 Dr. Brent Krasik. I've been at ARL for about seven years. Prior to ARL I was at First University of Illinois where I got my PhD in physics and then at the Institute for Computational Engineering and Sciences at the University of Texas. Throughout my career I've been working on multi-scale models and a lot of the working toward understanding how we can connect the fundamentals of the multi-scale models to some specific physical problems. And so what I'm going to talk about today is using a lot of the ideas that Kenneth's just talked about which saves me on talking about a lot of things he talked about to some specific applications that we're working on in electronic materials. So moving from one CRA the one having to do with extreme environments to the electronic materials. So basically as we've been discussing things as you've heard today there are many specific problems that the Army is worried about and in the area of electronic issues one of the key areas that the Army is interested in is developing the devices that we need to be able to overcome specific challenges. One of these challenges is communication for example in a mega city where you need to be limited on line of sight where we may have jamming and so one of the key ideas behind this is to use ultra violet communication that you can bounce off the ozone layer you know how the ozone layer protects us from being sunburned we can use it the other way as well. This is one application. Other applications were interested in a lot of different laser applications from directed energy to manufacturing at the point of need. In each of these cases one of the key material families that the Army is really interested in is the nitride semiconductors. Nitrides are active in the blue and the UV which provides a lot of these portions of the spectrum that we're currently interested in. They're also able to handle very high amounts of energy. They're much more resilient to high power than a lot of the other semiconductors that we know. So the nitrides are very important. That's where we're going to focus on nitrides but a lot of the stuff I'm talking about here we're actually looking at applications to gallium arsenide as well and to some of the materials that are used for night vision. So mercury, cadmium, telluride in the context of what's being done in the technical community right now for the most part the way this modeling is done is it's done in a what we would consider a sequential multi-scale fashion. That is you compute the parameters that you think are going to be important. You do this in a combinatorial fashion as best you can and then you use that to bootstrap into your higher scale models for simulating the devices themselves. There have been some different approaches to this but for the most part that is what the approaches are currently limited to. And so what I'm going to talk about today is using a lot of the same ideas that Ken talked about where we want to be able to do what's called adaptive sampling so we can address many more parameters than are possible in our then doing a straight combinatorial pre-computation so that we can more accurately accurately represent the materials that we're seeking to model. What does this support? The cyber and electromagnetic technologies and complex environments the RA obviously and also there are a lot of other places as I noted. So I already said a lot of what's on this slide but let me just focus on this on this figure right here. This figure is a schematic it's not representing what often goes into these semiconductor devices. In this case you'd have a lot of different layers of different alloys of gallium nitride so these alloys include you had aluminum you had indium different things and then depending on how you structure the material to get different response out depending on how you dope it you get different response out. We want to be able to predict ahead of time be able to say this type of material this type of doping this type of layering will give us this type of response. Right now the best we can do is we can do some measurements we can do some calculations but we're not able to do to true prediction of material properties and that's where we'd like to head and that's a lot of the the direction that both of these CRAs that we've talked about are really focused on is how do we do to true predictive modeling. And so this is part of a collaboration as I said we have the ARL materials enterprise which is here within ARL we have the MISME which is the CRA we talked about for electronic materials there's also an ARL Center for Semiconductor Modeling. This effort here is to bring in a lot of these computational science aspects into the other modeling that's happening within the center. So on the theory side we have several collaborators in the materials campaign on the side of it actually doing the microscale models for these materials we have external collaborators in particular Enrico Bellotti at Boston University we've collaborated with very closely. We haven't collaborated as much with Francesco Bertazzi yet but that is on the it's in the future plans that's that's set up already we're also working with experimentalists in the materials campaign to validate some of these models. But right now what I'm going to talk about is a central part where we're working about worrying about the computational sciences aspect of this. Where do I need to point this? There we go. Okay so for this specific model we have essentially six components that we want to put into it. I'm going to talk mostly about component number three here. I'm going to talk a little bit about component number one. Those are the two I've personally worked on the most. I've also been collaborating with Bellotti once again at Boston University on number two and then four, five and six are in the future. So specifically what are we looking at? We need a micro scale model in this case we're going to look at how does a laser propagate within a nitride material. We need to have the micro scale model of the material as it responds to the illumination and then we have to have we're going to use machine