  The complexities of information processing across Dynamic Data Driven
Applications Systems drive the development and adoption of Artificial
Intelligence-based optimization solutions. Traditional solvers often suffer
from slow response times and an inability to adapt swiftly to real-time input
variations. To address these deficiencies, we will expand on our previous
research in neural-based optimizers by introducing a machine learning-enabled
neural approximation model called LOOP-PE (Learning to Optimize the
Optimization Process -- Permutation Equivariance version). This model not only
enhances decision-making efficiency but also dynamically adapts to variations
of data collections from sensor networks. In this work, we focus on mitigating
the heterogeneity issues of data collection from sensor networks, including
sensor dropout and failures, communication delays, and the complexities
involved in integrating new sensors during system scaling. The proposed LOOP-PE
model specifically overcomes these issues with a unique structure that is
permutation equivariant, allowing it to accommodate inputs from a varying
number of sensors and directly linking these inputs to their optimal
operational outputs. This design significantly boosts the system's flexibility
and adaptability, especially in scenarios characterized by unordered,
distributed, and asynchronous data collections. Moreover, our approach
increases the robustness of decision-making by integrating physical constraints
through the generalized gauge map method, which theoretically ensures the
decisions' practical feasibility and operational viability under dynamic
conditions. We use a DDDAS case study to demonstrate that LOOP-PE model
reliably delivers near-optimal and adaptable solutions, significantly
outperforming traditional methods in managing the complexities of multi-sensor
environments for real-time deployments.
