 So, today the title says we will have the summary discussions on the course and the kind of course wrap up presentation, but still there is some activity for Thursday I will come to that end of the lecture it is not yeah. So, let us quickly or we can take a time we have an hour to look at the various aspects of the systems course that we have done and then we can take a look at what we were what I thought have a try to convey and see whether you have also have the same thinking. So, we started with systems in fact, we when our first question we asked ourselves what is the system and then we talked about that it is you know systems something made up of many interacting components or parts is what we define, but then immediately almost immediately abandoned the system because even though the course title is called system dynamics you only model the problems or issues we never model the system that is the first kind of ironical that we did not really model system, but we took a systems view of things and started focusing on the problems and issues. So, what we overall what we want to model we want to model the assumed or perceived underlying structure of largely closed world closed loop real world problems what we mean is we want to find out endogenous explanations for whatever phenomenon we are observing or whatever thing is happening we want to observe we want to incorporate that as part of our model. Sometimes we need to make assumptions and we need to bring out this underlying structure outside it may not be readily apparent. So, we end up having discussions and then making some assumptions creating table functions to actually elicit this model and come kind of build a closed loop model of the entire scenario. We ended up using various structures like delays, metal flows, information flow decision making etcetera were all incorporated. How did we do systems thinking? These are the some of the components that we went through we started dynamic thinking that is graphs over time or behavior over time graphs were constructed and we have been looking at it for the entire semester. Then we started to think about feedback loops using causal loop diagrams and the notion of causation variability affecting variable B and what manner is discussed. Then we tried to incorporate it in a stock and flow thinking where accumulations are clearly modeled and then we moved to simulation modeling of it and thinking endogenously then system is the cause like what is within the system that is driving the behavior that is explanation we were trying to seek then all the models that we are trying to build. Again summary we need to remember these all characterizes system dynamics approach that we have done. So, this behavior of time graphs again what does it mean? The behavior of time graphs what we want to represent is they are also known as a dynamic reference modes. So, when you are actually building a new model we might want to look at what is the behavior of the system over time in the past right what is historical behavior and then what might be the behavior in future also this is helpful in understanding the problem. But of course, as soon as we start talking about the historical behavior we need to also worry about the time horizon like how far in back we really want to consider and when did the problems come out and then that will give an idea of what we want even actually model. So, for the first part what we call as a reference modes, reference modes are nothing but behavior over time graphs, BOTG means behavior over time graphs. This is the kind of explanation if you want to say model real system or you want to look for something where you feel maybe a systems approach will be useful may not necessarily you are using system dynamics modeling, but you want to do a systems approach in the sense that you want to look for endogenous explanation within the system you want to see how the variables are being interlinked. So, then one of the first thing we might want to look at is this reference modes and reference modes again x axis is always time this is some variable of interest some variable x of interest that we are looking at and if this behavior is a linear straight line not interesting if it is linearly increasing again not much interesting linearly decreasing not much interesting even if it exhibits an exponential growth that also we know it can be modeled as a very kind of simple system. If it is exponential decay the underline structure is quite straight forward that we want to model so it may not or if it is a you know goal seeking model it does not require too much effort we can actually make the things explicit. What will make it interesting is suppose we have a graphs like that where we can see pronounced non-linear effects non-linear behavior that is happening something is causing it to increase something is causing short term fluctuations something is causing long term fluctuations in the model something is increasing and decreasing. So, whenever there is at least some increase or decrease or it is shift increase and decrease denote there is a shift in the feedback systems that means at least there is two feedback systems to operating. So, one is driving growth the other is diminishing growth and there is a shift in those feedback system is happening endogenously. What it is now becomes an interesting question this is try and uncover. So, now the first thing we want to do is look at some of the key behaviors and see what kind of behavior patterns are we actually seeing. So, these are called as reference modes because mainly they look at the historical historical behavior. So, suppose