You're listening to Data Skeptic: Graphs and Networks, the podcast exploring how the graph data structure has an impact in science, industry, and elsewhere. Welcome to another installment of Data Skeptic: Graphs and Networks. Today, the core idea we're talking about is brass paradox. Asaf, is this a popular topic in network science? Are you covering brass paradox in your course?

Well, it's more of a games theory, right, idea. You know, it's very interesting and thought-provoking even, but I don't think we have time for it. But maybe next time. Well, Benjamin will define it best, but I'll give it a stab. Brass's paradox is the idea that, let's talk about in terms of Rhodes.

You have road systems and you think adding a new road would only make it better. That's another option people could take. Maybe it could be a useless road, but it shouldn't make it worse. It just seems intuitive. Why would adding something make the network worse? But actually it does. There are edges that can be added that make the overall topology of a street network less efficient and slows everybody down overall.

You know, I'm not a traffic or a power grid expert like our guest, but you can find it even in sometimes in social networks. Usually organizational network analysts will say that your organization will need more connections. You don't want people kept in silos and stuff.

But still, too many connections can cause a waste of time and so on, too much bureaucracy. But it's really very unintuitive and gives a really hard time to people who are researching this subject. I'm glad you made the analogy to organizational analysis. I hadn't considered it. But as I think about where Brass' paradox could come up there...

Um, there's like a type of employee I've had from time to time, an analyst who's very bright, very good at getting the data, but also very good at over promising some things to people in miscellaneous departments. And sometimes I don't want to link, you know, somebody with an MBA to, uh, the right analyst who will just spend their time chasing tails, making reports and whatnot. So we want to be a connected group, but have optimized connections.

Usually it's the other way around, right? People don't use their connections or don't initiate connections enough. Yes. I guess most of the people in charge don't like their employees making too many connections. You want to run a tight ship usually. And that's a problem. In general, I agree.

I think it's sort of natural once you say it like that. It seems like fortune cookie wisdom. But I do believe in the engineering world there are times when two groups should only interact via a specification. Like you build to the connector, I'll build to the other connector, and they have to plug in exactly as said. And we don't want too much creativity. You solve your problems, I'll solve mine, and we'll connect in a very rigorous standardized way. Okay, Boomer. Okay.

But yeah, Brass's Paradox, as Benjamin will talk about, they apply and are most interested in Brass's Paradox in the power grid world.

Do you think this could be a universal property that one could find in all networks? What do you mean? That adding an additional edge would somehow negatively affect the overall structure of the network. It's interesting you say that because we had a talking class about closeness and between the centrality, which is more, let's say, robust. And you can say that closeness is...

It's a centrality measure that has its problems. When I say closeness, I mean how close are the nodes to other nodes in the network. Between centrality, I mean which node do most of the shortest path in the network go through. The problem with a shortcut in the network, it makes between centrality less robust because

Each shortcut makes the network smaller and changes the topology and sometimes the dynamics on the network, making between us maybe less robust than the closeness centrality. I am Benjamin Schäfer. I am an assistant professor at the Karlsruhe Institute of Technology, KIT, in Karlsruhe, Germany.

I joined about three years ago and I started to build up a group of researchers, interdisciplinary at the interface of, broadly speaking, AI, artificial intelligence for energy systems. Since two years now, I'm an assistant professor at the informatics faculty or KIT department for informatics, it's called. So I'm teaching, I'm researching, and I'm educating the next generation of scientists now on my team. Very exciting.

What are some of the challenges in energy systems that AI can help with?

So there's actually a great review by some colleagues, including, for example, Priya Danti and people from Mila, where they summed up lots of potential for AI and machine learning for climate change in general and for the energy system specifically. One of the things to understand is that we need to keep balance of generation and consumption at all times.

This means that we go all the way from generating electricity, for example, with maybe new PV materials, over transmission, potentially optimizing the layout of networks, to storing electricity in the grid, to demand management. So all of this AI can help you with optimization, with forecasts, with designing new materials. So there are plenty of opportunities.

