理方面具有潜在的应用价值。