by Iulia Chifu & Ivan Milic
by Iulia Chifu & Ivan Milic

During the European Space Weather Week, we had the honour and pleasure to interview Sabrina Guastavino and Enrico Camporeale, very active scientists in applying ML to Space Weather. Sabrina Guastavino (https://sites.google.com/view/sabrinaguastavino) is an Assistant Professor at the Department of Mathematics (DIMA), University of Genova. Her particular focus is on space weather, solar image reconstruction, solar flares and Coronal Mass Ejections forecasting. Enrico Camporeale (https://ecamporeale.github.io/index.html) is a faculty member at Queen Mary University of London and affiliated with the Space Weather Research Technology Education Center (SWx-TREC) at the University of Colorado, Boulder. His main interests cover Space Plasma Physics and Machine Learning, with a focus on Space Weather, solar wind turbulence, radiation belt and magnetospheric physics.

I&I: Sabrina, I know you have a degree in mathematics. What attracted you to apply mathematics in solar physics and not any other direction in astrophysics?

Sabrina: Yes, I’m a mathematician in the Department of Mathematics at the University of Genoa. For my master’s thesis project, I joined a group called MIDA (Methods for Image and Data Analysis), which I’m still a part of, that works on space weather and solar physics applications. They asked me if I wanted to start working on a project called “FLARECAST”, which I did. I liked it very much, which motivated me to continue in this direction for my PhD.

I started by developing machine learning techniques for the project. I also got deeper into the mathematical aspects, such as formulating the problem and studying convergence results. Later on, I applied these techniques to observational data, which turned out to be more challenging than the standard mathematical methods applied to synthetic data.

I&I: Did you have special machine learning courses, during your mathematical degree?

Sabrina: No. Recently, we started introducing these techniques in the master’s curriculum. Currently, I teach a course on the applications of mathematics in astrophysics. In this course, I introduce many machine-learning techniques for applications such as solar flare forecasting and image reconstruction

 I&I: Enrico, I believe you’ve also independently learned these techniques. As I understand it, you earned your PhD in plasma physics. When did your interest in machine learning begin, and how did you navigate and choose among the wide range of available methods?

Enrico: I had a very non-linear path and I have been working in many different fields over the years. I am the type of person who, after a while working on a topic, feels the need to try something new. I don’t know if it’s a good or a bad thing. As a postdoc in Los Alamos, I did computational methods for plasma physics. After that, I searched for a permanent position, and I obtained a tenure track position at the National Dutch Centre for Mathematics and Computer Science (CWI, Centrum Wiskunde & Informatica). CWI had a very small group working on plasma physics, and I was hired as a computational plasma physicist.

Being in that environment, I’ve been exposed to machine learning. That was around 2014 when there was this kind of big wave of the restart of deep learning. I didn’t even know what a neural network was at that time. The discussions with my colleagues at that time and the advice from some senior people guided me in the right direction and I think they pointed out that machine learning will have a strong impact on space physics or space weather. Like Sabrina, I had to teach myself the foundational aspects of machine learning—methods, mathematics, and statistics. Over two to three years, I decided to steer my career almost entirely toward applying machine learning in space physics and space weather. I was betting on the future growth of the field—but fortunately, it turned out to be the right move. I suppose I was lucky!

Three major factors for the machine learning boom

I&I: We have a question for both of you as experienced scientists in machine learning, even though you are self-taught. Machine learning as a concept has been around for a long time, but its popularity increased significantly over the last decade. What would you say to someone new to the field about why machine learning has become so popular now in our field?

Enrico: Looking at the history of AI, as you mentioned, we can say it experienced periods of “winters” and “springs”. Even though AI existed since the 50s, it hasn’t reached its full potential for a long time. I think we started using the term deep learning in 2012 due to the success of a deep learning algorithm in the ImageNet competition, which was a computer vision contest for image classification. That was probably the starting point of “modern” deep learning.

