Dancun Manyinsa - Fringe project
Fringe effect is a result of boundary conditions not being completely ideal.
According to Maxwells Equations we know ∇.D = ρ. This implies n.(D2 - D1) = ρs where n is a normal vector to the surface of the capacitor and ρs is a surface charge density. Assuming all surface charge is on the plane closest to the other plate and a conducting material, D field on the smaller sides of the plate would equally be zero. Slight imperfections in the material (like thickness and some surface charge in the wrong places), we will experience some fringing - which comes directly from Maxwells Equations.
This project compares the accuracy of an Autoregressive Integrated Moving Average model and a Recurrent Neural Network based on Gated Recurrent Units (GRUs) with regards to real-valued time series prediction. The input will be a one week sequence of national hourly electric load demand data for Austria, and the output expected is a prediction of the following week's hourly load demand data. This approximation is solely based on a real-valued time series analysis of historical data.
For the Recurrent Neural Network: To train the model, run:
python recurrent.py train
This will train the RNN on the entire training data. Internally, the function shuffles different 168-hour-long sequences to increase the entropy of the training data.
For testing:
python recurrent.py test
Testing simply shows a matplotlib graph of the true and predicted sequences plotted on the same axes for comparison. Using the test evaluates the immediate one-week sequence following the training data.
For the ARIMA model:
To fit the model, run:
python time_series.py train
To test:
python time_series.py test
To calculate the average Mean Absolute Percentage Error on all test data:
python recurrent.py mape
or
python time_series.py mape
The following graphs show the resultant predictions against the targets for the neural nets:
The graph of the sample test of the autoregressive method is shown below:
Autoregressive methods on average perform better than neural nets. The extra features offered by AI seem to be useful in tasks such as language processing. Equations are still better at math than neural nets.
This software is released under the MIT license.