So energy systems are not new. We've had them for decades, maybe a century, depending on how you want to count it. Surely some engineers have figured out a few things along the way. What's the opportunity? How much efficiency can we find in the future?

Yeah, I would say the engineers did an amazing job, right? So I don't know how public this was in the US or the rest of the world, but in Europe we had quite a stir up, let's say, because of the Spanish blackout, the whole blackout of the Iberian Peninsula last week, where Spain and Portugal lost power for the entire countries and millions of people were without electricity for hours or up to days.

This is a very, very rare event, and that's why we're talking about it. So this in itself stresses that supply of electricity is so stable and so reliable that we typically don't have to worry about it.

The system is undergoing rapid change. So previously we built this up slowly. So we electrified consumption and we built up cables, we built up generation, we increased our demand. But more and more, we are now replacing some of these old systems. So we replace headlight.

heavy machines with not large inertia. So think of something like a huge gas turbine rotating in the system. And we're replacing this with photovoltaic PV systems or wind turbines, battery cells to buffer some of the storage.

Right. So this just means that we are rapidly changing how the system operates on the generation side, while on the same time on the demand side, increasing the volatility and also the mobility. Right. So your house typically doesn't move. At least we don't have mobile homes that much in Europe. So.

Your house stays there, so you know where the consumption is going to hit. But if you introduce lots of electric vehicles and lots of charging stations, then suddenly quite a respectable share of your demand is moving and can suddenly appear somewhere in the grid to some extent unpredictably. You could say, obviously, there are patterns, right? So we have both this paradigm change on the generation side and on the demand side in an unprecedented speed.

So this then opens up opportunities from a data perspective to say, okay, let's investigate this. Let's see, can we understand this better? Can we support this somehow? Can we, again, on the material side, drive innovation? Can we optimize the system for the control for the network operation, etc.?

Well, upgrades and maintenance are going to be a big part of that, but probably also the network needs to grow. If we anticipate there's going to be a bunch of new EVs, let's add links to this network and just invest in it. And that's how we'll get there. Is it as simple as that? Or could it be problematic depending on how we grow it?

Yes. So, I mean, if you go from a kind of classical engineering perspective, what you think of is so-called N minus one criteria, right? So you're thinking of the system and you're imagining one component of your system fails, right? So then instead of N components, you're left with N minus one components. So this could be a transmission line failing, a generator failing, something like this. What is typically not considered is something like an N plus one contingency where you add something, right? So obviously, why would this be bad to add something?

And intuitively, you would say, okay, adding anything makes a lot of sense. But actually, in one of our research articles, we found that this is not always the case in the energy system. So adding a component, adding new lines could actually create at least some cases where the system performs less optimal than before.

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visit techgradcertificates.com to learn more and apply before the August 1st deadline at techgradcertificates.com. So this seems shocking almost. Is this a known result or a recent discovery? Let's say for the energy system, I would say that this is somewhat recent in how we are understanding this. In general, it's not super novel.

So this is something that goes back to the 60s. So I'm going to get you on a short time travel. Imagine there was a mathematician called Dietrich Bress, and he actually investigated Bress paradox. So this is something that was named after him, after the fact, in traffic systems.

You just imagine a system where you have a couple of streets and then someone comes up with the idea to build a new shortcut to connect some points in your street network. What he showed back then mathematically is that you can create situations where this new street actually increases the travel time for everyone in the network.

So this seems quite unintuitive. So to give you some idea of how this works is, roughly speaking, you have shortcuts that are maybe independent on the load of the traffic. So you just have roads that more or less have infinite capacity, but maybe they are long. So maybe you have to take quite a bit of detour to go through them. And then there are streets that don't have as much capacity. So the more cars are on there, the slower you're getting.

If you now start to connect those capacity sensitive roads with each other, then suddenly you mess up everything because people will use these traffic lanes that are heavily populated.

Let's say you're starting somewhere, right? So you start, then you can go via A or via B, and then you have a goal where you want to end, right? Everyone assumes the same starting and same final destination. Let's call this top and bottom road for now. And what you're doing is you're starting on your top road, and initially you're just taking the road that has infinite capacity. So

You're traveling a fixed speed and then you're continuing on the road that has a traffic sensitive capacity. So the more traffic there is, the slower you're getting. But not everyone takes this route, right? Because half the people will take the top road and half the people will take the bottom road.