I think at least three different factors led to this exponential growth. One is related to computing power. As we all know, training these models is fairly expensive, and it wouldn’t have been possible 10 or 15 years ago. The advancements in GPUs have made this level of computation possible, enabling the rapid development and application of deep learning. Nowadays, Nvidia is the biggest player and is reshaping this field again, probably having the vision of the future. It used to be a gaming company, and maybe it is still active in this direction, but now the major focus is on AI, with GPU being the main factor for this shift. Another key factor is the significant investment by major tech companies like Google, Microsoft, Facebook, and IBM. Platforms like, for example, TensorFlow and PyTorch, developed and released by big companies, have democratised access to machine learning, making it far easier for a broader audience to use these tools. And there was also a third factor that I’m missing now…

I&I: What about our specific fields, like solar physics and space weather? How does all this apply to these areas, considering you were speaking more generally? Sabrina, would you like to continue?

Sabrina: One key point is that these techniques are well-suited for handling vast amounts of data. In our field, we have large amounts of datasets from different spacecraft missions, and exploiting deep learning allows us to process and analyze this data more efficiently than humans could. The availability of such large datasets is a major driver for adopting these methods. In the Space Weather field, an important aspect is real-time forecasting. These techniques can process data much faster than classical models, enabling real-time predictions. The viability of the computational power is one of the main factors for the feasibility of demanding deep learning applications.

Enrico: … of course, the third factor was Big Data, which is particularly relevant to Space Weather! The reason I decided to apply more and more machine learning, almost exclusively now, was big data. Space weather is still a young field, about 20 years old, and I think significant progress has been made and much has been learned, but the focus has largely been on physics-based models. In my view—and, as far as I know, the opinion of many others— the predictive capability of those models is not much better than it was 20 years ago. I believe this opens the possibility of exploring alternative approaches, and machine learning is the best candidate.

I&I: Would you say with machine learning you get better results than with the physical methods?

Enrico: I think you get better results in some fields, like, for instance, geomagnetic index prediction. In this case, I would say machine learning is unbeatable with respect to physics-based models. In other fields, I think there’s still work to do.

We are at the point where most of the techniques have been shown to the community, promising proof-of-concept results across various fields. But for example, in the solar flare forecast, which is possibly the hardest task, we haven’t seen a breakthrough yet. While machine learning has shown some improvement over traditional methods, it hasn’t delivered a major advancement in the accuracy of solar flare prediction.

What is happening with the flare forecasting?

I&I: It’s interesting that you mention this, as I know machine learning has been applied to flare forecasting for almost a decade. However, I still get the sense that, as you said, there hasn’t been a real breakthrough in this area. Why is that the case? If machine learning is supposed to be so revolutionary, what’s holding back its impact in this field?

Enrico: Part of the issue is that the community is still learning how to use these methods effectively. About 10 or 15 years ago, the machine learning techniques available were less advanced, and the architectures were simpler, we had less data to work with. And so, I would say maybe the first attempts were kind of naive in a sense. I would add that, even though we haven’t seen a breakthrough yet, I think right now we’re in a much better position, and I think ML is way more promising than it was 10 years ago. But you’re right. I mean, people have been trying for a long time to forecast the flares. In the end, it’s not as easy as it sounds.

I&I: Sabrina, what is your perspective on this topic, given your involvement in flare forecasting since your master’s thesis?

Sabrina: In my opinion, the problem with deep learning techniques is the necessity of a high-quality data set. Then, the creation of the data sets is extremely important because the technique learns from the samples we present. Also, labelling the data requires significant effort, and we need a huge amount of data to make better predictions. A hot topic in mathematical science right now is the “double descent curve.” Usually, if the model is too complex, there is an overfitting, but recent empirical experiments suggest an interpolation threshold for which the test error decreases. Some applications showed that using complex deep learning techniques with many hyperparameters improves the overfitting problem. I think understanding why this occurs is an important area of investigation, as crossing this threshold could show improvement in the predictions. And I think a crucial point is the revolutionary approach of physics-driven AI techniques that, in some way, insert the knowledge of physics that we must guide the artificial intelligence techniques. Forecasting flares can be particularly challenging due to the complexity of the processes involved compared to models of phenomena like CMEs, for example.  But I think we should try to incorporate, in some way, physical knowledge to guide the machine learning techniques to improve the predictions.