learning using Gaussian process regression as can discussed. In this case though we want to be able to capture the internal states of the material so we're going to be targeting many more parameters within our machine learning than Ken was discussing. They want to go there as well but we're finding that we need to do this sooner than they do and so that's how we're approaching this. We believe that this type of approach will enable the sort of high fidelity modeling that we want to do of the micro scale and plugged into the macro scale in order to allow us to do materials by design and ultimately to be able to integrate this into doing actual device design using these types of approaches. There we go. So Ken talked about the basics, went over how this whole multi-scale, higher the whole multi-scale method works. The basic idea is we have a macro scale, we have a micro scale and then we have a lot of stuff in between which hopefully will reduce the total amount of computation we have and in particular if you look right here at this representation of the laser pulse passing through our our semiconductor this we would represent by some sort of continuum model in this case we'll say we're using a finite element mesh. We would want to know the macro state at every point on this mesh. That can be a lot of calculation but at the same time as was noted before there's a lot of symmetry that's going to be in this problem. If we can exploit that symmetry and use adaptive sampling and use and create these types of databases in a sense through our machine learning approach then we should be able to reduce the cost of the computation significantly. So on the macro scale then what we're using is we're using we're using this model here right now we've had some discussions with some other people who do electro dynamic modeling. This particular model though allows us to reduce the laser propagation problem to what is essentially a fluid dynamics type problem. The commonly known is the advection diffusion reaction equation. So we can leverage a lot of the stuff that has been developed already for continuum models. The biggest difference here is that this is complex rather than real we have to deal with complex numbers in this case but it seems to work just fine we haven't had too many problems. We can then divide this equation into two parts one which is pure macro scale and then one which incorporates all the micro scale inputs that we put in. Thus far we've used empirical parameters that we've plugged into this part here we have not yet been able to get the we've not yet gotten the micro scale incorporate so it's not a true multi scale method but we're on our way to that point. The nonlinear response is all represented through the micro scale that's correct. So depending on how hard you drive a system the system with the laser you know at low amplitude there's essentially no nonlinear response at all. As you drive it harder the material itself responds in a nonlinear manner and we'd like to represent that through our through our micro scale equations because that's where it comes in and presumably if we do our if we do our regression properly that won't that won't increase the cost too much. Let's you know we'll see where that goes. Okay so as I noted this can be rewritten as the advection diffusion reaction equation micro scale comes in through this point and our quote unquote multi physics solution here using empirical parameters but the same machinery that we will use when we put in the actual micro scale responds as we expect. We get something that's known as self focusing at the laser. This is a well-known phenomenon that's been studied both experimentally and computationally. As far as going to a multi to multi scale where we include the high fidelity models doing a simple back of the envelope calculations Ken was saying the minimum number of CPU hours we're looking at is about three billion as we increase the complexity of our models obviously that's going to increase and so already the simplest model that we might try to do without doing some sort of surrogate modeling is intractable and so we need to find more efficient ways to do this and I will put in my acknowledgement here well as I said before this is all based on the work that's been done in the Bellotti group with this micro scale model for gallium nitride specifically and that's the model I'm going to use as we move into the as we move into the incorporating the micro scale model as well. Why this problem has more higher dimensional parameter space? The reason this has a higher dimensional parameter space is we don't have so in Ken's case they started out with a very specific problem that they could do with just a few degrees of freedom in this case the deformation of the material and just those parameters that they could extract from the DPD. We could potentially do that but the population profiles which you'll see as soon as I change the slide now that I can we find that we need more parameters to simply represent the internal states and so in a sense you might say that we skip the step that they did by not using pure parameters but I don't really know of a good model that we could use that would not incorporate that many parameters and that's really where we're stuck at the moment. So this shows what I was talking about. As calculated in the micro scale model we have essentially four different parameters at this over 5,000 bins. So we're looking at on the order of 20,000 parameters that are used to represent the micro scale at every time step. Now 20,000 parameters is out of reach for Gaussian process regression right now and frankly we don't want to deal with that much data anyway but it looks like we can reduce it down to somewhere on the order of about 100 parameters that we can use to represent these internal states. And it turns out that unless you're actively illuminating the material itself you don't even need that many you only need about half that. So we're hoping to get away with about somewhere between 50 and 100 parameters. It's still a lot but that is considered to be accessible to these types of