 So hello everyone, and welcome to this seminar series of 30 terms for the machine learning and physics particle and physics seminar series. So our speaker today is Edu Westa, he is the lead for translation on AI at the Arkan National Laboratory with faculty appointments in the department of science and the University of Chicago, and in the department of physics I've at the University of Illinois at Burbank at Champaign. He is a theoretical astrophysicist, a mathematician, and a computer scientist, so his research interests, his research interests are numerous as his positions are, but he tends to focus on the interface of artificial intelligence, theoretical astrophysics, mathematics, extreme skepticism, and scientific visualization. Today he will discuss how to transform new AI approaches into a framework for scientific discovery in his talk titled AI for Science, Let's Talk Business. The talk is recorded and will be shared on YouTube, so if you have any questions regarding how to access it on this day to send it to us. Thank you very much Edu for joining us. All right, great. So I'm going to share my slides and I hope you can see them well. So I hope that this becomes a conversation. If you want to interrupt me any time during the presentation, please feel free to do so. I will not have access to the chat, so maybe if you can unmute and just interrupt me that will be fine. Okay, so I want to start this conversation with a few quotes from Bertrand Russell that are related to how we should be able to size problems and how we try to find solutions for them. And so these two questions I think are quite revealing when we are trying to innovate or to change the state of practice or the state of the art. And as you can see here, first thing that we need to ask is what are the facts? And the other one is what is the truth that the facts bear out? And so in the context of science, what we can see now is that after many years, even decades of effort, we now have large-scale scientific facilities that enables us to study the universe in high fidelity, high precision. And we now have other fingertips, a massive amount of data that we could use to go and answer the bigger questions. The origin of the universe, where the black holes come from, what is the preferred formation channels for them, we can see the universe through many messengers. But the truth is that while scientific facilities are delivering on their promise, now we encounter that we have these large volume, high velocity, multivariate, complex data sets. And we are at the brink of discovery. And we have samples of that in different domains. The discovery of the Higgs boson, the discovery of gravitational waves, that the collision of neutron stars is associated with the emission of gamma rays, sure gamma ray bursts, etc. So all of that is awesome. The problem is that as the amount of data continues to grow, and there is no end to it, what we realize is that the computing approaches that we have been using for many years and the signal processing tools that we use are not up to the task. They really are not keeping up with the pace of discovery that could be possible. And so people have realized that instead of just using machines to accelerate computing, we can use them to boost human intelligence. And we want to talk about that in this presentation. So what are the challenges when you say, when you realize the method I am using to extract knowledge from data from observation is not good enough? Well, the first thing that you realize is that innovation is not easy. Because you need to go against the flow, against programs that have been developed over sometimes decades. And there is like a frame of thought about how you do things. And so here you encounter sociological factors. And the fact that some longer programs have been funded by different agencies want to see some continuity. Disruption sometimes is not well perceived. And if you have been in this AI business for a long time, you do realize that this is an issue. And when we started changing the landscape of AI applications in physics in the early 2010s, well, people were not taking that lightly. And so what are the opportunities here? Here is where diversity is important. Because to change how people perceive things, you need to bring in people that have different perspectives. You cannot have the same group of people and then expect them to innovate. It's hard. You need to bring in new thoughts, new ideas, new perspectives. And critical thinking is important. And sometimes you will realize that people don't like your ideas. And so if you think that they are watertight, then you need to also have some resilience. Because at the end of the day, this is just a human endeavor. And there is not just scientific thought involved in this. There is also the human aspect. And we also need to realize and acknowledge that when you are pursuing knowledge, when you are trying to find answers, there is no established paradigm to accomplish that. It's all about creativity. And so sometimes ideas that have been held for a long time may not be the actual solution to address problems. And if there is something we have learned from the revolution in high performance computing, many people did not like, for example, MPI now, who is not using MPI in supercomputers. Several years ago, people hesitated on the application of deep learning. Who is hesitating that now? So I'm going to drive this conversation now based on a work that I have been doing with my research team in a few institutions. And I'm going to start talking about gravitational wave astrophysics. And let me just reframe, change your mindsets and put it in this context. So what is the challenge in gravitational wave astrophysics? Well, the idea here is that we have scientific facilities like observatories, and they are observing