Observers for PDEs are themselves PDEs. Therefore, producing real time
estimates with such observers is computationally burdensome. For both
finite-dimensional and ODE systems, moving-horizon estimators (MHE) are
operators whose output is the state estimate, while their inputs are the
initial state estimate at the beginning of the horizon as well as the measured
output and input signals over the moving time horizon. In this paper we
introduce MHEs for PDEs which remove the need for a numerical solution of an
observer PDE in real time. We accomplish this using the PDE backstepping method
which, for certain classes of both hyperbolic and parabolic PDEs, produces
moving-horizon state estimates explicitly. Precisely, to explicitly produce the
state estimates, we employ a backstepping transformation of a hard-to-solve
observer PDE into a target observer PDE, which is explicitly solvable. The MHEs
we propose are not new observer designs but simply the explicit MHE
realizations, over a moving horizon of arbitrary length, of the existing
backstepping observers. Our PDE MHEs lack the optimality of the MHEs that arose
as duals of MPC, but they are given explicitly, even for PDEs. In the paper we
provide explicit formulae for MHEs for both hyperbolic and parabolic PDEs, as
well as simulation results that illustrate theoretically guaranteed convergence
of the MHEs.

基于反步法，本文提出了适用于 PDE 的 MHE（移动时域估计器），通过将难以解决的观测器 PDE 转化为可明确求解的目标观测器 PDE，实现了在任意长度的移动时域上的状态估计。模拟结果证明了 MHE 的理论保证收敛性。

1-D 中的双曲线和抛物线 PDE 的移动边界估计器

Moving-Horizon Estimators for Hyperbolic and Parabolic PDEs in 1-D

A key challenge of dialog systems research is to effectively and efficiently
adapt to new domains. A scalable paradigm for adaptation necessitates the
development of generalizable models that perform well in few-shot settings. In
this paper, we focus on the intent classification problem which aims to
identify user intents given utterances addressed to the dialog system. We
propose two approaches for improving the generalizability of utterance
classification models: (1) observers and (2) example-driven training. Prior
work has shown that BERT-like models tend to attribute a significant amount of
attention to the [CLS] token, which we hypothesize results in diluted
representations. Observers are tokens that are not attended to, and are an
alternative to the [CLS] token as a semantic representation of utterances.
Example-driven training learns to classify utterances by comparing to examples,
thereby using the underlying encoder as a sentence similarity model. These
methods are complementary; improving the representation through observers
allows the example-driven model to better measure sentence similarities. When
combined, the proposed methods attain state-of-the-art results on three intent
prediction datasets (\textsc{banking77}, \textsc{clinc150}, \textsc{hwu64}) in
both the full data and few-shot (10 examples per intent) settings. Furthermore,
we demonstrate that the proposed approach can transfer to new intents and
across datasets without any additional training.

本论文旨在提出一种有效的适应新领域的可扩展模型，该模型使用观察者和基于示例的训练方法提高了话语分类模型的概括能力，并实现在银行，CLINC150 和 HWU64 上进行的语言意图识别中，采用以上方法获得了最先进的结果。