Constructing ordinary sum differential equations using polynomial networks

Quart J Royal Meteoro Soc

Sokol

2018

Self Cite

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.

Section: Appendix Bmentioning

confidence: 99%

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

Quart J Royal Meteoro Soc

Sokol

2018

Self Cite

“…The binary PSO uses binary operators and the corresponding coefficients settings in the standard PSO (velocity) equations to form new individuals [15]. Parameters of polynomials and PDE term weights are represented by real numbers, randomly initialized from the interval <0.5, 1.5> and adjusted by means of the gradient steepest descent method [17] combined with a difference evolution algorithm (EA) [16], performed simultaneously with the best-fit neuron combination search [18]. The D-PNN (also GMDH) approximation ability of complicated periodic functions is possible to improve by means of a sigmoidal transformation (sig) of the squared power items together with their parameters in both the neuron and block output polynomials (30).…”

Section: Fig 4 3-variable Multi-layer D-pnn With 2-variable Combination Blocksmentioning

confidence: 99%

“…While using 2 input variables an equivalent 2 nd order PDE (3) may be expressed in the form(18), which derivative variables of the PDE terms, correspond exactly to all the GMDH polynomial (2) variables. The 2-variable block neurons form and substitute for all the relevant partial derivative terms, so each block includes 5 simple neurons formed with respect to 2 single linear x1, x2(19), 2 squared x1 2 , x2 2 (20) and 1 combination x1x2 (21) derivative variables of the 2 nd order PDE substitution (18) in a searched 2-variable u function model.…”

mentioning

confidence: 99%

A substitution of the general partial differential equation with extended polynomial networks

2016 International Joint Conference on Neural Networks (IJCNN)

Snášel

Ojha

et al. 2016

Self Cite

General partial differential equations, which can describe any complex functions, may be solved by means of the dimensional similarity analysis to model polynomial data relations on the basis of discrete observations. Designed new differential polynomial networks define and substitute for a selective form of the general partial differential equation using fraction derivative units to model an unknown system or pattern. Convergent series of relative derivative substitution terms, produced in all network layers, describe partial derivative changes of some combinations of input variables to generalize elementary polynomial data relations. The general differential equation is decomposed into polynomial network backward structure, which defines simple and composite sum derivative terms in respect of previous layers variables. The proposed method enables to form more complex and varied derivative selective series models than standard soft-computing techniques allow. The sigmoidal function, commonly employed as an activation function in artificial neurons, may improve the polynomial and substituting derivative term abilities to approximate complicated periodic multi-variable or time-series functions in a system model.

“…Differential equations can describe physical or natural systems which it is difficult to model by unique exact functions; the solutions can apply power [8] or wave series [9], genetic programming [10] and neural networks [11]. Polynomial networks may be extended to apply some mathematical principles (Section 2) to form and substitute for general differential equations [12].…”

Section: Introductionmentioning

confidence: 99%

“…Multi-layer differential polynomial neural network A multi-layer PNN forms composite polynomial functions (Fig. 2); the previous layers form internal functions y i (12), which substitute for the next hidden layer input variables of neuron and block polynomials to form external functions f(y) (13). Composite PDE terms, i.e.…”

Section: Introductionmentioning

confidence: 99%

Wind speed forecast correction models using polynomial neural networks

2015

Renewable Energy

Self Cite

a b s t r a c tAccurate short-term wind speed forecasting is important for the planning of a renewable energy power generation and utilization, especially in grid systems. In meteorology it is usual to improve the forecasts by means of some post-processing methods using local measurements and weather prediction model outputs. Neural networks, trained with local real data observations can improve short-term wind speed forecasts with respect to meso-scale numerical meteorological model outcomes of the same data types in the majority of cases. Large-scale forecast models are based on the numerical integration of differential equation systems, which can describe atmospheric circulation processes on account of global meteorological observations. Several layer 3D complex models, which involve a large number of matrix variables, cannot exactly describe conditions near the ground, highly influenced by a landscape relief, coast, structure and other factors. Polynomial neural networks can form and solve general differential equations, which allow to model real complex systems by means of substitution derivative term sum series. The proposed adaptive method forms a correction function according to real observations and consequently applies forecasts to revise a desired prognosis in a selected locality.