we are here this is the current time typically we would end up drawing couple of patterns in it like what we call as hope or fear. These two trajectories represent what you hope system will behave in future and what you fear the system may actually end up doing in the future. It can be other way around you might want to hope the system goes down and fear could be it worsens it is just an assumption here that larger is better. So, hope is higher versus that is just a implicit assumption, but it can be other way also increasing can be fear and decreasing can also be a hope that system actually subside ends you know like if it is your whatever if somebody is sick and this is their fever profile you might want it to your hope is system will subside and this people become better right. So, it can be that one also. So, but this kind of we want to see whether if we are able to build a model which reasonably predicts reasonably replicates this behavior then in future we may see what happens in future and have more trust in the model. So, that is why the reference mode becomes important to see what we want to replicate or behavior over time graphs or BOTGs. So, one exercise or one thought process for when you feel you know various projects in various fields you may want to look at some of the data that is actually changing over time and see what kind of dynamics are there. So, most often the system will look highly non-linear and with short term fluctuations and long term fluctuations ok. I have few examples about this time horizon. So, time horizon affects how much we want to see for example, given from Sherman's book this is looked at a 10 year time horizon of the oil production and consumption. The consumption is kind of flat the inputs production in lower states are this line here and in Alaska fills the gap. So, the rest of the consumption is handled through inputs it is fairly stable with a slight decline in production and slight increase in consumption is flat. So, production seems import seems to be increasing steadily. This is a dollar price per barrel it seems fairly flat for a 10 year horizon. However, if we increase the time horizon to since kind of oil was discovered you can find a nice rapid exponential growth within the model and see a peak seems to be the first oil crisis hits 1970s and since then it has been kind of falling down over time. So, this currently changes a perception of what is the model that we want to have. The previous one may sound like we have enough reserves you can keep going, but here there is a kind of a rapid decline that is being nicely captured in this kind of a time horizon and price huge fluctuations especially recently. If you have too large a price spike probably just a simple pulse change the time scale is really high some 5000 years in future then you are just pulse in pulse change that has happened without affecting anything else. So, it is important to select the time horizon. Then we through various examples we try to do this part of articulating what the problem we wanted to solve. Ideas to what is the issue of the problem? Why is it a problem? Is it just a symptom or difficulty? What is the purpose of the model that you want to do? Then we ended up determining some did boundaries for the model like we told some variables are endogenous some are exogenous. Let us assume that demand is exogenous for example. So, those are the assumptions are reasonable or not we have to question and then appropriately we drew the boundaries for the model. We had in effect key variables and concepts and used it in our model. Examples include business model to understand production 20 dynamics of firm we did that. Model to explore policy to mitigate global warming we did not work on that, but these are some examples where the scale is completely different. When you look at a business model you are looking at one company's model their perspective, their policies, their management structure, their management policies etcetera are built in and how they interact with the consumers is the model. But when you start talking about policy mitigate global warming suddenly you are looking at thinking of a model which talks about the entire world and how various industries does not matter what type of industries or activities happens, how it contributes to this global warming is what we are interested in. So, the scale, the dynamics, the type of variables all are going to differ. In how detail a map you want of it affects the size of the model that we want do you want the entire world or you want to look at a small isolated region is it one business or is it multiple businesses, one city, multiple cities what is it that we want is up to us. From to you know we model the system's view of things, but we never lost track of the we do not want to lose track of the problem that we are trying to see like when, but the approach taken to teach it could be that there are descriptions given. So, it felt like the problem is already defined or was not really apparent, but we wanted to see is ok there are some fluctuations in say housing dynamics that happen, they are seeing some population increases and decreases. We are trying to look at model trying to explain that. So, we want to revolve around it. So, we have some variable and say how does this variable affect the next one, how does that affect the second one etcetera we keep going. So, that is the approach we want to take. So, why never a system is because then whenever we start then we will end up modeling the entire world then only model that will ever work is the entire world model that also may be limited