I&I: Do you see any improvements in flare forecasting using machine learning compared to when it was first applied to this problem? With the evolution of methods and approaches over time, are the results getting better?

Sabrina: I believe the difficulty is that we now see many papers showing different results, but there is no validation strategy to determine which method is better. This aspect represents a crucial point in understanding if there is an improvement because it depends on which samples you are testing these techniques. At this moment, I think there isn’t a real improvement in the flare forecasting, and there is still much to do in this direction.

I&I: That’s interesting. From the talks and published papers, I had the impression that flare forecasting was a largely solved problem. However, could it be that there’s been a significant increase in noise in the published work and a decline in the quality?

Enrico: Yes, but that is a general problem in machine learning, right? Because there is the promising and novel aspect, but there is also the hype aspect, right? This has a negative impact on the number of papers, making it more difficult to discern high-quality papers from the rest.

“Physics-informed neural network, one of the best methods at this moment”

I&I: Can you think of any examples where machine learning enabled something truly groundbreaking—something that couldn’t have been achieved without these techniques? Perhaps something innovative in space weather or solar physics that highlights the unique capabilities of machine learning?

Enrico: One of the things I was excited about a couple of years ago was using physics-informed neural networks. As Sabrina mentioned earlier, the focus isn’t entirely on data-driven methods but instead on incorporating physical constraints into the learning process. From a physics perspective, I think a big challenge is still to solve inverse problems, which are still very demanding computationally. For example, I used a physics-informed neural network to solve the inverse problem to find the optimal parameters in the diffusion and advection equations for electron transport in the Earth’s radiation belt. I think PINN is one of the best methods at this moment because it’s free from any parametrization, it’s much faster than standard inversion techniques.

In geophysics, the typical approach for this would be using Monte Carlo methods or Markov Chain Monte Carlo, which can become computationally expensive if the forward model itself is demanding. This is where physics-informed neural networks offer a revolutionary advantage; they enable us to address problems that would have been infeasible with traditional techniques. It’s one example that comes to mind.

I&I: Sabrina, do you think you can give more examples?

Sabrina: I think from the point of view of re-utilizing the vast amounts of data we have, it seems crucial to develop techniques that can effectively integrate this information. Currently, there may be a gap in how well we integrate all these datasets. For example, in the case of 3D reconstructions, leveraging multi-spacecraft observations and applying deep learning techniques to combine and interpret this data could significantly enhance reliability and accuracy. This type of integration could be a key advancement in the field.

I&I: Which machine learning techniques or applications have you used that, from your perspective, have contributed to notable advancements in the field?

Sabrina: Right now, I’m interested in developing physics-driven machine-learning techniques. At this moment, in solar flare forecasting, our focus is to try to use many different kinds of data. We will try to incorporate EUV information and not just magnetogram data. We think that this multi-data approach could help improve the prediction. Regarding the prediction of CMEs’ travel time, we explore physics-driven AI techniques, which include the drag-based model in the loss function in the training process of the neural network. Initially, we started with a baseline model, really simple. Now, the idea is to try to use more complicated models and to evaluate if there is an improvement. For geomagnetic storm predictions, I think machine learning gives good results, but it would be important to have earlier predictions. Tracking a CME from the moment it begins could enable more accurate predictions well in advance. Additionally, updating the forecast dynamically as the CME travels toward Earth would further refine the prediction. The goal would be to provide reliable forecasts of the storm’s intensity much earlier.

I&I: Enrico, from your perspective, what technique or method that you’ve used do you think has had the most significant impact on the field or deserves special recognition?

