 Okay, so good morning everybody and I must thank Professor Ildho for his kind words. Now let me come back to start with my lecture formally now. I am going to speak on applications of soft computing in water resources and coastal engineering. Now frankly, I am basically a coastal engineer, but I many times dabble into hydraulics and water resources. Now I am going to mainly talk about techniques like ANN, GP that is the genetic programming, the technique of MT that is model 3, LWPR that is locally weighted projection regression. Some of these techniques may be quite new to you, well some may be you may be already aware up to some extent. Now because some basic information about the artificial neural network has already been covered by Dr. Krishnamohan, I think I am not, I am going to steep this basic information if it is available in textbooks and I do not want to give you the information that is easily available in textbooks. Nonetheless, very quick brush up of the basic ideas will be given and then I will give more stress or more importance to the application side because with the view that you may note the conclusions that we have arrived at from these studies. Now as regards applications in coastal engineering is concerned, it is possible that you may not have worked in that area or you may not have a direct interest in that area, but despite the fact you see what are the problems to which we have applied these techniques, what are the salient features of those application details and what are the important conclusions that we have arrived at from these studies. So these things should stand you in good state when you yourself apply these techniques to your problems which may be different than the actual problems that we have studied. Again coming to GP, MT and LWPR, I will not go into all the theoretical details, I will give you the basic concepts and tell you what are the applications that we have made. LWPR is concerned, we have recently started with this technique. So also we, there are techniques like support vector machine, relevant vector machines with which we have started and I will briefly touch upon these in the lecture. Now you may have been hearing so many things about soft computing and I hope you are all aware that when we say soft computing, it means it is that computational technique which is soft towards something. Now what is that something? That something is problems with data, a given input information, given data may have lot of problems like partial tools, uncertainty, imprecision, inaccuracy, etc. Now the soft computing techniques are softer towards this technique, they basically they are focused or oriented in solving these problems with data, they note that the real world in which we are living has certain inbuilt tolerance towards this information and this tolerance is exploited in a certain way in real world and the soft computing tool basically targets that tolerance of the real world towards data deficiencies or problems with a view to arrive at more meaningful solutions to the problems that we are facing. Now the ideal before soft computing tool is the human brain. The cognition process that goes on in our human brain is something that is imitated in the soft computing tools. Now in that way there are so many techniques which are overlapping between soft computing, artificial intelligence, data mining, machine learning. But these all the different terms have got some I mean slightly different focus we can say, most of the techniques are same, they overlap but when we say typically artificial intelligence technique, it means we talk more about you know object oriented programming or these kind of languages programming languages etc. When we say machine learning, I mean we focus on those techniques which make a machine or robot to learn. They will involve all these components which we have listed here but the focus is something else, I mean the objective is something else. But nonetheless the computation techniques are more or less the same. Similar things are true about any general data mining technique which mines the data and comes up with and meets certain objectives of data analysis. Now here we have to note that again when we say artificial intelligence, it is the intelligence that we try to look to through our computations. For example, you know we say that some persons are intelligent, we are all teachers, we normally say that some students in our class are teachers. Now what does it mean, I see in a given class of 40, 45 people, there may be five or six students whom we call as intelligent. Why, because you are giving the same information to the entire class, you are giving the same information to the entire class. But these five or six students, they are able to draw inferences correctly compared to other students from what you give to them. So these five or six students we call intelligent because they overcome these problems of partial tools, uncertainty, imprecision, innocuous, etc. if they are present in your delivery and find out the exact solution to the problem or they meet your exact requirement. And in other words, I mean applying our criteria, they pass the exam with color. So then we call them intelligent. So the word intelligence here again means drawing correct inference from the available data. In that way, this word is used. Now, as you know, we have intelligence bureaus within government. What they do, they look for different clues of some, you know, criminals or something. And then they reach to the conclusion that this crime must have been done by XYZ or this is the way in which the crime must have been done and like that. So in that way, basically all these techniques means playing with the data, even though they are insufficient or having, they may have some problems, you play with them and interpret them most correctly. That is the basic idea behind all these things. Now then you have this neural network, various components of saw point computing or AI, like neural network, fuzzy logic, genetic algorithm, genetic programming. Then you have these model trees, various other methods, hybrid systems, etc. Now you may be aware that it is basically very difficult to give the precise definition of each thing because these terms are all engineering terms, unlike scientific terms, they don't have any, it is very difficult to confine them into correct definitions. But when we say neural networks, we mean basically it's a technique that is used to map any random input quantity with corresponding random output quantity. That is the basic purpose rather, when we, civil engineers or engineers in general, when we use them, then the fuzzy logic is the multi-valued logic. That means it goes beyond yes and no, two values. It is a multi-valued logic. It recognizes something between yes and no. And its major use is to quantify the linguistic variables. For example, we say that I am a thin person, somebody is fat person, somebody is moderate in build. Now these kinds of linguistic