regression solutions. And so to get a sense of what we actually need out of this. These are our states as we saw in the last slide. If you take a mean over 5,000 simulations you can see the mean is pretty smooth. There are a few features here. I'm guessing we won't capture that one there but we'd like to capture most of the rest of them. But the other thing that we need because we're representing something that is a statistical sampling of the system. We also need to get the standard deviation right. We need to have a representation of the statistical response of the material. And so what we're seeking then is we're seeking to capture from our calculations. We want to capture a representation of what we would get so that at any point as was mentioned before we could restart the calculation. We can see that with reasonable parameters and calculate the next point. In this case because our micro scale is time dependent we need to be able to do that. We need to be able to step forward with each new step. And so some of our input parameter then is the previous step. We also have to incorporate the incoming radiation. So that's what we're going to capture. As I mentioned before we have 20,000 states that we want to get. And the big question is I showed an average over 5,000 but I don't want to have to do 5,000 calculations for every micro scale point. The question is can we extract from a single calculation all the data we need to get that representation? And so that's the question I'm going to focus on in the balance of my talk. And we looked at different potentials. What surrogate models might we use? We looked at PCA. PCA is not doing well with this problem. And so we just dropped it. So it's not going to get there. We can look at interpolative methods such as stochastic collocation or something but most cases there at least the base of those models they assume that the points are exact whereas we want to capture the noise as well. Not only that but if we go back to this slide before we'll notice that as far as by bin number goes the standard deviation varies by orders of magnitude. And so we need a representation that can capture that as well within the noise. Where is the computer? Oh is it here? Oh just hit next here. So then we are going to go with Gaussian process regression. The only thing is that we're going to have to do some external fitting and tuning to develop our regression models. So what I'm going to show you is the baseline. We've looked at some different approaches as well on top of this but this is how we started out. Basically if we take that curve that we saw, do some sort of mean, do some sort of fit to obtain a mean and then once we subtract off the mean obtain a standard deviation and then from that mean plus standard deviation run our regression and see if we can get a model out that represents the data we have both the value and the noise. And so one mean standard deviation together giving us Gaussian process regression. It's imperfect and we're looking at some different types of kernels to improve this but it works. And as I said it reduces the number of degrees of freedom significantly. I'm going to skip this slide. I presume you understand this or if not it's not that important. We're using a fairly standard kernel right now. One of the things that I've been looking at recently is some use of some different kernels to improve upon that. And so I'll skip down here. So looking in terms of statistics, how does this match up statistically? From our regression if I go ahead then and I generate a new 5000, new 5000 samples based on this mean and standard deviation, do I match the original statistics? The answer is it's imperfect. In particular the regression itself is very sensitive to the calculated standard deviation. So any errors that we have within the standard deviation itself get amplified. And so as I said we're looking at some different means to capture that better. Obviously where the data goes to zero we have issues with the skew and the kurtosis in particular but overall the match appears to be pretty good and when you plug it back into the Monte Carlo simulation the micro scale model that we're using before it can just take off the move as it had previously. So that's a good sign. It looks like we're on track to having the system work together. And so did I have a slide in for a roadmap? I'm going to do the roadmap first and come back to the conclusions. So basically this is our target somewhere beyond 2022 having some materials by design capability. This is something that is of great interest. We have as I said the semiconductor modeling design center. The SIRDEC night vision is quite interested in these types of approaches. And for communications and the other applications we'd like to be able to at least have a start of being able to get this to work within that time frame somewhere within about the next five years. So on the left side here we have the track that I've essentially described right now. Hopefully within two, three year time frame we'll have an adaptive sampling based multi scale method working based on which is the specific topics I discussed. As that matures then we'll start to incorporate defects. We'll start to incorporate how do you deal with the layers, the interfaces between these layers and those things as I said before those will be handled through collaboration as well working with the Bertazzi group in Torino in Italy. And then the final thing is that we have been talking with people within the materials campaign about we've been working on some things that we can do for quantification also validation to put into these models. And so that's an ongoing thing. I don't have a good timeline on that yet. I will say this we hope to have one paper on validation out this year based on the micro scale model itself particularly. And so then going back or coming into the conclusions here we have a macro scale solver that works. We have a micro scale solver that works. We appear to have an approach that will allow us to do the regression on the micro scale so that we can plug it back in. And so we're putting together