Towards Reliable Neural Optimizers: Permutation-Equivariant Neural Approximation in Dynamic Data Driven Applications Systems

Dynamic Data Driven Applications Systems (DDDAS) motivate the development of optimization approaches capable of adapting to streaming, heterogeneous, and asynchronous data from sensor networks. Many established optimization solvers, such as branch-and-bound, gradient descent, and Newton-Raphson methods, rely on iterative algorithms whose step-by-step convergence makes them too slow for real-time, multi-sensor environments. In our recent work, we introduced LOOP-PE (Learning to Optimize the Optimization Process, Permutation Equivariance version), a feed-forward neural approximation model with an integrated feasibility recovery function. LOOP-PE processes inputs from a variable number of sensors in arbitrary order, making it robust to sensor dropout, communication delays, and system scaling. Its permutation-equivariant architecture ensures that reordering the input data reorders the corresponding dispatch decisions consistently, without retraining or pre-alignment. Feasibility is enforced via a generalized gauge map, guaranteeing that outputs satisfy physical and operational constraints. We illustrate the approach in a DDDAS-inspired case study of a Virtual Power Plant (VPP) managing multiple distributed generation agents (DERs) to maximize renewable utilization while respecting system limits. Results show that LOOP-PE produces near-optimal, feasible, and highly adaptable decisions under dynamic, unordered, and distributed sensing conditions, significantly outperforming iterative algorithm based solvers in both speed and flexibility. Here, we extend our earlier work by providing additional analysis and explanation of LOOP-PE design and operation, with particular emphasis on its feasibility guarantee and permutation equivariance feature.