variables, thin, fat, etc. are very difficult to quantify. But with the help of fuzzy logic, we do quantify them and take these things into our computational, incorporate them into our computational procedures. Then you have genetic algorithms. And I think there must have been a couple of lectures on that. Basically in civil engineering, it has been used as a optimization tool. And this optimization tool has been modeled on the basis of natural selection process of evolution that goes on in the, in nature. And it works by the principle of what is called the survival of the fittest concept. Now genetic programming is actually analogous to genetic algorithm. But basically there is a difference in the processing of the information in genetic programming. In genetic programming, we follow the principle of survival of the fittest and the natural selection process that goes on in nature thereby. But we end up with an equation or a computer program or a computer algorithm to solve a problem. Whereas normally when we say genetic algorithm, our outcome is in the form of a number or set of numbers, some optimized quantity like that. But genetic programming is essentially a regression tool. It is used to carry out regression between a set of input quantity and a set of output quantity. The whole processing is different right from start. But the components, namely the crossover, mutation, reproduction, et cetera, they are similar in concept. So then we have this technique of model trees. And in the technique of model trees, we split the input space or input domain into various subdomains using some criterion and fit linear models within each subdomain. So it is something like a piecewise linear model. Then you have other methods like this locally weighted projection regression. As the name indicates, these are local models. They are not global models. That means output is not linked to the input through one common kind of model. But there are output is again split into different domains. And within each domain, local models are fitted. Now it is called projection regression because locally weighted projection regression is again a special type of locally weighted modeling. And the term projection here comes into picture because again the input space, the input data are projected into directions which are mathematically orthogonal to the original one. And within each orthogonal directions, linear models are fitted. And then they are by following an average process, averaging process, they are combined. And then the final solution comes. So this was something brief concept of the locally weighted projection regression. Then you have support vector machine and support vector regression. Again support vector machine when you say it is again in optimization tool when you say regression, it is used to find out a relation between y vector and x vector and so on. In support vector machine again, the idea is same. That means you map or convert or transform the input space into what is called the feature space. And within each feature space, you fit the linear models with the help of quantities which are called support vectors. Now support vectors indicate selected input patterns occurring to some criteria. The input patterns are selected. And with the help of the selected input patterns, local models are built. And then the quantities are predicted. Now there is again a improvement in the support vector machine technique. It is called relevant vector machine technique. Relevant vector machine technique is something which is an advancement to the support vector machine of support vector regression technique. And the advantage comes because it uses certain probabilistic description of the features involved. Whereas in none of these techniques, any probabilistic treatment is given to the problem. But relevant vector machines have got that advantage. And they have been specified. Now all these techniques, they have come because of the efforts of communication engineers, signal processing experts, and so on, control engineers. In our engineering application, especially in civil engineering, they are all very new. The neural network typically started, as you know, in 1992 applications I'm talking about. Neural network applications started in 1992. Around similar time fuzzy logical applications started. Genetic algorithms, I think, more or less in the same year, maybe two, three years prior to that. Genetic programming is very recent. I mean, as we will see later, there are papers, publications started appearing only three or four years back. So model tree is even slightly more modern in its application type. And papers in model tree started only three, four years back, isn't it? It's three or four years back. Now, there is no reported application of locally weighted projection regression in water, so far. But two of our students here have worked. And we have recently sent that paper for publication. Support vector machine, relevant vector machine also, I think as regards support vector machine, currently some handful of single digit publications are available, if I am correct. They have just started appearing, isn't it? And relevant vector machine, there is actually no application. But one new assistant professor named Subimal Ghosh has joined us recently, some two days back. And he has worked in this relevant vector machine. So I don't know whether he has published his results. But the point that I want to stress is that these are very new techniques. Neural net worth, fuzzy logic, genetic algorithms have been existing since last, we can say, 15 years or so. But the latter techniques are very, very new. And therefore, there is a very big scope to apply these techniques to your problems and ensure how far they are useful to your cases. Now, of course, having said this, the latest trend is to go for what are called the hybrid systems. Yesterday only I was discussing this problem with some ISRO people in Ahmedabad. And they were also saying that they also come to this conclusion that rather than this individual model, say, neural networks, genetic algorithm, and so on, if a combined modular approach is taken to solve a problem, then that works better. That is more beneficial. For example, as your water resources are concerned, you see, let's say you are predicting a river discharge along a river on an annual basis, a daily river discharge for one year. Now it is quite possible that some particular model may fit better. Let's say monsoon discharges may be better predicted by neural networks. It is quite possible that fair weather discharge may be predicted better by, say, genetic programming. Then have a system wherein a inbuilt software or package or whatever you may call wherein, if the expected discharge, let us say, is less than something, the pointer will go to that particular approach and the prediction will be made accordingly. If it is a monsoon discharge exceeding a certain value, another model will be picked up. So like that, they are saying that this modular approach