Enrico: I agree with Sabrina. I think the PINN will be more and more promising because even simple intuition tells us that if you apply a machine learning model completely data-driven, you have too large a parameter space, you have no physical constraints so there’s no guarantee that your result is physically valid.  That’s where the physics-informed part will come in. Let’s take the example of geomagnetic storms. I’ve been working for a while doing Dst (Disturbance Storm Time) predictions, which I think it’s fairly easy to do with a neural network. What we observe, especially with zero-time lag (nowcasting), is that solar wind quantities at a given moment are strongly correlated with the Dst index at the same time or shortly after, within 10 to 20 minutes. Neural networks are highly effective at capturing this nonlinear relationship. However, each storm is different, right? For reasons we don’t fully understand yet, a neural network might perform exceptionally well for one storm but less effectively for another. This variability presents an opportunity to delve deeper into understanding these nonlinear relationships, which could ultimately lead to new insights about storm dynamics. That’s kind of a holy grail of machine learning applied to physics – using completely data-driven approaches to uncover new insights and then “opening the black box” to discover something fundamentally new. At this stage, it’s still more of an emerging idea, but I believe that the discovery of new physics using machine learning techniques will become a topic in itself. The physics we currently use to characterize many processes is often overly simplistic, with significant gaps in understanding. And neural networks and other machine learning methods have the ability to discover pretty much any nonlinear relationship. Of course, the challenge lies in avoiding overfitting and ensuring proper application of these techniques. While neural networks are inherently difficult to interpret and don’t provide explicit formulas, explainability tools offer a way to shed light on what the network is learning. This opens up big questions: What is a neural network learning? Why is it able to make this input-output map? And, going back to the storm topic, why does it work well for this storm, and not so well for this other storm? Addressing these questions could lead to significant advancements in both machine learning and physics.

…But I haven’t answered your question.

Black boxes or not black boxes?

I&I: It’s all right, and your response leads perfectly to one of the next questions. What you’ve just mentioned seems to relate mostly to supervised learning, correct? While this concern is often tied specifically to supervised learning, it also applies more broadly to machine learning as a whole. People frequently criticize machine learning, particularly neural networks, for being “black boxes.” However, you both have presented compelling arguments that challenge this notion. Let’s explore that further—what’s your perspective on this? How would you convince someone that neural networks aren’t necessarily black boxes?

Sabrina: I think that’s an important theme. I think it is important to convince people that we can create and use explainable models. It’s really important to understand – not just blindly trust the neural network or deep learning –  how the artificial intelligence model arrives at its conclusion. Why is it saying yes or no for the occurrence? And we can do it by using some explainability methods to understand, which are, for example, the relationship of the features involved in the response of our machine learning technique that can be explained. We have to investigate this process to understand why it is saying something correct or wrong. That’s a crucial point, and we must keep in mind that humans created artificial intelligence, so we have the means to have control of it and not become dependent on it.

Enrico: Another perspective to consider is the comparison between physics-based simulations and data-driven models. Before working in the field of machine learning, I worked on kinetic and particle-in-cell simulations. I see that after so many years, there is still a kind of misunderstanding that physics-based simulations have a level of supremacy over data-driven models because they’re physics-based, right? This is partly true, and for that reason, we understand what is going on: that is not really so! First, the information provided by simulations is inherently incomplete. Second, these simulations are often just as much of a “black box” as machine learning models. For example, in MHD simulations, there are numerous parameters that must be empirically derived, adjusted, or fine-tuned. These adjustments introduce their layer of opacity, making the simulation outcomes less straightforward than they appear. Moreover, just as you can overfit a machine learning model, you can also “overfit” a simulation to align with observations.

I&I: In this context, how well do you think machine learning is applied in solar physics and space weather? Do you believe researchers fully understand the methods they are using? What’s your opinion on the quality of the work being done? There seems to be a proliferation of papers, but as we’ve discussed, there may also be a lot of noise in the field. How do you see this affecting the progress and credibility of machine learning applications in these areas?

Enrico: I think the community has grown. And what I’ve noticed in the last maybe 10 years is a clear improvement in the quality of papers being published. A simple example is that some pitfalls or common errors that were once prevalent—such as how datasets are split for training, validation, and testing—are now better understood. And five or ten years ago, it was typical to do a random splitting in a time series. Now, we know that’s not the right way to do it. I see the community has learned from these mistakes, and today, if a reviewer sees a paper that uses random splitting, it’s likely to be sent back for corrections.

Sabrina: One can also see papers in which the approach seems to be simply testing a deep learning technique, presenting the results, and stopping there. It’s unclear how useful this type of analysis is, using one or another deep learning technique with different datasets. Sometimes, it can be unclear if it is working better because it uses a particular splitting. But there are certainly good and interesting papers on this topic.