the sky in real time, trying to find gravitational waves. The data sets that contain the gravitational waves are not huge. They are actually lightweight. But the challenge that we have when trying to find these gravitational waves is that they are embedded in very noisy, very large backgrounds. And that the parameters that describe these gravitational waves is highly dimensional. And so in this movie that you see here, the parameters of these astrophysical parameters of these two black holes, they resemble one of the detections that Lago reported. You know, when you look at the waveform, and then you try to extract the astrophysical parameters, it is a very challenging endeavor. And again, when you're trying to identify this signal in a noisy background, some people have been using large template bands that describe astrophysically motivated scenarios. But that very fact slows down the process. And so when we had just detected the collision, the first collision of neutron stars, I was working with colleagues across multiple institutions and collaborations to demonstrate how we could harness state-of-the-art scientific computing in the U.S. with a diverse set of tools like containers, the open science grids. And so we connected Lago resources to Blue Waters that at the time was the leadership class supercomputer in the U.S. And we showed that we could very readily, very fast process the data and then confirm that indeed Lago had detected a neutron star collision. But through that exercise, we did realize how computing-intensive these template matching algorithms were, and that we needed really to do something else because Lago was going beyond their own resources and then expanding into other resources like the open science grid, XC, Blue Waters, etc. So while technically appealing the idea of using available resources, you still have the question, is this really the way to go forward? Or can we rethink how we are doing things? And so with my research team, what we started to do was exactly that, to challenge what we were doing and to try to rethink the problem. And so if you step back and you look at the problem, what are the challenges? Well, number one, you have very noisy backgrounds. There are signals embedded here. And it is not just the known Gaussian and non-stationary nature of the noise that complicates the problem, but that the data has a lot of noise anomalies. That could mimic gravitational waves. At the end of the day, a gravitational wave is a noise anomaly, right? But it has some very well-defined physical parameters. So how do you tell apart a real gravitational wave from the zoo of noise anomalies and from these type of very complex noisy backgrounds? So what we did was to break down the key challenges and then start addressing them one by one. We also learned from what had been done already by other scientists. So it is not about discarding what has been done in the past, but to take in the gems of knowledge that had been produced through many years of research and then bring this together with new methodologies. And then we were also very conscious about looking at what was being done elsewhere, what people were doing in the computer science community, in the high performance computing community, and then try to harness these different ideas. You know, this is the value of an interdisciplinary approach. You don't have to recreate the wheel every single time. And so what we did by the end of 2016 is to present a novel approach in which we showed that neural networks can learn the physics of waveforms in a hierarchical manner. What this means is that you no longer need a massive bank of signals, model waveforms, and then filter the data with every single one of these to see whether something in the data resembles these physical models. Rather, what we did was to graph some neural nets, expose them to all these different signals with multiple realizations of nodes. And then we ended up with basically an executable that was just a few megabytes in size and that could process simulated data faster than real time. This was perceived as, you know, a great idea by some, something that was unfeasible, maybe something wrong in the analysis by some others. But the key thing here was that we were trying to address the problems that had been identified by this community, and we were presenting a novel solution to this. So I think the main criticism that we received at the time was that we were using simulated data for this analysis. So we started working on using actual real LIGO data to train the neural networks. And a few months later, we again demonstrated that we could develop these deep learning algorithms and then go and process advanced LIGO data faster than real time and identify real gravitational wave sequences. So there was no doubt anymore these neural networks did provide a novel solution to the challenge of identifying gravitational waves. And we were at the time focusing on black hole mergers. So this was all very good. But then again, when you are developing this new approach, you need to be, you know, very honest with yourself. And then ask again the questions, well, what are the facts? This is great progress. And then what is it? So that the facts were out. Even though this approach of deep neural networks exhibits great promise, what are the weaknesses and what are the strengths of these approaches? And so the positive thing is that we were able to analyze real LIGO data and find signals. But that was not a production scale framework. It did not have the depth of the state of practice violence used by scientists to find gravitational waves. And the truth of the matter is that these algorithms were making a mistake for every 200 seconds of search data. So, you know, there were remarkable, there was remarkable progress, but there were again, many things to