or hybrid system is something that should be more welcome because artificially or unnecessarily, you don't try to fit the entire data into one particular model. You try to decompose it into component and you can apply different models to different parts of data provided they are significantly proved to be better than the other one. So this is something that you may remember and with the advent of this computing technology these days and all those palm computers and so on, it should not be difficult to implement all these things even though they are computationally really extensive. Now you may be aware that when it comes to problem solving hydraulics or water resources of coastal engineering for that matter, four generations of computing have been identified. When we say in next generation, it means there is a jump in technology. The migration is not gradual, there is a sudden change. For example, in let's say 40s or 30s or 50s, you have only analytical equations to solve the problem. For example, the equation to model the turbulent boundary layer, equation to model the laminar boundary layer, clear cut analytical equations were there. But the soon people found that the use of these analytical equations was indeed very limited because the real world, the real phenomena are indeed so complex that it is very, very difficult to conceptualize the all these phenomena into a single analytical equation. Then people started working on various experimental methods. Various electron equipments also got developed. So experimental method also got a boost. With along with the experimental methods, the field data used to get collected and then empirical methods based on the analysis of those field data also started coming into picture. But these experimental methods or empirical methods, they suffered from subjectivity in their interpretation because there was unlike analytical equations, the objectivity was less in that. Then people went to numerical schemes wherein the phenomena were conceptualized into differential equations. Like for example, the fluid rooting in open channel, the phenomena was conceptualized into continuity equation, equation of momentum and so on. And these equations were solved with the help of numerical methods. Now this numerical method as you know got a big boost because of the advances in computer technology and they have proved to be indeed very, very useful. Especially the knowledge that people get often out of numerical methods over special, large spatial domain and large temporal domain, time and space. That particular knowledge was found to be indeed very, very attractive. But numerical methods again as you know have the problem that you should be sure that the phenomenon that you are going to analyze can be conceptualized fully in the form of differential equations or mathematical equations. If there is some problem with that, if that involves a lot of assumptions, et cetera, then naturally because the basic starting point is somewhat weaker, there is no point in using the advances in computer technology and using so many advanced solution techniques because the basic concept also had itself involves some kind of an acceptability in it. That's why in last 10, 15 years, the fourth generation models coming under data-driven modeling scheme have come into picture. Now all the soft computing AI, you know, artificial intelligence, machine learning, data mining techniques, they all come under these data-driven methods. Now these methods are indeed new and because they are new, their applications are relatively less compared to numerical methods or experimental methods or analytical methods and they are yet to be widely accepted. It is the responsibility of people like you to apply these new techniques and prove to others that yes, they work as fine as numerical methods or for that matter even analytical and empirical methods. Now, coming to neural networks, I think I need not go into all these techniques because first of all the professor Krishnamohan may have already explained to you these techniques and also because they are very easily available in textbooks. Now, but you know that probably it was Ian Flood who is very active in ASEE. He basically did a pioneering but apparently he applied this technique of ANN2 construction activities and from that a lot of applications and civil engineering resulted. Now, as you know, a typically artificial neuron mimics the biological neuron processing and in that case, basically the cognition process of biological neuron involves taking the input, summing it up, comparing that input with some kind of threshold value and taking a decision whether the strength of the input is more than the threshold value or less than. If it is more, then only you fire that information to the subsequent layer of neurons. If it is less, you don't fire it. Now, that is the basic understanding of the biological neuron. Now, it is very difficult to follow that procedure exactly in our mathematical computation because obviously how to obtain the so-called threshold patterns. So, in that case what we do, we do some kind of a modified procedure. We take the input, we multiply it by certain weights, w1, w2, w3, et cetera. There may not be three, there may be more than that or less than. Then we add a bias term, a sum numerical figure to that. Then allow this product or sum to pass through a transfer function, typically a sigmod function, SCF function. Now, the property of the sigmod function is, I mean the sigmod functions are chosen because of so many things, but one reason is that we want to take a decision whether the strength of the input is sufficiently high or sufficiently low. Sigmod functions will give either high value or low value. For most of the range, it will be converging either to high end or low end. So, they become very convenient to that. And then the result is fired as an output to the subsequent layers. So, this kind of input combination and processing is also called a processing by a perceptron. But when we say perceptron like an activation neuron, it is just the same thing. It means the input is summed up compared with the threshold or alternatively bias term is added and the result is transformed through a transfer function. And if this sum exceeds the threshold, you give it out, let the output be one. If it is less than the threshold, you don't fire it out, let the output be zero. Now, so this is the basic thing that lies at the heart of the neuron processing. You may be aware that there are two types of network architecture, feed forward architecture and feed back architecture. Feedback on the recurrent architectures are such that they involves connection not only in the forward direction like a feed forward network, but also in the backward or lateral direction with the advantage that they can act as moving averages if the data are too noisy. That means a lot of fluctuations are there. And then many times people are finding that recurrent networks are good. But in a feed forward