Key aspects when applying ML

I&I: What are the key aspects that the community, particularly those writing papers and applying machine learning, should focus on? What is the most important thing they should be mindful of, or the biggest mistake to avoid?

Sabrina: I think that one of the most important things is the data set preparation. That’s very important because the network learns from the data that we present. One important thing is the splitting strategy, but now I think that in the papers I have seen, that’s clearer already. It’s extremely important, and the validation step is one of the main important phases in the data set. You don’t just train the neural network one time. That could be a lucky hit. You must make many splits, many training to assess the performance, to do some statistical robustness, maybe using also uncertainty quantification methods. It’s extremely important the assessment of the performance. I think this is crucial to make good work on this kind of technique, on this kind of data. Then we know that the data are noisy and complex, so also the data, the dataset preparation is very important, I think.

Enrico: I agree with everything Sabrina said. As an editor, I see many papers from different areas. Within the journal guidelines, we emphasise several things. First and foremost, we fully support the use of machine learning, but we need to make sure that the people are not just following the hype, right? The first thing should be to justify its application. Too often, papers jump straight into using deep learning with complex architectures, like 100 layers, without considering that the same problem could be effectively solved with something simpler, like linear regression. One needs to do it one step at a time. You need to justify why you’re going all the way to more complex problems, and I think this applies to every science problem. With machine learning, though, it’s particularly tempting to skip this step because of how accessible it has become; you can just use a few lines of code from an off-the-shelf library. But that convenience is a double-edged sword Then, as mentioned earlier, establishing a clear baseline is essential. You need to demonstrate that your model outperforms the baseline, explain how much better it is, and in what parameter space. One thing I would like to emphasise is the reproducibility of the results. I think the community is starting to understand that, when you publish, you’re almost obliged to share the data and the software. Without this transparency, results can’t be easily verified or built upon, which limits their value. Sharing everything, data, code, and well-documented software, is essential for fostering a collaborative environment where others can improve your work, cite your paper, and drive progress. This is a challenge for many physicists, myself included since we’re not typically trained in software development. For instance, some journals, like those published by AGU, enforce strict policies about sharing data and software.

I&I: That’s a broader issue within the community—whether it’s solar physics, space weather, or physics in general. This challenge isn’t limited to machine learning codes and similar areas. Ideally, it should be addressed comprehensively, but unfortunately, that’s not what we’re seeing in practice.

Enrico: It was a big problem already, say, in the 90s or early 2000s, when the cutting-edge physics was done with huge computational simulations. And people were very reluctant to share their code because, you know, my group has been working for five years building this code. I’m not going to give it to you.

I&I: It’s still happening.

Enrico: But maybe less so because I think people realize that if I share my code, people are going to collaborate with me and ask me. So, it’s kind of a win-win situation most of the time. But yes, machine learning is not very different.

Except that maybe writing machine learning codes is easier than writing thousands and thousands of lines of code for large simulations.

Shall we change the skeptic’s views on ML?

I&I: I think you’ve given us a great introduction to the next question, which ties into these longstanding habits. Many scientists often express skepticism about machine learning. When these techniques first started being applied—maybe around 10 years ago—there was a lot of dismissal and doubt. What do you think we can do to help shift this perspective and build trust in results obtained through machine learning?

Enrico: Perhaps an unfiltered answer is that I don’t really care anymore. It’s not that I haven’t tried. If you spoke with me maybe five years ago, I was trying hard to convince people. And if you saw some of my talks at that time, I was kind of almost trying to sell these techniques. I reached the point where I realized it’s not my responsibility to convince anyone. I mean, you’re exposed to various approaches, and then it’s up to each individual to evaluate and decide what works and what doesn’t. You can’t do someone else’s homework. What I’ve also come to realize is that this is mostly a generational issue. I don’t find it very hard to convince an early career or a student. I always tell them it’s almost a necessity for them to learn some machine learning, to be fluent to some extent in machine learning tools. It’s like when we were students you needed to know what a Fourier transform is because it’s in your vocabulary. Now you need to know at least the basics of how a neural network works. It’s not expected that you become a super expert in machine learning or that you can code and so forth, but to know the basics. I think at some point it will be part of their vocabulary. So, I think it’s not hard to convince young people.

