Multi-variate soft sensor seeks accurate estimation of multiple quality
variables using measurable process variables, which have emerged as a key
factor in improving the quality of industrial manufacturing. The current
progress stays in some direct applications of multitask network architectures;
however, there are two fundamental issues remain yet to be investigated with
these approaches: (1) negative transfer, where sharing representations despite
the difference of discriminate representations for different objectives
degrades performance; (2) seesaw phenomenon, where the optimizer focuses on one
dominant yet simple objective at the expense of others. In this study, we
reformulate the multi-variate soft sensor to a multi-objective problem, to
address both issues and advance state-of-the-art performance. To handle the
negative transfer issue, we first propose an Objective-aware Mixture-of-Experts
(OMoE) module, utilizing objective-specific and objective-shared experts for
parameter sharing while maintaining the distinction between objectives. To
address the seesaw phenomenon, we then propose a Pareto Objective Routing (POR)
module, adjusting the weights of learning objectives dynamically to achieve the
Pareto optimum, with solid theoretical supports. We further present a
Task-aware Mixture-of-Experts framework for achieving the Pareto optimum
(TMoE-P) in multi-variate soft sensor, which consists of a stacked OMoE module
and a POR module. We illustrate the efficacy of TMoE-P with an open soft sensor
benchmark, where TMoE-P effectively alleviates the negative transfer and seesaw
issues and outperforms the baseline models.

本文提出一种适用于多个质量变量的多变量软测量方法，通过改良神经网络结构和优化目标函数，实现了对质量变量的准确估计。在这个方法中，作者利用目标专家混合模块（OMoE）和帕累托目标路由模块（POR）解决了模型中存在的负面迁移和平衡问题，实验结果表明，该模型表现出了先进的性能。

TMoE-P: 面向多变量软测量的帕累托最优

TMoE-P: Towards the Pareto Optimum for Multivariate Soft Sensors

The 2-spin Ising model in statistical mechanics and the 2x2 normal form game
in game theory are compared. All configurations allowed by the second are
recovered by the first when the only concern is about Nash equilibria. But it
holds no longer when Pareto optimum condiderations are introduced like in the
prisoner's dilemma. This gap can nevertheless be filled by adding a new
coupling term to the Ising model, even if that term has up to now no physical
meaning. An individual complete bilinear objective function is thus found to be
sufficient to reproduce all possible configurations of a 2x2 game. Using this
one-to-one mapping, new perspectives for future research in both fields can be
envisioned.

通过比较统计力学中的 2 自旋伊辛模型和博弈论中的 2x2 标准形式博弈，发现只考虑 Nash 均衡时两者有相同表现，但在考虑 Pareto 最优解时则不然。但是通过在伊辛模型中添加新的耦合项，可以弥补这个差距。因此发现，单个完整双线性客观函数足以模拟 2x2 标准形式博弈的所有可能情况。使用这种一一映射，可以展望未来在两个领域中的新研究方向。