be done. And so what we did was to believe in the promise of these algorithms and to take them to the next level. And I'm going to walk you through that journey. So we, at the time in 2017, we had approved concepts. As I said, it was working very well. We were considering just the masses of the black holes. And we could train an neural network to do gravitational wave detection using 40,000 model waveforms. Only one GPU was needed. And the nets were trained within three hours. Now, if we want to take this to a production scale algorithm, we need to consider the same depth of the parameter space that the state of practice computing test pipelines have. And so this would be a four dimensional parameter space, the masses of each of the black holes and the spin of the objects. And now this takes us to a training sets of about 30 million signals. And so we did some benchmarking and we realized that if we continued to use one GPU, then this was going to take us about a month of training. And that is really sad because who's going to be giving you access to, you know, one GPU in a dedicated fashion for one month. And that for researchers and students, you're spending one in one month is basically not acceptable. And so we had to, again, create a lot of infrastructure in terms of algorithms, in terms of physics inspired neural networks. Because if we're going to dive into this challenge, we cannot be doing this blindly and just hope for the best. So the first thing that we did was to, again, start creating these neural networks, but incorporating physics knowledge into them, in the architecture, in the optimization scheme. And now we abandoned the idea of just using a handful of GPUs. We started developing algorithms to scale the training, first to tens of GPUs, as you can see here. And eventually, when I got access to the Summit supercomputer at Operates National Lab, all the way to thousands of GPUs. What is the advantage of this approach? Well, that now we can train our neural networks with a deeper signal manifolds within just a few hours. Again, there are some trade-offs here. You need to realize that when you are training these models at a scale, sometimes the performance is not as good as when you're using just a handful of GPUs. So you need to develop the algorithms to make sure that while you reduce time to insights, you obtain optimal performance when you're training the algorithms. And I think there are questions. So if you want to unmute and ask, that would be great. Can you unmute or someone can read the questions in the chat? Hello. This is not really a question. I think someone has some problems in your slides, but they're working at the moment. Okay. So let me continue. So the next stage is once we are able to train neural networks, incorporating domain knowledge, like for example, the physics behind the spin configuration of black holes, how fast these objects can move and all of that. Once we had that infrastructure and we were able to train algorithms at a scale, then the next question was, okay, let's go back to the detection challenge and let's see what we can learn. So we applied all this knowledge to train a new class of algorithms that now covers these four dimensional signal manifolds and that we can train with hundreds of GPUs in a couple of hours. And what we found is that when you deploy these models on GPUs, then you only need four GPUs to process LIGO data faster than real time. And in this study, what we also realized is that instead of using just one model, what we could try to do was to develop models that are trained with LIGO data that is sampled at different frequencies. So we developed a model that was sampled at 16 kilohertz and a different model that was with data that was sampled at four kilohertz. And we used them in tandem to process LIGO data and we found that they were very good at identifying real events. And now we reduce the number of mistakes from one mistake every 200 seconds to one misclassification for every 2.7 days of search data. And here is where you say, okay, this is great. We are addressing two critical problems with these new methodologies. Number one, we are covering the same signal manifolds of state of practice pipelines. We can still process this data faster than real time. And we have reduced the number of mistakes significantly by orders of magnitude. Okay, so this was again, you know, evidence that we were going in a good direction. And we again took this to the next level. And so what we do now is we realize that using ensembles of AI models is improving the detection capabilities of AI. And so what we did now was to train a suite of models, tens of them in the Summit supercomputer, and then retain the top performers, created an ensemble, and then fed in data in each of these models. As you can see here, each model is processing concurrently Hanoff-Renlinson data. And then we look at the output of the four models. If all of them agree that there is something interesting in the data set, we channel that through post processing. And then we look at the outputs of these analysis. And here, for example, you see that for this particular gravitational wave signal, when there is a real event, there is a sharp response that comes out of these algorithms. And that was what we needed to number one, be able to process data at a scale, and then obtain outputs in real time that is telling us about the existence of an interesting noise trigger in the data. And so this is the first part of the analysis. We use supercomputing to reduce time to insights. Now, that is not enough because, you know, learning from our own experience, we did realize how valuable it is to share knowledge with other researchers. So we realize that not everybody is going to have access to supercomputers. Not everybody is going to have time to go and learn supercomputing