We propose a novel Spatio-Temporal Graph Neural Network empowered trend analysis approach (ST-GTrend) to perform fleet-level performance degradation analysis for Photovoltaic (PV) power networks. PV power stations have become an integral component to the global sustainable energy production landscape. Accurately estimating the performance of PV systems is critical to their feasibility as a power generation technology and as a financial asset. One of the most challenging problems in assessing the Levelized Cost of Energy (LCOE) of a PV system is to understand and estimate the long-term Performance Loss Rate (PLR) for large fleets of PV inverters. ST-GTrend integrates spatio-temporal coherence and graph attention to separate PLR as a long-term "aging" trend from multiple fluctuation terms in the PV input data. To cope with diverse degradation patterns in timeseries, ST-GTrend adopts a paralleled graph autoencoder array to extract aging and fluctuation terms simultaneously. ST-GTrend imposes flatness and smoothness regularization to ensure the disentanglement between aging and fluctuation. To scale the analysis to large PV systems, we also introduce Para-GTrend, a parallel algorithm to accelerate the training and inference of ST-GTrend. We have evaluated ST-GTrend on three large-scale PV datasets, spanning a time period of 10 years. Our results show that ST-GTrend reduces Mean Absolute Percent Error (MAPE) and Euclidean Distances by 34.74% and 33.66% compared to the SOTA methods. Our results demonstrate that Para-GTrend can speed up ST-GTrend by up to 7.92 times. We further verify the generality and effectiveness of ST-GTrend for trend analysis using financial and economic datasets.

Optimizing over the stationary distribution of stochastic differential equations (SDEs) is computationally challenging. A new forward propagation algorithm has been recently proposed for the online optimization of SDEs. The algorithm solves an SDE, derived using forward differentiation, which provides a stochastic estimate for the gradient. The algorithm continuously updates the SDE model's parameters and the gradient estimate simultaneously. This paper studies the convergence of the forward propagation algorithm for nonlinear dissipative SDEs. We leverage the ergodicity of this class of nonlinear SDEs to characterize the convergence rate of the transition semi-group and its derivatives. Then, we prove bounds on the solution of a Poisson partial differential equation (PDE) for the expected time integral of the algorithm's stochastic fluctuations around the direction of steepest descent. We then re-write the algorithm using the PDE solution, which allows us to characterize the parameter evolution around the direction of steepest descent. Our main result is a convergence theorem for the forward propagation algorithm for nonlinear dissipative SDEs.