Sabrina: I would add a little bit more to this topic. Over the last five years, the Department of Mathematics at my university introduced many courses on mathematics in machine learning. I think that the new generation is growing in a community in which we need to understand machine learning and use it in a good way. Another point is that, for example, the parallel session on artificial intelligence at the ESWW has only been around for a few years. In past editions, there were just a few community-driven sessions focused on machine learning. Now, there is a dedicated full session on this topic.

I&I: That tells us something. I think most of the conferences today are like that, and whenever you go to a conference, there’s always a machine learning/AI.

Enrico: I think we’re in a growth phase. At some point, if we keep the machine learning session, I think too many presentations/works will end up in that session. I find it would be more natural to have, for example, a solar flare session where 80% of the papers are related to machine learning or a CME session with a similar pattern. This is actually what we’ve started to see at the AGU annual meeting. At AGU, for about eight years, I’ve been convening a session called Machine Learning for Space Weather. And this is exactly what we saw. At the beginning, it was a small session. Then, I think two years ago, we received 80 abstracts and we got four oral session slots. That was the peak. This year we are back to one session with maybe 20 or 30 abstracts. So, it goes back to what it was at the beginning. One of the reasons is that now there are many different machine learning sessions.

Challenges in the machine learning field within the scientific community 

I&I: We have another question, this time related to your career path in machine learning and your personal experiences over time. What were some of the major challenges or setbacks you faced in your machine learning research, and how did you manage to overcome them?

Sabrina: I have an example from the space weather prediction. Extreme space weather events are rare events, which makes their prediction challenging. One way to tackle the problem is to optimise the process of the neural network, of the deep learning or machine learning technique and to exploit or develop a good loss function that accounts for the scarcity of positive samples. The fact that you have few samples related to these extreme events it’s a challenging point. Another critical aspect is managing large datasets. The pre-processing step is important for creating good datasets that can be efficiently used for training machine learning models.

I&I: Enrico, would you like to continue?

Enrico: Yes, I’m going to turn it a bit more political. One challenge I find, but not necessarily as a barrier, is that funding agencies are not ready for the full AI potential. This is something I’ve noticed from my experience in both Europe and the US.

I&I: Do you talk about now or some years before?

Enrico: Even now, yes. What is still happening is that an AI or machine learning proposal has a higher burden than a physics-based proposal. The typical job of a reviewer is to be critical in evaluating and identifying the weaknesses of the proposals. However, you’d never see a comment questioning whether MHD (magnetohydrodynamics) itself works. At this point, it’s taken as a given. But with AI proposals, it’s common to see critiques like, “You didn’t specify the neural network architecture”. The problem is manifold. One is that the reviewers are not knowledgeable enough, and this is a community problem, right? We don’t have enough knowledgeable people to assess these proposals properly. Another problem is that the agencies themselves are not in the position yet to open calls specifically for AI or machine learning, which I think should be done. The point is that you want to have a machine learning proposal competing against another machine learning proposal. Otherwise, it’s very hard to judge whether the results of an ML approach are going to be more promising when compared with a classical approach.

Another thing I wanted to mention, in line with the discussion about the funding agencies, is that the agencies are not ready for this revolution in AI, which started about 20 years ago and is still happening. Most of the breakthroughs in AI have not been funded by public money. All the technical improvements (e.g., GoogleNet, dropouts, etc.) came with private money. Even now, in the field of weather prediction, which we always see as our big sister. Numerical weather prediction has become very accurate and has been continuously improving over the last 50 years. But in the last five years, I would say, again, Google, Microsoft, and NVIDIA have developed AI weather prediction models which are comparable with the classical ones. Weather prediction is something that affects the entire planet and all humanity, but AI models are paid for by private companies. One can think that it is still fine because we have our classical, community-based models. But right now, we are at a point where only a few companies can develop this kind of AI models. These are huge models which cost hundreds of millions, maybe billions of dollars only to train. In my view, this could become problematic in the future. We don’t want a few IT companies to be in possession of that data, that knowledge, that technology. And the only way to avoid that is to invest more public money and allow academia to be competitive with the private sector. It’s probably not going to ever happen, but it’s almost an ethical issue at this point. It’s kind of divergent from space weather, but returning to space physics, I believe funding agencies are significantly lagging behind in this area and need to catch up.