and the AI at the same time and combine them to produce these models. So what we did was to release these models and then type of processing analysis through the data learning hub for science. And this was, I think, a great connection between two independent teams. When I was at University of Illinois at Urbana-Champaign, and I had the opportunity to get to know Ben Blasey, Brian Chard, and Ian Foster, and Ergon and Yuchikado. And they told me about these great resources that they were developing in the context of material science. But this is pretty much domain agnostic. So the main idea here is that they take the models, the AI models, and then they containerize them so that they can be used on disparate hardware resources. And so you go to the DL Hub, browse the models, and you get executable to get the model and run it on a compute resource. Now, that is good, but that is not enough. What we want to do is to further lower the barrier for researchers who want to use the models. And what is that approach? Well, the approach is that once you have the models in DL Hub, you can now connect the models with a compute resource. And you can see this computer cluster at the National Center for Supercomputing Applications. That is called the hardware accelerator learning cluster that has 64 GPUs. It is an IBM Power9 machine. And so what we do is we release the models in DL Hub, and then we use FunCakes to connect it to DL Hub and your compute resource. And then FunCakes is going to be the overall workflow manager. It is going to start workers at the cluster, it is going to do the inference, and then it's going to allow you to look at the output of these models. And so we share the models with them, the post-processing scripts. And on their own, they were able to rerun the analysis. And what they found is that they could process an entire month of advanced LIGO data, almost 2017. And then by distributing the inference over the entire cluster, the 64 GPUs, we were able to finish the analysis in about seven minutes. And as you can see here, throughout that month, we had no mistakes. So greening here means the two LIGO detectors are up and running, collecting data. These lines mean that there are four binary black hole mergers reported in that month. And this is the ensemble prediction for the existence of gravitational waves. And they coincide. And there are no misclassifications here. So this was the first time that an end-to-end AI framework for gravitational wave detection at scale was introduced. And you see all the pieces, supercomputing to train the algorithms, domain knowledge that goes into the optimization and training, architectural design of the models. Then you harness scientific data infrastructure as the data learning code for science. You connect these two with, again, supercomputing resources through phone cakes to distribute the inference. And then you look at the output of the analysis. Now, think about this. One month of data process in seven minutes. That is really good. But then we wanted to go the extra mile. And the extra mile here is that these models, ones that were released in DL Hub, they could be used by any researchers. And since we released them in July 2021, they had been invoked over a thousand times. And this is good. This means that there is interest in the community to harness this type of resources and to use them. Now, let's see whether we can do something else. Well, this is the outreach that we got out of this analysis. It was published in Nature Astronomy, and I was invited by Nature to write a blog about the human aspect of how this is done. This is obviously a very nonlinear process. And when you're trying to address this challenge, sometimes it seems that it will be really hard to solve some of the problems. But we just kept plowing through and addressing these problems one by one. This is why I mentioned at the beginning that you need a little bit of resilience as well. So the next step was we have learned how to harness disparate resources, supercomputing, data infrastructure, advances in AI, et cetera. Can we do something else? And so what we did here was to start automating this process. We now have infrastructure to train tens of models in summits. We have developed algorithms to identify the top performance using, for example, ROC curves, using long data segments of real LIGO data. Then we know how to optimize these algorithms for inference, for example, through quantization or using TensorFlow RT. And then the final step here is once you accelerate the models for inference, now let's go and use tools like TensorFlow RT that are going to optimize your model using, for example, a different precision. And now we are going to fully utilize the SATA GPU supercomputer at Argo National Lab. And through this approach, we realize that if we go back to that one month of data with 2017, we could process the entire month in just 50 seconds using 160 GPUs. And then the question that arises is, okay, this is pretty good. What about processing longer data segments, not just one month? And so what we did here was to do some time slides to these one month long data sets, shifting one of the LIGO data streams and for Livingston one second with respect to each other, and then continue doing that process until we had five years worth of data. And again, we blazed through that synthetic data set. And we found that on average, this ensemble of AI models was making a mistake for every month of search data. And now compare that to the results we had in the beginning back in 2017, when we were reporting one mistake for every 200 seconds of data. And the additional advantage of using these resources for accelerated inference is that we could process data 53,000 times faster than real time. So think about that. When we first introduced these ideas, people were