Now, if you tune the parameters correctly, then what you can achieve is that even if everyone takes one of those roads, these traffic sensitive parts will still be faster than the traffic insensitive ones. So let's say you start on the top road. First, you take, let's say, 12 minutes on the insensitive part. And on the second part, you take your traffic portion, let's say 50%. So let's say five minutes. So you take a total of 17 minutes.

And on the bottom, we just invert this. So you first take five minutes, and then you take 12 minutes. So everyone splits up evenly. You have 50% traffic top, 50% traffic bottom. Now, if you introduce a shortcut in between those two stops, so now what you can do is you can start in the bottom, take the five-minute trip,

where 50% of the people go. Then you take the shortcut, which for simplicity we assume is infinitely fast, so it takes you no time. And then you take another five minutes. So instead of 17 minutes, now you're taking 10 minutes. That sounds great, right?

Unfortunately, everyone will get to know this. So what happens is that everyone switches to this new road. So everyone now takes 10 minutes, gets kind of stuck in the traffic jam on the kind of efficient short route, which is now completely overcrowded, then takes the new shortcut and then takes another 10 minutes. So everyone in this system reached a new Nash equilibrium, right? So no one has an advantage of changing.

but everyone is worse off, right? So the only thing that would really help the system is that everyone commonly agrees that no one takes the shortcut.

And obviously, in individualistic communities, this might be a bit difficult to really enforce. So in this system, you introduce the shortcut in your street system. Okay, it's a bit arbitrary and a bit specific of how I define these parameters. But you introduce the shortcut and everyone is worse off than before.

And this was actually empirically observed in Stuttgart and in New York where street closures now, right? So imagine you start with this suboptimal system. Someone closes this shortcut. Everyone now splits up evenly between this top and bottom road. And we're like, wow, I'm faster at work than we were almost before. I'm no longer stuck in this stupid traffic jam. And I don't want to use this weird detour anyways. But now you suddenly use the part of the road that was always jammed plus maybe a bit of a detour. But overall, you're still faster, right?

So this is not something purely theoretical or hypothetical. And now you could think, okay, is this unique to traffic? And it turns out it's not, right? So this is, again, something that was researched more and more in the past years, that this is a general flow network phenomenon, right? So that if you introduce additional flows in the network, so shortcuts where flow can go, then this is something that can happen in plant networks, can happen in

in traffic networks, as we said, and could also happen in, for example, the electricity networks. So this is something which would be an approximation of a just simple flow network. Well, I was going to ask you about empirical evidence and how well theory matches. You'd mentioned like New York and Stuttgart as these examples. So I can see how there's like an intuitive agreement. How well does theory describe those circumstances? Could we have like predicted the result in advance, those sorts of things?

Okay, I have to admit, I'm not a traffic expert. Sure, sure. With these, I'm not sure you could model them one-to-one as they exactly happen. I mean, the main thing I'm taking advantage of here is like the general principle to say, okay, you have a network, you kind of improve it by adding a new link and suddenly actually your performance decreases, right? So that's how I would generally define brass paradox in like,

adding capacity but decreasing performance. Like the, let's say, strictly historic press paradox is you add a new line and now you have larger traffic time or larger load on certain roads. What I try to describe, right, this idea of you have

roads that are completely insensitive, how many cars there are and other roads that are directly proportional in terms of travel time to the amount of cars that go through them. This is super simplistic. And I'm quite sure that traffic planners don't operate with exactly these models. So I would be cautious to say this is exactly what they saw in Stuttgart and New York. They did saw that traffic jams decreased and travel times increased.

Well, traffic's complicated in that every car has a human being in it, or at least for now it does. They're a complex person with a lot of variants and things like that versus electrons, which are going to do what electrons do, which presumably follow the rules as best we know them of physics. Does that make the problem more solvable in some way?