then we want to model for the entire universe or whatever. So, it is too it will become too big too quickly like if you want to model the say agricultural pricing like right now potato is a big issue right in some districts in Uttar Pradesh I do not know if you are following the news earlier it was sugarcane, last year it was turdhal here there is lot of inventory of turdhal. So, it keeps happening in cycles. So, those are actually called as production commodity cycles it has been well studied and how it keep changing because it is just driven by the supply and the demand and because of the lead time things get to accumulate and things like that which affects in a longer term. So, people looking at short term solutions because election comes more often than people are going to see the cycles. So, people are interested in short term fixes which anyway that is the policy part. But, then if you want to model that then we are going to focus on let us look at what is the dynamics of the potato inventory that is happening. We do not want to model every agricultural product with entire northern belt. So, you are looking at let us model the potato and inventory of potatoes or the pricing of potatoes and the money the farmers get within a region say Uttar Pradesh. So, that is what we mean by focus on a problem. So, the entire system may be slightly bigger than what we want. So, to do all these problem articulation we actually used causal loop diagram. What the causal loop diagram actually captured is what is called as a dynamic hypothesis. In statistics and other fields you must have studied about den hypothesis and testing of hypothesis. Here it is probably our first time we are actually defining something called a dynamic hypothesis because there is a actual behavior over time that we are capturing and the causal loop diagram does not capture system in static capture system as it changes over time. And we want to define that causal loop and say this this diagram we expected to you know cause the underlying dynamics that we are actually seeing. So, that is the hypothesis that we want to then validate using simulation model and verifies in simulation models. And always we try to seek for this endogenous explanation of the phenomena. We drew many many such causal loop diagrams as shown here we identified variables use arrows to say how say birth rate affects rat population plus all causal links had polarities plus sign indicates as birth rate increases population increases or negative sign indicates that birth rate death rate increases the population actually comes down. The impact is in the opposite direction. If in a loop all the links are positive then we have positive feedback systems. If odd number of links are negative then it becomes a negative feedback system as shown here birth rate rat population population density increases population increase increases infant mortality infant mortality increases birth rate effective birth rate kind of decreases that becomes a negative feedback system. You can remember try to use noun and noun phrases the action is already captured by the arrows that we want to that we have been using. But going from this to this there is a stock flow diagram usually results in increase in the number of variables in the model at least to match the units. So, you may need to end up having some more variables like for example, in this case if you see here just infant mortality here you are looking at female rat population sex ratio normal rat fertility average lifetime etcetera. So, extra variables do come in. But these stock flow diagrams have been helping us doing the simulation. We had only three things stocks flows auxiliary variables just three things stocks are usually physical or things we are going to use the information of decision making. Again if you take a snapshot or a picture of the system what we actually see there is also the stocks. So, if we freeze the system in time whatever is left is the stock and stocks can only be changed to rates. So, do not be in any doubt if this is a stock put an inflow rate and outflow rate you can figure out what the rate names is later I just call it in rate and out rate you can always figure it out what it is. Choose an appropriate time step sometimes large time step cause unnecessary dynamics like time step should be at least one eighth of your smallest delay in the system. Units are also important please make note and see what all because main thing help of this units is it helps fix a real in reality if you want to measure it how will you measure it. So, this units allows forces us to think in the terms and ensure that a model is valid and we do not end up multiplying things which are not to be multiplied wherever possible. Using these structures causal loop and stock flow models mainly stock flows for most of a semester. We looked at various patterns of behavior, we looked at exponential growth, goal seeking, S shape, oscillations, growth overshoot, overshoot collapse. We made simulations understood the underlying stock flow models for each. Some are simple systems like exponential growth and goal seeking, combination of that with delays causes oscillations, change in the positive and negative feedback system causes S shape growths and more delays within those loops actually causes oscillations within the system. So, these are the things that we had actually seen with various examples. How we learnt it was through various models? First we started with the techniques like for example, we went through various modeling techniques and positive negative feedback systems S shape