network, normally there is an input layer where we give the input, there is output layer from where we take out the output. Then there may be more than one hidden neuron. Now, normally mathematically it has been established that two layers of hidden neurons are sufficient, but even then one hidden neuron layer is quite common. This kind of feed forward approach, feed forward architecture shown over here is also called multilayer perceptron. It is multilayer because it involves not only input and output, but also the hidden layer. Now, there are other types of networks also, this Koh-9 network, Hofveld, Hamming, et cetera, but they are not very popular in most of our civil engineering applications. But nonetheless, there are other architectures like this radial basis function ANFIS that is adaptive neurophosene inference system, GRNN or generalized regression neural networks which are also relatively recent and people are finding that very useful. Many of our students have also found these architectures quite useful. Now, I don't want to go into those details because they can be easily found in textbooks, first of all. But I can just briefly tell you that when it comes to a radial basis function, the name radial basis function is derived because the activation function in the hidden layer is of Gaussian type, there is a center and the information flows to the central, something like a radial flow of information and the input is classified into these neurons, hidden neurons or clusters and in a supervised learning process, the network is learned and then network gets trained and the information is passed on through the output layer. More or less similar considerations are there for GRNN or generalized regression neural network also. The input is compared with the stored patterns in the pattern layer, the difference is found out. So, there is some kind of clustering, then that is fired out to summation neuron, then this S summation neuron, D summation neuron and their division of the values gives the output. Similarly, you have adaptive neurophosene inference system wherein there is a combination of neural network and fuzzy information processing, the input information X, Y, Z or more, it is converted into membership functions A, B, C, etc. Membership function means in the rough word, as you know, it is a value between 0 to 1. Then these membership functions are multiplied here, there is some kind of averaging is done in this layer, then with the help of input information and these averaged out values, fuzzy, then rules are generated in this layer and they are fired to the output layer where they are combined and a output value is obtained. So, these are some of the architectures. Now, there are so many commercials and free download software that are available in neural networks and that list is there. Now, there are so many software that are available. Earlier, our students here used to use this software, what is this, Stuttgart, this S is missing here. It is Stuttgart neural network simulator. Then nowadays, I think you are all using this MATLAB toolbox, isn't it, in neural networks and also this neural dimension. Is it neural dimension or neural solution? Neural solution, yes. So, these are very popular. They have a lot of versatile it is, they have a lot of versatile it is. But the MATLAB toolbox and neural network toolbox and MATLAB environment that seems to be very popular. It is versatile and so many options are there. Now, again, as you know, the applications of artificial neural networks can be found in all branches of civil engineering and you may be aware that publications of the results or applications have been mentioned in various journals like American Society of Civil Engineers. As you know, ASEE publishes about 30 journals. International Association of Hydraulic Research also publishes dozens of journals. ANN applications have been referred to many journals, have been appearing in many journals. Various journals of ASEE, the journals of interest to you could be Water Resources Planning and Management, Journal of Hydraulic Engineering, Journal of Hydrologic Engineering, Computing in Civil Engineering and so on. Then, LCVR publication, they also publish this journal of Engineering Applications of Artificial Intelligence. And they also give a lot of information about applied site. Then, there is a Advances in Engineering Software published by LCVR. There also is a good source of information. Now, there are isolated papers. These are all journals which are devoted to soft and AI techniques. But isolated papers related to soft computing AI are available in water resources research, hydrology, hydrological sciences, hydrological processes, when it comes to your water flows. There are also annual conferences on applications of applied artificial intelligence worldwide. Then, there are conferences of Neural Networks in Civil Engineering. Now, as a piece of advice, I suggest that it is always better to go to these classical neural networks journals and classical neural network conferences because there the latest ideas will be presented by communications engineers. There is also a publication called Civil Comp Publishing. If you go to internet and give this keyword search, Civil Comp, you will find so many publications which deal with applications of soft computing tools or AI techniques in different branches of civil engineering. And you will get a rich source of information through that. Now, coming to the applications of hydrology, ANN have been applied in hydrology in so many areas. And all of our students have worked in these areas and they have developed their own ANN applications in this. The techniques have been applied to real-time flood forecasting, real-time flow forecasting on a routine basis, flood routing, that means given the flood hydrograph at the upstream station, find out the same at the downstream station. Then forecasting of river stage or water levels using ANN on continuous basis, say daily water level forecasting, rainfall runoff modeling has been done. Then prediction of monsoon rainfall sufficiency has been very vigorously pursued using ANN. Now, what does it mean? It means that, as you know, the 20 years back department of science and technology government of India, they developed what they call a 16 parameter model to forecast the sufficiency of rainfall around our country. Typically, the total rainfall around our country is of the order of 80 centimeters. Then that is regarded as a sufficient rainfall for the country. Now, this rainfall can be calculated with the help of causal parameters like let us say the atmospheric pressures, then the temperatures, then what is called the alnino effect, alnina effect and so on. So like that, there are so many parameters which can give you an idea whether the rainfall in the next monsoon season is going to be sufficient or not. So for that purpose also, neural networks have been used and one of our student also has used and found that it was better than statistical