I&I: You both highlighted physics-informed neural networks as a groundbreaking development, and it seems that more people are starting to recognize their value. Interestingly, even some individuals who are typically skeptical about machine learning tend to appreciate physics-informed neural networks. This might be because these networks often serve as elegant parameterizations of physical spaces, like neural fields. Do you think, in a sense, this represents a kind of full circle? That we’ve ventured into AI, but with physics-informed neural networks, we’re perhaps moving slightly away from traditional AI?

Enrico: It’s a tough question. I don’t think we are leaving AI because, as I said earlier, it’s a new technology. The crucial point is, does that allow you to study or to understand things that you wouldn’t be able to understand without that technology? So, I don’t know if it’s a full circle.

Going back to the idea of a fully parametrised MHD, there was some interest, though not much recent work, in the idea of building a complete surrogate model for MHD simulations. In our space weather case, take WSA (Wang-Sheely-Arge) – Enlil, a 3D global MHD simulation of solar wind propagation; it’s computationally expensive. If you look at the output of the simulation, even just the movies, it’s effectively a non-turbulent fluid simulation, so you can imagine that a neural network will learn this smooth dynamics. People agree we can build a surrogate, but if you talk to older people, they will argue the neural network cannot be a complete surrogate because there’s physics in the MHD equation. That’s where the bridge comes in, by incorporating physics-informed methods to enforce the underlying equations. On the other hand, if you think about how, you solve an MHD equation, in fact, any set of partial differential equations, you end up doing a very complicated code that, at the end of the day, most of the time, does linear operations on elementary functions. You take the field here, you add it to the electric field there and the velocity field, etc, and that’s exactly what a neural network does, right? That’s what a neural network is built for: to make elementary functions and concatenation. As I see it, from a theoretical, algorithmic standpoint, there’s no reason why a neural network shouldn’t learn exactly the MHD equations, right? If the data is consistent with the MHD equation, that’s the point. If it’s not consistent, it’s going to learn whatever physics is driving the data.

Sabrina: Yes, I agree with Enrico. But I think the idea is that, at the starting point, we use just the physics. Then there is just data-driven, so maybe it would be good to use the knowledge of physics in some way in the machine learning technique. A very simple example, when you consider a solar image reconstruction problem, you know that the solution is positive, so you need to include the constraint that the solution is positive in your optimization process

Enrico: Another thing which I think is very exciting, tangential to physics… when we do physics or science, at the end of the day, we build algorithms to solve a given problem, to discretise equations. I think a field which is already happening but it’s going to explode in the future it’s the discovery of algorithms. That, to me, is just mind-blowing, right? I mean, examples like AlphaGo and DeepMind; the inventor of the AlphaGo algorithm got the Nobel Prize for a reason. There was this paper where they discovered a new algorithm (AlphaTensor) for matrix multiplication, which I didn’t even know was a challenge, right? If you do it numerically, there are different ways to reach the same result, and until recently, the best algorithm has been out there for about 50 years. The idea is that we have a collective knowledge that humanity has built over generations, like for the game of Go or for how to multiply matrices, and then you just feed the problem into a neural network, and that finds a better algorithm than we can ever imagine. To me, this represents a revolution. As some have said, machine learning and AI will be the fourth pillar of the scientific revolution. Alongside theory, experimentation, and computation, AI will fundamentally reshape how we conduct science.

I&I: I think it’s a good sentence to stop with. AI will be the fourth pillar of the scientific revolution.

Thank you very much to both of you!

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Ivan Milic is a solar physics scientist at the Institute for Solar Physics(KIS) and a lecturer at the Faculty of Physics in Freiburg, Germany
(https://www.leibniz-kis.de/de/lehre/dr-ivan-milic/)

Iulia Chifu is a project scientist at the Institute for Astrophysics and Geophysics, University of Goettingen, Germany
(https://cgauss-psp.astro.physik.uni-goettingen.de/pro_members.php)