So it depends kind of on what you look at, right? So in, again, I hinted at this already in DC nets, we have effectively just flow networks. So similar to if you just had like a water network or kind of a stupid traffic network or, all right. So if, if people just would follow like the, the past of least resistance effectively, right.

This is what electrons do. They just are driven by resistance, by voltage or potential differences. But in general, the setting I described of, let's say, capacity sensitive or how much flow we have through a

part of the network, this translates more or less one-to-one to the electricity system. So it's not more or not less complicated at that point. When it gets more complicated is if we on the traffic sides would include more an agent-based modeling, which I did not discuss. And again, I'm not really an expert on that. And on the electricity side, it gets more complicated as soon as we introduce alternating currents.

There's some empirical examples in the traffic domain. What about in power systems? Have we seen the effects of brass paradox in the real world?

As far as I understand, no one has like, as in, let's say the Spanish blackout, for example, no one has said, okay, this was because of an additional line that was built. So this is not something that happened empirically on that scale where we could just say, oh, someone had a construction going on and suddenly the traffic was faster. So on that scale, I don't think it happened yet. So this is why we sat down.

in our research team, and this is actually research that dates back like 10 years ago, where we started it, and it just took a long time to get all of the results finished. One thing we thought of is, okay, let's actually try at least laboratory scale experiment of a power grid to prove that this effect, which we are seeing theoretically, actually also happens in the real world. So on a lab scale,

So thinking of more of a kilowatt scale generators. So not huge generators, but still roughly the size of my table, of my desk I'm sitting at here. So that's kind of the size of the synchronous machine we're working with.

There we build a small network. So I sketched you this idea of kind of your starting node. Then you go via either the top or the bottom road with kind of an intermediate stop. And then you have your final destination. So this would be kind of a four node network effectively.

And we did exactly a four node network as well for the electricity grid in the experiment. There we could see that this happens as well. So we didn't really see a blackout in the system. We couldn't drive the machines to that extent. Also, the engineers were kind of happy that we didn't crash the system.

Right, so disclaimer, I initially studied physics, now I'm a computer science professor, so not super on the hardware side, let's say. What we did see, however, was that you start a network and you have one line that is already carrying the most current in the network, and then you introduce...

either an additional line or upgrade a capacity of an existing line. And then what happens is that you also increase the loading on another line in the network, right? So think of it as you're having kind of two lines in parallel. You're upgrading the left lane, let's say, but the right lane also gets an increased current, but it was never upgraded, right? So if this was already operating close to capacity, then this right lane would also at some point potentially decrease

overload, have to disconnect, etc. So maybe no instances of blackouts as a result of brass paradox, but could something more insidious be going on that these power systems have had some well-intentioned links added that we could now detect are actually making the system less efficient overall?

What I'm assuming in this modeling for the power grid is also quite simplistic. So I'm assuming that this is more or less stupid copper, you could say. So as for the traffic brass paradox, we said, okay, let's assume that everyone just uses the shortest road for themselves and that we introduced this shortcut that is instantaneous and that we have these roads that scale exactly with a number of participants.

In the electricity system, you would assume something like, okay, if we change the complex resistance in general for the AC grid, then you increase, for example, the current over a certain line. What you do have in reality is that you do have these changes in power flow over these lines, but you also have phase shifts that you can put on the given node.

To give you one example where this started to happen is that in Germany, we build up wind power capacity at the north of Germany. And then we have actually most of our consumers in the south or some quite heavy consumers, let's say, in the south. But we didn't reinforce the grid enough to transport all of this electricity from the north to the south.

So what happens now is that you take a detour, right? So some of this power will flow, for example, via our neighbor to the east, which would be Poland and Czech Republic would flow from the north of Germany via these neighboring countries down to the south of Germany. But these neighbors say, okay, now you're using our electricity grid. We don't necessarily like this. So what they can do is they can actually change the phaser on their side, meaning that they don't

transmit and import as much electricity from Germany. Depending on how large the shift is will determine how much power we transmit from A to B. So I get that there's some aspects of this that are maybe fuzzy in terms of a precise solution, but if you had the appropriate data set, you knew every link in the graph and the exact copper, what material it was, all of this, is there an algorithm that could identify a brass paradox?