hesitant to believe that AI models could process data faster than real time. Now, after years of developments and harnessing disparate resources, we are at this level. So I'm going to pause here because I'm going to transition from black holes to neutron star mergers. So if anyone has a question, I think this is the time to do it. So I'm going to go on. So the next source that we have been exploring for the application of these deep learning algorithms is the collision of neutron stars. And they differ from black hole mergers in that they could be observed using multiple messengers, right? Not only gravitational waves, but also electromagnetic waves. And, you know, if these source what was sufficiently close to us, even astroparticles. Now, the beauty of these signals is that they stay in LIGO bands, not just for a fraction of a second or for a couple of seconds, as in the case of black hole mergers, they could be in LIGO band for tens of seconds. And once the LIGO detectors attain the science in CDFT for a long time and even imagine what you could do with third generation gravitational wave detectors. So here there is a great opportunity to do something else than just gravitational wave detection. And what is that? Well, that is forecasting. And the idea of forecasting, you know, this comes from, for example, what people study in the markets. Is it going in the right direction? Is it going to be a crash? What are the elements that may trigger the market to move in one direction or the other? Or when you are speaking, you say a few words and then algorithms predict what is the next word or the next few words that will complete that sentence. And so we adapted these ideas to predict when we would see the merger of one of these type of sources, neutron star signals in advanced LIGO data. And what you can see here in this panel, for example, is that for the first neutron star detection, you can see that the signal becomes noticeable in this spectrogram tens of seconds before the merger. And so we developed this algorithm to process data and then trigger a signal that says, I perceive that there is something of interest and there is going to be a merger that is imminent. And so in these algorithms, what you can see here is that for the real data contained in this event, neural networks could tell us 10 seconds ahead of time, that a neutron star collision is going to happen. What is even more remarkable is that irrespective of the existence of this pretty, pretty loud noise anomaly here, the performance of these neural networks is the same. You can see here that when there is no glitch in the data, we have removed it. You see it is around zero here. And here we stopped the analysis before reaching that noise anomaly. The neural net still predicts that there is going to be an interesting collision 10 seconds ahead of time. So this is really good. This means that even if we have some noise contamination, these algorithms can tell us valuable information about the existence of multi-messenger sources in complex experimental data. And again, you can see here that this is no longer about real-time detection or faster than real-time. This is about looking at the future ahead of time. So we extended this analysis and now we ask the question, okay, this is for neutron star collision. What about neutron star black hole collisions? And we conducted an analysis of this nature and we realized that for different types of configuration signal to noise ratio cases, we could see the sources 10 seconds ahead of time. And in the multi-messenger astrophysics community, they are very soon developing this type of early warning systems as they call it. Again, the beauty of neural networks is that these algorithms are very compact. They are portable and so they don't have to be run on supercomputers. You can just deploy them at the edge in seed to other detectors or on satellites that are observing data in real-time. And you can do the computing there. You can get a trigger that something interesting is going to happen in seconds ahead of time. So it is quite remarkable how you can transform algorithms that were originally developed to study the markets for speech analysis to predict the existence of multi-messenger sources. Now, we took this again to the next level and we started now considering signals that are much more complex to what we have been studying in the literature. So now considering not black holes or neutron stars that follow quasi-circular orbits rather that they follow eccentric ones. And you can see here that there are some beats in the signal and eventually the signal becomes noticeable in the ligament. What we realize is that irrespective of the eccentricity of the signals or how complex they are, the neural net can tame that complexity in the signal and still predict the existence of these mergers ahead of time. We also conducted another analysis which is, okay, the neural network is telling you that something interesting is going to happen in seconds ahead of time. But how certain is the neural network about its own prediction? And so you can see that analysis here. And in addition, we also studied, if you, for example, make a prediction 15 seconds ahead of time, that there is going to be a collision of this type of neutron stars or black hole neutron stars. The area in the sky that is going to be covered at the time is shown here. And so you can see that it is going to be a very broad area in the sky. Of course, only using two detectors. This is going to be further reduced when you use more detectors across the planet. You can see how the area in the sky is shrinking. So, you know, this would be a beautiful exercise to actually use the neural nets and all these different analysis concurrently. There is a tree here and then you see how the area in the sky is reducing and you're eventually