assembling the components so that we can have a fully operating multi scale model. And we're fortunate in this sense that we already have Ken's results. We know that the system that we're going to actually run the code, the libraries that we're going to use to make this work are already operational in their projects. So we're not worrying about that so much right now. Instead we've been assembling those pieces. The regression models seem to work. There's some things we'd like to do a little bit better. We also would like to improve... Well, once we have that we believe this will improve upon the means that people have been doing these calculations in order to put the micro scale into the full type of calculation so that we can do these high fidelity models and capture the physics where the actual excitation is taking place. And I think that's where I'll stop. Quick question. You mentioned that the equation you were solving in the reaction diffusion convection equation is linear. Does that mean that that velocity B is constant? Sorry, not constant but known. Well, so that's a good question. We're going to make that assumption right now. Obviously the speed of light is fixed. However, within a material that is under elimination you have some polarization. The speed of light will vary a little bit and of course the direction will vary as well. And so within the model itself, there's nothing that keeps us from using multiple macro scale solvers to handle different directions. And then there's some things that you can do with the phase to work through the delay having to do with the slight speeding up and slowing down the speed of light. It probably won't be a perfect match but it'll be pretty close. So the reason you need so many computational resources that they're great because of all of the different, the stochasticity of the problem. You have all these like hundred or a thousand, ten thousand simulations essentially each time. So I hope that we don't have to deal too much with the stochasticity. As I mentioned it looks like we can extract from a single calculation most of time. It's pretty close. The bigger issue has to do with the different parameters. If you look at come back here to this slide if you consider that this is the evolution of those states and as you illuminate it the populations of the different carriers change as it propagates in time and things relax, those populations change as well. So the big cost comes from this state to the next state either under illumination or not how is that going to change? And as I said that if you were to just calculate it in a combinatorial fashion is intractable. And so what we need instead is we need to use these adaptive sampling type methods so we can target the specific portions of the parameter space or the phase space so that we do the calculations that we need. And so in a manner similar to what can discuss we would pick out and do the calculations as needed where they're needed. And that's where the real cost comes in. The finite element solver compared to the microscale solve is essentially free. That's really what it comes down to. Have you been indexed energy or momentum? Momentum. Yeah. Which for for many semiconductors as long as you don't drive them too hard there's a fairly simple relationship between the momentum and the energy. In the case of nitrise you can't assume that it's quadratic but in many assembly conductors it is a simply quadratic relationship. How far into the audience of those states we're taking? At the moment we're not I think I'm going to say that falls under the that falls under collaboration here where we rely on our partners who are working specifically on the microscale representation on how they want to do that. I don't understand this curve of momentum. Is it momentum? It's too smooth. They're three basis directions, right? So the portions of the brand zone and the specific dispersion surfaces within the brand zone where the electrons and holes tend to stay those are essentially spherically symmetric. In this case we're making that assumption. There are situations where you that's what you have a quadratic relationship. In the audience group they have a different code that does actually account for that where they have different directions. That's actually, it's in my roadmap but I didn't stress it. We're going to get this working first before we drastically increase the freedom again. But presumably there and here there are a lot of degrees of freedom but you're not going to explore the whole space, right? Instead you're going to have very specific sections of the space of parameters that are very active. But most of it won't be active at all. And so by using the sampling techniques we can avoid those portions of the phase space completely. Yes? Good question. What are the engineering challenges involving putting something like that together? But what are the science challenges? We're the new research in building a system like that. In doing what you want to do. So a lot of the research is going to focus on this development of the adaptive sampling and how do we deal with it. So are you saying that that type of I just want to listen to hear from you which area you think is going to be like the new research that you guys are going to do here at ARL versus the stuff you're going to rely on collaborators and so forth. So that is this type of sampling. How do we do the representation of the states? How do we handle just the vast volumes of data? Can we represent it in manners that will allow us to render these calculations tractable? We're presenting volumes of data. Is it a question of how you deal with the HPC side of things? No, we're looking at this algorithmically. It comes back to this regression process. It's more the mathematics behind it. So really how do you build those reduced-order models? That's right. How do we build these models? How do we handle the different types? We're looking at use of different kernels, thinning out some process regression itself in order to capture this information with as few degrees freeing as possible. All right. Let's bring the speakers there.