methods. Then there are attempts to do this kind of forecasting on catchment level. That means you have a software, so as to say, wherein the map of the catchment will come, you click on particular station, you specify the method of analysis and it will provide the forecast of water level or river stage at that particular location. So these kind of studies are already there. Now as regards coastal engineering is concerned, again there are so many applications that have come, neural networks have been applied to predict environmental parameters like wave height, wave period, wave directions, tide levels, sea levels, meteorological and ocean graphic parameters of other nature, wind speeds, characteristics of a student, density mixing and so on and also predictions of currents and sediment transport. They have been also used to estimate or predict forces on structures to know the structural damage, to work out ship design parameters, to know the barge motions. That means, heave-pitcher-roll motions of floating structures, then depths of scour and so on. Then in our own lab, there are so many studies related to this coastal engineering application that have been made by different students. The list is here. In fact, all these studies have been published by various research workers, by various students in various journals. I wanted to say one thing that we have applied this technique of neural networks in many different ways. First, we have applied it to work out a causal relationship. That means to model a cause-effect relationship. For example, the generated height of wave and generated period of the wave, they depend on the speed of the wind, the direction of the wind, the phase or the distance over which the wind remains constant and the duration of the wind and also the water depth and so on. So, we developed neural networks that will map these input quantities with that output quantities or cause-effect modeling has been done using ANN. We have also applied ANN to map the spatial relationship. For example, as applied to your case, suppose the rain gauge data at different locations in a catchment is given. How to find out the discharge at the outlet? So, this kind of mapping was spatial relationship. Space dependent relationship has also been done. The neural networks have been also applied to work out temporal relationship. That means time dependent relationship or time series modeling. You may be aware that the concept of time series modeling is like this, that you take a sequence of preceding observations, allow the network to recognize a hidden pattern into it and with the help of that unknown hidden pattern recognize the network will produce the future value. So, this kind of prediction goes on in a recursive manner every time adding the measured value or predicted value in your training. So, like that the temporal or time dependent relationships have been also successfully mapped using neural networks. Then neural networks have been also used to carry out what we call property resolution and property integration. For example, if there is some parameter from which you can resolve that parameter and obtain a resolved value over various input quantities, then that can also be very successfully done by neural network. Let me see if I get, yes, this is that. See, this is where the prowess of the neural network will come into picture. So, when you select a problem to analyze, you must see that the neural network is really required for that purpose. For example, this is the case of property resolution. Many times while designing a structure, we have the problem of getting this what we call wave spectrum. Wave spectrum is a graph of wave energy versus various wave frequency F. And this has to be obtained from only two design parameters, namely design significant wave height and design significant wave period or average wave period. Now, the design course like American Petroleum Institute or DNV, they specify a certain theoretical equation called theoretical spectra for this. But when we use spectra for our locations like Bombay High or Mangalore or somewhere, they completely fail. For example, see this, this is a graph of wave spectrum which gives the wave energy versus various wave frequency. Wave energy is reflected in terms of a mathematical function called spectral density function. Now, you can see this is the actual observed spectrum. You put the wave measuring instrument and if you work out the spectrum, it comes out like this. Now, this design course recommend the use of this PM spectrum, John Swab spectrum, Scott spectrum for this purpose. But you can see there is a very big difference between the observed spectrum and the spectra predicted by those equations or models of this PM, Scott and John Swab. Instead of that, if you develop a neural network like this, then the result is phenomenal. You can just see how the network derived spectrum matches with the theoretical derived spectrum by with the observed spectrum as compared to this theoretical spectrum. So, tremendous improvement in the accuracy can be achieved. Provided, you use the network for the purpose for which it is really going to be helpful. For example, we have also done many studies 10 years back where we used to only analyze simple problems. For example, as I mentioned, just work out some score depth or score width or location of scour based on, say, geometry of the scour then the hydraulic parameters and like. It's a very simple modeling. Now, 10 years back, the studies were appreciated because at that time everything was new. But today, people expect you to apply these neural networks or their techniques to only those problems where really the help of neural network is required. If it is a simple regression problem, then the application of neural network may not be justified. But I can just give you a summary of what we have observed so far. After doing all these works, which may be around more than three dozen applications of two different problems of AN and others, I came to conclusion that we are finding that the neural networks are better than almost all deterministic, statistical, stochastic or even numerical methods including finite difference and finite element method. Now, that doesn't mean that these methods are bad, but we are saying that in many applications, neural networks perform better than them. Many existing design practices are based on statistical, stochastic or numerical or empirical kind of equations. And we argue that neural networks should henceforth be used as a replacement for them. Now, we also find another thing that neural networks can be either complementary or completely substitutive alternatives to many complex numerical schemes including finite element, finite difference. In fact, if we say this, the people working in finite element, finite difference will simply pounce on me, they will start giving so many virtues of FEMFDM. Now, my suggestion to them is that we should not look in neural networks or for that matter any other