pinpointing to the location where the signal is going to be detected. So that is related to neutron star collisions and forecasting. If you have any questions here before I transition to another topic, this is the time. Anyone? So when we are thinking about signal processing algorithms, and detection or regression, we often don't think about how you produce the model signals with which you are going to train the algorithms. You take them for granted, right? You build upon what numerical relativists have done and then data analysts have done part of their job, which is to produce efficient waveform predictors. But sometimes, you know, these assumptions are not so good. And what happens is that you need to start thinking about how to produce signals faster to train these algorithms. So when we were thinking about this, we had this idea. If we were to train a neural network, is it possible, you know, still in the context of forecast, is it possible for the neural network to learn the complex physics of black hole mergers? And just to contextualize this, if you look at the signal that we present here, this early part is known, you know, in the literature as the inspiral evolution. And you can model this with pretty good precision with post-neutronian theory, which are semi analytical descriptions of the dynamics of black hole mergers or neutron star mergers, if you want. But you don't get into the highly dynamical evolution of the binary. And then when people try to model, you know, the late part of evolution, like what you see here, well, they realize that they could use black hole perturbation theory. But things that are here, which are later inspired all the way to merger, they are very difficult to model because you need to solve Einstein's equations. And for that, you need supercomputers. Okay. And so here we have a very natural question. If we are able to use neural networks to forecast the collision of neutron stars, is it possible for neural networks to learn this complex physics that is here? You know, this is at the heart of Einstein's equations, the evolution of black holes, and then to see how they eventually merge and then form stationary black hole. And so we developed something that is called a transformer model that has a few advances in AI like attention. And we realized that when you consider this signal manifold that I show here just one part of it because we consider a mass ratio sort of way to eight, when you train this transformer model, it is able to output all these dots that you see here that resemble very well the dynamics of these mergers. And here I show three different scenarios for different spins for the black holes when they are anti-aligned. And what this means is that the merger happens very fast when they are not spinning and then when they are spinning very fast. And you can see here the number of cycles that are completed before merger. As I said before, negative spins means that the merger happens really fast. Here you have the non-spinning case. And when you have rapidly spinning black holes and the two of them are aligned with angular momentum, then now the merger is extended. And what we found is that the neural net is able of predicting these highly nonlinear dynamics. In addition to that, we also wanted to understand when we are feeding the early part of the signal into the algorithm to predict the final part. What are the bits and pieces of the input data that are responsible for a good prediction? And what you see here in these diagrams is that, for example, to predict this part of the signal, the neural net is paying close attention to the early and spiral evolution. And when it is predicting this part, the transition between latest spiral into merger, the neural net is paying close attention to the final part of the signal. And this makes sense, right? Because what the neural net is doing is it takes one input, makes the prediction, takes the previous one, makes the prediction of the other one. And you can see that here, right? It is a causal prediction. You take the input and make a prediction of this one, look at the previous output and make the prediction for the next step, etc. So this all makes sense, right? You cannot predict something that happens in the future if you don't have a previous time step. And so these interpretable AI studies are available. You can go and take a look at them and they are interactive. You can select a portion of the signal and then look at the attention heads and see how that information is being used to predict a given part of the output signal. So when we were at this stage, now we were thinking, okay, this is pretty exciting. What we are seeing is that we can predict the highly nonlinear dynamics of black hole mergers. Can we now go and try to do something else in the context of partial differential equations that are now used not to study black hole mergers, but neutron star mergers? And this is a very complex problem because now you need to combine general relativity with microphysics, with neutrinophysics. So it is a very complicated problem. And yes, it is true that over decades, people have developed PDE solvers. But when you need to combine different grids because you need a lot of resolution, for example, to study the amplification of magnetic fields. And you don't need a very detailed grid when you are studying the dynamics of the neutron stars when they are separated. Now you start scratching your head because honestly, how do we combine these so that we complete one of these simulations in a reasonable amount of time. And so researchers, compelled by this, have started developing neural nets that solve PDEs very rapidly while keeping the error under control. And we have also started looking at this. One of my students, Sean Rossofsky, started looking at this in the context of magnetic