One point I wanted to stress before I answer your question is actually that if you just have more lines in the system, this just gives you more options. Just let's say by adding new lines, you're not automatically making the system worse unless you're assuming it's stupid copper and no one is operating or intervening. And in reality, people are obviously smart and we have transmission system operators like, for example, Red Electrica in Spain, who then restore the system, who monitor the system constantly.

Okay, so do we have a way to optimize this? And actually, from an engineering perspective, this is kind of what we started this podcast with. Isn't this solved? And to some extent, we can say, yes, it is already solved. So this is a well-known optimization problem.

optimal power flow, where you think of line constraints, you think of generator constraints, you optimize the system in a way that economically and also technically you don't violate anything and you find an optimal solution so that you pay the least and everything works smoothly. The caveat with that is, is that it tends to be expensive, right?

Right. So I mentioned earlier that we have n minus one stable grids. So n minus one means one component can fail. Now you think, OK, if I have 10,000, maybe 100,000 or more components that are modeling in my grid because I have lots of different transmission lines, then I have, let's say, 10 to the five, 10 to the six cases for n minus one. If I now want to do n minus two, that's getting quite expensive. Right. So if any two components fail,

Then I'm suddenly looking at at least 10 to the 10 or 10 to the 12, depending on whether I start with 10,000 or 100,000. So this explodes quite heavily. So this is why in current standards set by the respective bodies on the European level, on the American level, on the international level by EEE, they don't consider N-2 stability.

because it would just cost a lot of compute to always update this right and then you optimize a certain state in the grid based on a certain consumption and generation pattern and this again changes over time right you know okay people will get home at some point they will maybe start to

cook, people will charge their EVs, maybe the sun will set, our PV will produce less, or maybe we have to update our wind forecast from what we knew two hours ago, right? So you have to always recompute, recompute based on the current state of the system. And while doing this, to find one optimal solution, which you're operating right now, you also have to make sure that it's N minus one stable. So you have to consider a failure of every single component.

This is where I would say our main contribution lies, to say we get an intuitive understanding for what can happen in these systems when you add a line that you do have this phenomenon of, oh, we introduced this shortcut, now we kind of have a traffic jam in terms of the power system, right? So we have an overloaded line or a more heavily loaded line than we had before, based on this understanding of brass paradox in general.

That being the main contribution that you're figuring out how to introduce this shortcut, if we could stay with algorithms for a moment, is that a hard problem or could you describe the procedure for how you find that key link that'll do that? Imagine you have like your four node system, two by two grid. So I have two at the bottom, two at the top.

Let's assume that we have power transmitting from left bottom to left top, right? So we just have a power flow this direction. And if I now upgrade this line, what will happen is we might transmit a bit more power this way.

But if we do that, we know from Kirchhoff's laws that actually the total current incoming and outgoing from each node in the network has to sum to zero. So you have to make sure that everything that goes in also goes out at some point, or at least has to be balanced with the consumption at the node.

If you increase the flow on this one line on your left of the network, then what happens is you decrease how much flow is coming from top right to top left. You're increasing on one end and you're decreasing on the other. So effectively what you can think of

This is a cycle flow that we are introducing. So the cycle starts on the left. We go from bottom left to top left and then we continue to top right. We go continue to bottom right and we continue to bottom left again. And depending on which direction the flow was oriented before, it will either increase or decrease how much flow was going on that line.

So let's assume in my example that the top left is a consumer and the bottom left is a generator. So now we are transporting more electricity from this generator to the consumer. But before this consumer was getting something from the right hand side of the grid.

The next link after that is more interesting. So from the top right to the bottom right, if you again assume that the top is a generator that was also supplying this consumer on the left, it's no longer needed as much. But it still generates as much power. So what happens, it will export more power, transmit more power to our bottom right node. So effectively...

