Local improvements in numerical forecasts of relative humidity using polynomial solutions of general differential equations

Abstract

Large‐scale forecast models are based on the numerical integration of differential equation systems, which can describe atmospheric processes in light of global meteorological observations. Mesoscale forecast systems need to define the initial and lateral boundary conditions, which may be carried out with robust global numerical models. Their overall solutions are able to describe the dynamic weather system on the Earth scale using a large number of complete globe 3D matrix variables in several atmospheric layers. Post‐processing methods using local measurements were developed in order to clarify surface weather details and adapt numerical weather prediction model outputs for local conditions. Differential polynomial network is a new type of neural network that can model local weather using spatial data observations to process forecasts of the input variables and revise the target 24 h prognosis. It defines and solves general partial differential equations, being able to describe unknown dynamic systems. The proposed forecast correction method uses a differential network to estimate the optimal numbers of training days and form derivative prediction models. It can improve final numerical forecasts, processed with additional data analysis and statistical techniques, in the majority of cases. The two‐stage procedure presented is analogous to the perfect‐prognosis method using real observations to derive a model, which is applied to the forecasts of the predictors to calculate output predictions.

Photovoltaic Energy All-Day and Intra-Day Forecasting Using Node by Node Developed Polynomial Networks Forming PDE Models Based on the L-Transformation

“…Past overnight changes in weather can be searched first in order to detect the following interval of data records applicable in training. Additional input data with another 24 h delay of the entire day can improve the performance of AI models in specific periods of pattern (dis)similarity in some of the previous days to predict daily PVP cyclic data, analogous to relative humidity or power load [26].…”

PV Energy Prediction in 24 h Horizon Using Modular Models Based on Polynomial Conversion of the L-Transform PDE Derivatives in Node-by-Node-Evolved Binary-Tree Networks

“…The statistically developed model may be completely out of date, unable to process unrecognized data series in prediction. NWP processing data can be applied in these sudden cases [5]. Figure 2 shows the frontal change in PVP patterns on 3 May.…”

“…Polynomial conversion applied to ODE derivatives results in a set of Equation ( 4), where the Laplace transform F(p) can be formulated through the complex conjugate p. F(p) is separated in a rational term (5) to define the L-image of the function f (t). The inverse transform of OC of the ration term restores the original f (t) of a real variable t (5).…”

“…The new differential learning is used to gradually elicit structures based on the form of a polynomial neural network (PNN), initially using one node, to partition and transform the general PDE of n variables into summation modules of single PDEs in blocks of two-variable nodes. The rational components are obtained in the form of Laplace transform images of unknown node functions, formed according to operator calculus (OC) procedures [5]. The inverse L-operation is applied to the node-produced rational components, based on the OC expression.…”

PV power intra‐day predictions using PDE models of polynomial networks based on operational calculus

“…The previous differential polynomial neural network (D‐PNN) concept, based on similarity theory, allows complex representation of the local weather dynamics [21]. Conventional and soft‐computing techniques usually significantly reduce the number of input variables leading to their model over‐simplification.…”