Neural Networks: Some Neural Network Applications

Proposed Project

A neat little project that I would like to do as a sample application is to replace the Vincenty forward and reverse geodetic functions, in my global navigator program, with multi-layer perceptrons. The one for the 'Vincenty Solution to the Geodetic In­verse Problem' is shown below.

The above illustration shows only the simplest form of network. Notwith­standing, to obtain results with the precision and accuracy of my Vincenty functions as implemented, more hidden neurons could well be required.

During training, inputs would be sent to both the perceptron and the corresponding Vincenty function. The outputs from the Vincenty function would then be compared with those from the perceptron to obtain the output error for each output. These output error values would be then back-propagated to adjust the input weights to each neuron in the network.

If training were done on hundreds of flights all over the world, the perceptrons would gradually become able to navigate the globe with ever-diminishing error. The global navigator program switches to the best-fit reference geoid automatically according to where it is in the world. This way, the perceptron would eventually model the planet very accurately, warts and all; meaning that the best-fit geoids would no longer be necessary.

Although this exercise could be very useful for navigation, its value to me would be mainly as a practical means of substantiating, what is perhaps, my most profound personal conjecture about the universe. It is that — contrary to the thinking of Plato and also of one of my favourite modern mathematicians [who, incidentally attended my old school] — the Laws of Physics are not mathematical.

Mathematics is simply a language [a thing that exists only within the con­scious mind] that provides us with a crude fit-kit of ideas through which we attempt to express how the Laws of Physics appear to work to us, from our points of view as we journey along our individual paths through time and space.

The real Laws of Physics that drive the objective universe are something else. They probably operate fractally at the finest scale within a continuously moving present with no past or future. And I think they will remain — fundamentally and eternally — beyond our ability to know them.

So if indeed it be possible to replace my Vincenty functions [which are wholly math­ematical in nature with their sines, cosines, elliptical corrections and iterative con­vergence] with a multi-layer perceptron [which is a digital simulation of a strictly non-mathematical analogue process] then my conjecture is strongly substantiated.

I have alluded to this conjecture also elsewhere in the context of the optimum form for the path flown by an aircraft, as it passes its waypoints along an air route.

Other Applications

Local Weather Predictor

Input parameters such as temperature, pressure, humidity, wind-speed, wind direction, relative day length, proportion of cloud cover, daylight intensity, solar angle, etc. to a multi-layer perceptron. Perhaps also enter the first and even higher-order differentials of these parameters as additional inputs. Pro­d­uce an output giving a useful classification of the weather at prescribed times into the future. The classifications could vary according to purpose, e.g. hu­m­an comfort, farming, building.

Harvesting Predictor

Inputs to a neural network from the local weather predictor (see above) com­bined with inputs from a spectrum analyser of the light being reflected from a crop could provide an output giving advanced advice as to the ideal instant to harvest a crop.

H.F. Radio Conditions Predictor

Radio path conditions on the H.F. band (7 to 30 MHz) vary in a way similar in nat­ure to (but not necessarily significantly related to) the weather. Input such things as the frequency and strength of V.L.F. whistlers, current signal condi­tions, time of day, season, phase of the 11/22-year sun spot cycle, to a neural network. With training, the output could be made to predict the communica­tion conditions at various prescribed lengths of time into the future for given directions, paths or destinations. This could even distinguish between diver­gent conditions on different bands, giving a probability conditions of good or bad contact.

Radio Signal Identification

A neural network could be trained to recognise its owner's call sign when someone else is calling its owner. It could also be made to recognise who is calling. This could fulfil for voice radio the role of the bell on a telephone to alert the person being called.

Relaxing Mobile Networks

The travelling salesman problem of finding the shortest route between a set of towns. The particular application of current interest is that of finding the short­est links in a communications network whose nodes are mobile. The conject­ure is that this is best solved by algorithm rather than by minimising the ener­gy function of an elastic network or by running a Hopfield network. However, these networks may be better at solving other constraint satisfaction problems such as best crop mix in view of climatic and market conditions.

Personal Identification

A neural network could be trained to recognise a person's face, signature, finger print, DNA or iris patterns all together to give a strong reinforcement to recognition.

Personal Compatibility Prediction

Given certain facts about a person, a neural network could be taught to pre­dict whether or not the person would be a good client, business associate, fri­end, spouse, employer, employee, advisor, confidante, etc. for you — a given indivi­dual. It could also be taught which type of companies would be good cli­ents or suppliers for you specifically. The network would have to be taught using good and bad past examples. It could also be used to assess which occ­upation or mode of working would be most beneficial or acceptable to a given person. It could also have uses in political analysis and psychology.

Maintaining Dynamic Trim

An aircraft (or ship) in rough weather could be kept in trim and on course by a neural network acting as the flight control and navigation computer. Inputs such as speed, rate of climb/descent, rate of turn, thrust, pitch, roll, height error, course error could be provided. It could then be trained to give appro­priate output of pitch, roll, flaps, thrust and rudder commands. The network could be taught by recording the conditions on a flight and the actions of an experienced pilot.

Predicting Market Trends

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