You overload, you don't necessarily overload, but you increase the load, let's say, on this one line on the right, connecting a generator and a consumer that were already connected, that were doing fine, but now they are more heavily loaded. And this is exactly the intuition that we then use to

code predictor where we went through each of the potential cycles in the grid and we identified, okay, which of those cycles would actually align with a heavily loaded line. If this new cycle flow is in the same direction as the flow that is already on the line, it increases. If it's opposite to the flow, it decreases. And decreasing is fine, right? Especially if you decrease the load on one of the most heavily loaded lines, that's

That's great. But if you increase the load on some of your heavily loaded lines, maybe not so great. I think the point we are making here is this intuitive understanding that you see, okay, with these cycle flows, you get this quite easily. This is kind of the elementary part where I, maybe starting from a physics background, just wanted to prove, okay, in this very simple setting, you see this experimentally. In the theoretical part, you see this and we can explain it with the cycles.

In the more complex systems, or we ran this for like the full German transmission system, you again see these effects and the same explanations hold. And then you no longer have your four node, four edge system where you're thinking, okay, obviously if I increase capacity there, it increases load there. But you have your hundreds of node system. And then you're like, okay, if I change something here, somewhere, like several kilometers away, something can happen that

increases load in the system. And it's still more or less the same explanation. So if I hadn't have read your paper, I might have thought...

that these kinds of things were local effects, that maybe the couple of my neighbors, maybe K equals two nearest neighbors kind of thing is how it's going to distribute. What's the potential for a small change in one area to have unpredictable or, I don't know if it has to be unpredictable, but strong effects in a seemingly different part of the network? Yeah, I wouldn't say it's very likely that it's like hundreds or thousands of kilometers away.

Most likely, it's still going to be somewhat local, somewhere in the tens to maybe 100 kilometers, right? But this still might be

somewhat surprising in that, okay, it's not exactly my next link, right? So if you're thinking of, okay, I have my maybe new build upgraded power plant, I need to connect this with a stronger link to the network, then using the traffic example as an intuition, you have your super efficient highway, right? This was the new shortcut we introduced.

But the roads that actually connected you to this highway, commuter roads that were already in use, and now everyone wants to commute to the super new highway to then fast travel somewhere else and then get off the highway to the part where they're working. Unfortunately, these supplementary supporting roads were not upgraded.

in our traffic example. And the same happens in the power system. If you build like one strong additional line that is maybe shoring up one weakness in the grid, you might actually still have the problem that the line's leading towards both ends of this line, but maybe not even exactly at the point of,

of each of those nodes, but maybe one or two hops away that these lines that actually supply the power from the rest of the grid there are distributed, that these then get quite heavily loaded. Well, we have to do something with upgrading the grid. Could insights like these help with predicting the best way to optimize your maintenance? So I think that we are hopefully contributing in a couple of ways, right? So one is, I think maintenance makes sense, right? So you have to think more or less from a system perspective.

which means that if I shut down one line, I have to think of, okay, what does that do for my whole network state? If I upgrade lines, I also have to think of, okay, what does that mean if I upgrade this one line? Which additional lines do I need?

What happens if I'm in the process of building new lines, but I didn't finish everything in time? So suppose there is a delay on like two projects out of your five projects you were planning. Okay, maybe you can't even start to operate these other three lines really before you finish the remaining two. So maybe all five are actually important for your full system upgrade to work.

So I think your paper conveys the intuition that I would imagine anyone in the industry would be able to kind of get the idea. Then if I was in that person's shoes, my question next is, well, how do I tie this into my process? Like a software engineer has unit tests and things like that. How can I systematize an analysis that helps me not be taken by surprise by the paradox?

From an N plus one perspective, so if you build a new line, you won't necessarily be taken by surprise because you would just run all of the N plus one scenarios. And then you would identify the ones that are best for you and the ones that actually decrease performance, you would just discard anyways. You won't really look at them. And this is what we did here. We really looked at those cases that your brute force approach would just throw away to begin with.

We do have this cycle flow approach that is at least the basis of an algorithm that you could implement. And I don't necessarily think it's at the moment

most efficient in terms of runtime, but it is something that would give you a quite good intuition to then run more detailed analysis. So this would be kind of a cascade of algorithms to say, okay, let's start with something that is fast to identify some cases we have to look more in detail in.