hydrodynamics and the type of studies that you can do with turbulence for this type of systems. And he realized that even using not very complicated neural nets, you could capture the real physics of these systems and outperform all the other methods that you have in the literature right now. And so, you know, the big goal here is to eventually replace some of the modules of these numerical relativity codes to accelerate the modeling of neutron star collisions. And the next step for him has to be, has been to look at a more complex PDEs, you know, gearing towards a magneto hydrodynamics. And so one of the recent PDEs that he has solved using physics-informed neural apparatus is the shallow waters equation. And this equation that you see here is used to model coastal dynamics and tsunamis. And it is the first time that three systems of PDEs coupled, as you can see here, are solved using PINOS. And just a few words about PINOS. These differ from physics-informed neural networks. PINOS have been superseded very rapidly by a variety of techniques. And these new type of algorithms, PINOS, really show great promise to solve complex systems. And what they are doing is they are learning the operators that you see here. And they incorporate a lot of knowledge about physics when you're optimizing them. So they are very powerful algorithms. And you can see here, for example, for some of the parameters that describe this shallow waters equation, like the velocity, you can see here the predictions of the neural network, the actual solution with a traditional PDE solver, and the error that they have. And you can see that it is tiny. So it is very promising. Same for another parameter, which is the height of the perturbation. You can see that the prediction that we have with PINOS are pretty good. And all the codes, all the code that has been used to solve these equations may be found if you go to this archive link. All right. So let me just give you the big vision, the 40,000-foot vision for the activities that we are conducting at a moment. I only talked about gravitational waves and multi-scale and multi-piece simulations, but the work that I am doing with my team goes well beyond this and enters into cosmology, agriculture, medicine, molecular dynamics, and some other applications. And what we find is that obviously the devil is in the details, but a general framework that is going to work for multiple communities. And how we can share knowledge, learn from models, and move faster is the following. If you have the skills to train, to develop these models using supercomputing, that is amazing. You can continue to do that and share your knowledge with others. And then use the data learning hub for science as a central nexus to share these models. They are ready to use. And then you can connect VL Hub with any computer source that you have available, for example, with Funkex. And you can harness other methods like TensorFlow RT to optimize your models for accelerated inference. But once you have a model that is working and, you know, time goes by and maybe the model is not capturing any more the statistics of your data, there is no need to go back to a supercomputer and stay in queue for days or hours to find in your models. What you can do is to connect your models to a cloud computing resource. And then you can perform active transfer reinforcement learning to find in the performance of your models and then continue here in discovery modes. If after a while, you see that some metrics that you use to quantify the performance of your model tell you that you need to refine your models big time, then you do go back to supercomputers and then retrain the model and then go back to discovery modes. And this is a virtue cycle if you wish, because we are using computational resources in an optimal fashion. You only go back to supercomputing when you really need to train the model at a scale and you use age computing resources to find in the performance of your model to continue doing your research. And, you know, this is a vision that is being embraced by multiple communities. And we are participating in the development of it. There are a lot of groups across the planet that are working very actively in the traditional way of astrophysics. I did not include many of them in the presentation, but this site I think has a comprehensive list of the important contributions that different groups are making to this endeavor. And so in a few words, what we are now trying to do is work with experimentalists so that they develop AI-related data sets, meaning that they can be readily used to train models or to find new things in these data sets. We can combine that with innovative computing, not only GPUs or accelerators, but we could use different systems like Cerebras, Samba Nova, GROC, etc. And then when you do this, the idea is that when you create fair, which is an acronym for findable, accessible, interoperable, and reusable data sets, and you incorporate your physics knowledge into it, then you can create models that will enable you to accelerate discovery. And at the end of the day, you know, these tools are not a replacement for humans, but to boost human intuition, to optimally use our resources. And quite frankly, if we are able to develop models that understand nature as it is, we will be able to go beyond the approximate theories that we have right now for a great number of different processes that we don't understand fully. So, you know, this is a great opportunity to go from the limited knowledge that we have with simulations and incomplete models and to allow AI to take us to the level that will allow us to understand very complex natural processes. And I end here acknowledging my funding sources. Thank you. Yeah, thank you very much, Elio. That was a very interesting talk. And let me pause recording.