growths, oscillations, overshoots, delays, non-linearities. If anybody is doubting did you really cover this? We did trust me look at the videos later we have done all this. Then we learnt to build lot of models. We built models by using lot of examples rather. For a given issue we identified variable stocks or flows. We did many examples and scenarios. We also learnt to do model testing, debugging, sensitivity analysis, policy analysis. Since some of these things especially policy analysis has to be rooted in a specific problem or issue then we took up a few problems and issues to work with it. Debugging we took up some small models to work on the debugging issues. Sensitivity analysis refers to small change in the parameter settings or table functions or any of the model assumptions that you want to test to see check the limits of the model that is what we call sensitivity analysis. In policy analysis about the kind of intervention we are actually thinking of modeling ok. I am going to take a policy as for example, if it is potato price then do we waive all the farm loans or should I give this minimum price and buy all the potatoes? What should be or should I give the incentive for the next round of crops? Instead of this say I will waive the loans of the next round of seeds or next round of plantation or fertilizer subsidy whatever those kind of decisions those are typically called as policies ok. Full circle we are there various level system thing people have classified starting with unaware shallow awareness, deep awareness, novice, expert and guru. Unaware you have no idea what system thinking was shallow awareness like you know some of the buzzwords, deep awareness is you can read the models and understand the results. Novice is when you start actually building your own models, experts is when you start building your own correct models and looking at open ended systems and trying to get what data and how to go about doing it. Hopefully many of you are here this novice part we are able to actually build a model, look at it definitely read models, definitely understand what people are saying when they communicate look at the results and see what kind of systems structures may be underlying the phenomenon that we are looking at and then keep practicing to become experts I hope we are all here. So, what next? Long term next not immediate short term. Read more on system dynamics if you are interested in this I hope some are. The system dynamics modeling by coil, business dynamics by extermination. There is interesting set of books system zoo by Bursal he has a what he called a zoo of models of various scenarios. Fifth discipline by Senge. The fifth discipline is a what can is a it is a more light read there is not heavy equations and stuff, but he tries to present systems thinking more. So, looking for journal article system dynamics review is the flagship journal here. So, lot of system dynamics will get published in this journal and there is also conference called a system dynamics society conference held every year that here happens in July. So, in the conference website they publish the proceedings and many of them we publish our papers as well as we upload our winsome models or powersome or whatever the model file also. So, that people can download and understand it. There is range of articles from teaching to implementing to really new ones, but if you want to move from novice and at least not rigorous back to a shallow awareness you have to keep working on some SDs incorporated part of a project or something that you may work on try to do some advance courses in SDs or only way to learn is to do a specific project. So, if you work on some specific project area then we can say can we use SD to look at it and then we learn through that under with some guidance. There are other notions in SD something called as group model building since many of the systems are so large and difficult one person to understand it. We need to go methodically in a as a group how we can actually model the entire system they talk to each other. We have all done group homework there it is not the same thing at all nothing compared to that we had actually get a model working and working as a group. So, two different things the various notions of control theoretic methods and optimal control which can be applied here to the models that is something you may want to read up and learn and see how it can be used. Again as I told you underlying are all differential equations as some of these notions are very useful in identifying our key variables and key point of leverage within our SD models. Exploratory modeling analysis another big area which is coming up in the last 8, 3, 5 years this is where machine learning means system dynamics again fantastic opportunity for people to do that because system dynamics with so many policies settings and so many sensitivity analysis it can generate rich amount of data. But then machine learning can help us figure out and classify all our system behaviors to figure out where is the leverage points in a very systematic manner that entire field is called as exploratory modeling and analysis. If you search for this particular phrase you may find a select literature on that one of my PhD students that has also done some when he has graduated he has done work on this exploratory modeling for supply chain and health care and stuff like that. This is also there for reading interact with SD community as I told there are nice conferences workshop that is held in India there are things happening you might want to do that so yeah that is it questions comments this is all we had done in the course