And I don't know if you have any insight into this, but to what degree has industry, I guess, taken this intuition and done some of those things you've just laid out? So from my experience, the industry moves quite slowly in what they implement on the operating rooms. And I think to some extent, rightfully so. So things have to be proven.

As far as I know, software that we shoot into the space typically is like several years to decades outdated in modern devices, but it's tested to an extent that we can hope and actually so far see in like some of the satellites that have been operating for decades.

So which means that what we can achieve at the moment is discuss with the R&D departments of these operators and see how they are picking up this idea and how they then can translate this into tools that would be used by their operating colleagues. I think...

Very interesting opportunity. I hope those sorts of things move forward. They're such big projects, it seems almost certain that it's worth the effort, right? I do think so. As I said, we are facing quite some challenges in the power system from...

rebuilding this, going carbon neutral, and also, even if you don't like this idea of reducing CO2 emissions, just being energy independent. I think this is something that was a huge narrative in Europe when the Ukraine-Russia war started, that we are importing so much gas from Russia, but if you change your electricity system to rely much more on wind and solar power, then you're not as dependent on energy imports anymore.

So this is, I think, a very important piece of getting a certain independence as well. But this means a certain restructuring of the network, of the power system in general, including transmission, distribution lines, etc. Well, Benjamin, I know this is just one facet of your research. Could you share some details on what else you're up to? Some of this research for the brass paradox has been going on for years. And since then, I...

Started a group and I have so many more research interests I can finally pursue with so many people supporting me. So that's amazing. We're here at the Data Skeptic podcast. So obviously we have also more data available in power systems. And one thing I wondered is, can we use that data to train machine learning models that, for example, forecast your electricity demand, right? So then to optimize your network state.

And what I'm really emphasizing in this setting is actually understandable or interpretability of these forecasts, providing an intuition to an operator so that they could, for example, include something like breast paradox or inverse breast paradox in the operation. Similarly, actually for our forecasts or classifications,

We are also following a similar line of reasoning to say, okay, let's try to identify not only how generation might look like, but also why our algorithms predict this so that then we hopefully get one step closer to implementing this with operators so that they trust what we provide them with. So that they say, okay, this makes sense to me. Now I'm acting based on the suggestion of.

of this machine learning algorithm instead of just relying on a black box. Well, if listeners dig into the archives, we've done a number of episodes on SHAP and Shapley values, which is but of one approach in interpretability. Are you doing something similar or quite different?

Actually, we started a lot working with Shep and Shepley values. One issue we ran into quite recently is the correlations in, I think, in general and variables. So if you think of something like the time of the day and the solar generation, right? So obviously these are features that are related if you put them into your system. And if you now assume I have a coalition of players and they are somewhat independent.

I could just exchange one without changing the other, then this doesn't make sense. We looked into, let's say, some of the more advanced Shep algorithms.

which are, let's say, somewhat newer than what happened in 2018, I think, when Lundberg bring this out, the SHAP algorithms. So this is, I think, one of the most promising algorithms, I agree. I think SHAP is amazing, but we still have to also modify it in a way that works with the real data we are encountering.

Well, Benjamin, what's next for you? I think one of the things you already teased that is like

transferring some of our insights into industry. And I've been a bit more active on that front, teaming up with companies like on the TSO level, on the transmission system operators, people who run the transmission grid, highest voltage grids. So all four TSOs we have in Germany, for example, are part of a recent research project we started where we're using graph neural networks. So maybe we'll come talk about

this in a future episode once we have some results to share. I think this is like a quite fascinating area to say, okay, how can we combine again this data-driven approach with insights and translate this to industry and making things more interpretable and pushing them towards more applicability is something that I think is on the horizon for the next years.

Is there anywhere listeners can follow you online? I have to say I'm not super active anymore on Twitter slash X, but they can for sure check out my Twitter feed, can check out my LinkedIn feed. And I'm happy to share like papers or respond to DMs or emails if they like that. Sounds good. We'll put some links in the show notes for people to follow up. Thank you so much for taking the time to come on and share your work. Thank you, Carl, for inviting me.