technique as a substitutive technique to these FEMFDM, they can be complementary to that. That means you may prefer those under certain conditions, but neural networks in some other conditions. For example, some people are finding that typically while working out the quantities using finite element method or finite difference method, if neural networks are incorporated as a part of that evaluation process, then the accuracy of the results increases substantially. So, there can be clubbing of neural network technique into the numerical methods. Conversely, neural network can also be trained with the help of finite element and finite difference methods. That also is possible. In fact, some people are finding, especially when it comes to our way flows, that the numerical models which are commercially very well used over the entire world and they are named as VAM, SWAN and so on to obtain the oceanographic characteristics in future time steps over different spatial locations. They provide a good simulation. That means at the same time step, if this is the input, then this is the output. But when it comes to forecasting, then they are saying that the neural networks and soft tools have an age over the FDM or FEM method. So, there can be good combination. If you want to simulate the current time step stage, you use FDM or FEM, but when you want to forecast, use ANM. So, that kind of what we call consideratory approach should be practice rather than exclusivity. These days, nobody likes exclusivity. Everywhere they say, educations should also be inclusive. You include everybody in education. You include every possible way in your education. So, that kind of inclusivity can always be incorporated in these our studies. Now, when it comes to usage of ANM, our suggestion to you is that you start with a simple fit forward, back propagation type of network. Many times it works better. However, if it doesn't work, then only you go for complex training schemes like as I mentioned, RBF, NFIS, GRN, and so on. Recurrent rates if you want, if you want that there is a need to improve the accuracy of FFBP. Then, if you want to do some kind of forecasting or evaluation in adaptive mode, that means there is a continuous measurement of data. You incorporate the just measure value into your training and forecast the value subsequently. For that purpose, we are finding that highly efficient and very less time consuming training schemes like cascade correlation, they work better. Then, if you want to incorporate memory or the past observations, then you better use the recurrent sets. Of course, there are many other recent algorithms like this LWPR and so on, where we incorporate memory into data. The locally weighted projection revisions or local learning methods have the advantage that they are memory based. They do not discard the training data. In ANM, what we do or even in any revision model, we have the data, we use it for training and then that data is of no use to us. But in memory based training, all these data are required. They are kept in the implementation or computation process. Whenever a new query or whenever a new input is given, we select the training patterns which are close to that, fit the local models and forecast the value accordingly. So the data are not discarded. We are finding that whenever there are very high variations in the input quantities, wherever there are very high warning times, for example, then or when you want to predict extremes, when you want to extrapolate beyond your observation range, then the current state of knowledge may not be sufficient. Certain advances in current knowledge are definitely required when you want to take care of all these uncertainties. Then we also find that depending on the results, you may make use of more than one network in the same formulation. That also is something which is called a modular approach and that also is something that needs to be tried. Then again, as I mentioned, we are finding that NN are generally more accurate and reliable than many traditional equation-based approaches. As you know, in NN and other soft tools, we don't start with conceptualizing the phenomenon into equations. The equations, if at all they are there, they come in the end because of the data. I mean, data themselves come up with an equation. We don't start with an equation to analyze. So in that way, we are finding they are much better in most of the applications than analytical, empirical, statistical, numerical schemes. Now again, this is very important. Success of neural networks or any soft tool in any new application is not guaranteed. You have to work for it because in many times, we are finding that if you just use NN in a traditional way, you don't get results which are more accurate than your nonlinear regression. Then you may be tempted to say that NN are not working properly. That is not the case. You have to work, try different architectures, try different control parameters, do everything that is possible to do by trials and you are bound to get results which are better than the traditional schemes. So one has to try out large network architectures and training schemes in order to get better results. Then there are some applications in which it is found that you can work with less amount of data. Now here, the advantage of neural network definitely comes into picture. In many applications, we are finding that although the accuracy level reached by neural networks is more or less same as the accuracy level reached by traditional schemes, neural networks reach that level of accuracy with a fraction of data than that is required for traditional schemes. Now this should be regarded as a very big advantage because many times, you find it is very difficult to get the data to analyze your problems. Then instead of getting such a vast data, you can use a small amount of data, apply the neural networks and get your results which are maybe of similar in accuracy. Then recently, yes, attains have been made to decipher what is called the black box type of functioning of the neural network. One of the objective, object objection that the, I should say traditional technology users, they raise is that they see your neural networks are like black boxes. You don't know how they process the information. You don't know what do these hidden neurons, hidden layers mean, but that has become a thing of the past now. There are so many applications, including two of our research students, they have also done that. And we are trying to decipher that black box nature of the neural network and we are trying to link the output of hidden neurons with the physical process. In all that procedure, we are finding that neural networks do some kind of partitioning of the input space and within this partition, they fit linear models. That is what we have found out. So, attains have been made to decipher the black box nature of the NN. And finally, you must remember that these are all emerging technologies and there is a great scope