  Accurate estimation of multiple quality variables is critical for building
industrial soft sensor models, which have long been confronted with data
efficiency and negative transfer issues. Methods sharing backbone parameters
among tasks address the data efficiency issue; however, they still fail to
mitigate the negative transfer problem. To address this issue, a balanced
Mixture-of-Experts (BMoE) is proposed in this work, which consists of a
multi-gate mixture of experts (MMoE) module and a task gradient balancing (TGB)
module. The MoE module aims to portray task relationships, while the TGB module
balances the gradients among tasks dynamically. Both of them cooperate to
mitigate the negative transfer problem. Experiments on the typical sulfur
recovery unit demonstrate that BMoE models task relationship and balances the
training process effectively, and achieves better performance than baseline
models significantly.