for research in these areas. The level, unlike numerical methods which have been there, like finite difference, finite element, I don't know how many they are there for 35 years or something, 30-35 years. And these methods have started only some 12-15 years back. So, in order to come up to the level of FEM, FDM, etc., they will take time, but nonetheless, the results are indeed very, very promising. And note that any new technology is going to be viewed with a very big suspicion by the established world. For example, sometimes back, I don't know how many students attended that. We had a lecture by one, I forgot the name, he is a professor in Cambridge and he said that his uncle actually devised this finite difference method. He was the first person to formulate this and when he presented his first kind of publication, first kind of report to a Royal Society proceedings, they rejected it, saying that this so-called finite difference method is not a mathematics, it's a pseudo-mathematics. There is no mathematical rigor in this scheme and therefore we are not going to publish your paper. So, but now can somebody say that this is pseudo-mathematics because so many design, structural design, all kind of sibling in applications have been made with the help of this finite difference method. So, you have to remember that similarly, people are in a similar way objecting to these techniques like NN. They are saying that this is not a rigor-rigor, this is not a mathematical rigor, but the time will soon come when all these NN and other methods will definitely form a part of the design codes in civil engineering. That day is definitely going to come. Now, this is something, you know, as in nutshell I wanted to say, now I will take you to some other things. Now, this is a very simple application of NN which was made by this Dr. Asmuth Ullah who did PhD with me recently, is in Malaysia now. Now, it pertains to just as an example I am showing, it has got some two, three different point that I am projecting this information. It pertains to estimation of scour downstream of a schism bucket type of spillway. Now, problem is in that way very simple. You have this schism type of spillway. Basically, it disposes of this flood water into air, a lot of energy gets dissipated and then the jet of water falls onto the bed even though most of the energy is supposed to have been spent, still the jet is quite formidable. It causes erosion over here. Now, the maximum scour depth which is defined like this depends on so many causative parameters like the discharge queue, then this head H1, then this radius of the bucket R, this lip angle 5. Now, the student did so many works, but basically, you know, his primary work was to link or to find out the scour depth, the location of the maximum scour and the width of this scour hole using neural networks so that the plunge pool can be designed using these dimensions. Now, there are so many hydraulic geotechnical bucket geometry related parameters which exist which can be linked to the scour depth. If you look into the IS code, they give this Veroni's formula to obtain the scour depth. HQ is discharge H1, H1 is head. And if you apply it to practice, this is what happens. At one location, the IS code specified formula gives you 18 meters of scour depth. Actual measured value is 27.4 meters. Another location predictor is 18, observer is 24.7. Another location predictor is 42 meters. Predictor is 42 meters, whereas actual observer is 70 meters. But despite that, people continue using the same kind of formula again and again in the new design. Then the student collected a lot of data by conducting experiments in central water power resuscitation where he was working. So these are some of the hydraulic model. This is how the scouring is taking place. He collected the data of all these causative parameters. These are going to spill my model and this is how the flow was taking place. Again another model. So what he did, he used all these causative parameters, developed different types of neurons. First he carried out a new dimension and analysis and found out the depth, location and width of the scour hole by using this Buckingham Pytheism dimensional analysis. Then he developed two different networks. In one network, he used the causative parameters raw. Whereas in other network, he used the non-dimensional causative parameters. Now non-dimensional causative parameters will reduce the scale effects involved. Now again, there is a very controversial issue in some applications we are finding that if you use the dimensionless parameters, you get rid of scale effects but accuracy many times suffer. As against this, if you use raw parameters like H1, DWR separately, then a lot of flexibility comes into modeling and you get better accurate results. So again, there is a lot of subjectivity in these recommendations. Again, this figure shows the comparison of the predicted score versus the observed score depth using different schemes. And it was seen, this is the length, this is the prediction score wheel. And you can see that most of the predictions are quite successful. And when compared with these regression techniques, they work better in terms of this correlation coefficient, average error, then this deviation index, then I think it is absolute error and so on. So then he recommended various networks for this. But in that way, this is a simple study, but more importantly is something incremental studies that he did. What we argued in this case is that many times it is found that you develop a neural network, you find that it gives good results. But many times it could be something practically misleading because the neural network after training must represent the physical phenomena properly, isn't it? For example, let's say if you develop a network to obtain the score depth with the help of these causative parameters, you must understand that your neural network should be such that if you increase the discharge over the spillway, you must end up with higher predicted score depth, isn't it? If you increase the stage, the head value, you must get increased values consistently of the depth. So like that, we have to do what is called parametric study of the trained network. Every time you have to vary one parameter and see how your output changes. If you find that the change in output matches with your physical understanding, then only you select that network. Otherwise you make change in that network, retrain it, use some different architecture and come up with some alternative network. So this is what we did. This is an example of that. This shows from the trained network how we obtained this graph, normalized depth of score versus various parameters like discharge, head, radius, sediment, diameter, etc. So as you can see, this developed network follows the physical process. Typically, as let us say this discharge increases, this score depth increases, and beyond a certain level, there is an equilibrium score depth. Similarly, as this, this is I hope D50, yes. As the sediment diameter increases, naturally the depth has to reduce because the scoring potential becomes less. So this kind of physically verifiable results must be there from your network. That is something which you may remember. So anyway, this thing, I need not go into those details because, but he used two models. One is field database, another is model, hydraulic model base, and he arrived at some conclusions. This is something which I want to tell. You also should make an attempt to decipher what is called the black box type of nature of your neural network. In this particular study, we saw how the values yielded by this fired out by these hidden neurons, they change with changing input. How far they influence the output? And in the process, we found that certain hidden neurons become very strong. We change this in only certain type of input. And hence we found that the new, and by doing similar analysis, we found that hidden neurons do some kind of partitioning of the input domain into subdomains. And within the subdomains, each hidden neuron does some kind of regression and models the causal relationship accordingly. In other words, in this study, we also found that a hidden layer probably appears to convert the input domain into another one, where the samples are made linearly separable and the data are not forced into particular fixed model like a regression. So like that, you can interpret the results of this. Is there any question from yourself? Yes, please. Sir, in the real neural network, there may be firing or not firing, but in artificial neural network, I think it will always... No, no, that is why we use the transfer function. The purpose of the transfer function is to arrive at a value which is significant or insignificant. If the outcome from the transfer function is insignificant, it is amount to the same thing, it is not firing. That is why we use... You say it is always output. No, no, no. We are talking about the hidden neurons. You know, we are talking about the hidden neurons. We are talking about the hidden neurons in that case. Hidden neurons are, you know, are inhibitory or excitatory as such. See, this is taken care... What you are saying is taken care of by normalizing 0 to 1. The input is normalized into 0 to 1 and that's why it is grouped. That is true. Output is there, but, you know, it is not that, you know, when it comes to output from the output neuron, there is some output, but that output is not, you know, of this type, what we are saying. There will be some output, but there is a difference between the output fired by hidden neuron, output fired by output neuron. That's why we use some of the different types of transfer functions in the output neuron. Yes, modular has to see. You know, modular has to try out so many architectures, so many schemes and see where, in which range of input, which model to fit. Again, you know, there is no, there are no guidelines. You know, these are all data specific. If your data permit you to use one particular model for lower values, medium values, high values, you have to do that. Yes, yes, yes. See, it is something like this, that for example, I am interested in predicting, say, design wave height value. I am more familiar with question engineering this one. Advances in the ANN, you see in the sense that current architectures, current learning schemes, they work better as long as the values that you are going to predict are within the observed range of the input. Yes, in the training data. If they are out of training data, then it becomes difficult. But again, there are ways. For example, as I mentioned, you know, we always normalize the input in between 0 to 1. Now, if you just normalize in between 0 to 1, you know, you will leave no scope for the values which are more than maximum value and minimum value in that range. So, what you do, you normalize between, let us say, 0.1 and 0.9. And so, I leave some scope so that the values which are slightly over and above or below that range can also be taken care of. But, you know, as I mentioned, still we are unable to get an answer for the extrapolation. The existing architecture training methods are not working better. One way, whenever possible, to do this is like this. You use the non-dimensional group of parameters as input whenever possible so that, you know, that scale effect, this is what we call scale effect. That scale effect will be taken care of thereby. So, instead of using raw values, you use the non-dimensional values. And then, you know, that will facilitate you to go beyond that actual observed value. Yes. Other studies are there. See, Asmatullah did this work when causal relationship was involved. That means, call depth was determined with the help of causative parameters. But, there are other studies. For example, K.P. Sudhir in IIT Madras, he did similar kind of study and drew similar inferences for rainfall runoff modeling. He showed that certain neurons they model the rising limb of the hydrograph. Certain other neurons, they model the falling limb of the hydrograph. So, hydrograph. Certain neurons, they model the values near the peak of the hydrograph properly. So, in that sense, he said that they do partitioning. Low discharge, high discharge, middle one. And then, they do some kind of piecewise repetition of the whole domain. That is what he was arguing. So, people have, you know, studied this kind of the deciphering of black box for causal relationship, for temporal relationship, for spatial relationship also they have done. And they have seen that some particular hidden neuron may, you know, model some particular station characteristics in a better way compared to others. So, these kind of somewhat, as I say, unstructured attains have been made. Yes, that's true. Just now I said, you know, that the different parts of the hydrograph they have been related for, to the different hidden neurons. So, how far these things are the problem? That is true. See, it is, as I mentioned, the atoms are very sporadic. And so far, people have only tried to link certain part of the neuron network structure to certain physical processes like base flow, peak flow, or infiltration and so on. But as I think, what you are saying, I have not seen a paper wherein more addition to the physical knowledge you know, has been contributed by the neuron network. There is a scope to do that. Typically, we don't know who may, for example, a train network. You may do a parameter, parametric study and see how some particular input parameter varies, how the output parameter is varying. Now, based on the behavior of that, you can interpret it why this happens. This, this can be done. The same neuron network is invested. Many people have observed like this that neuron networks give the same level of accuracy with small amount of data. Anyway, I am there in the afternoon. You can also contact me in the afternoon. But now I presume we have to break. And then we will assemble at 2 o'clock. Thank you.