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AI finds formula on how to predict monster waves

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AI finds formula on how to predict monster waves


Long considered myth, freakishly large rogue waves are very real and can split apart ships and even damage oil rigs. Using 700 years’ worth of wave data from more than a billion waves, scientists at the University of Copenhagen and University of Victoria have used artificial intelligence to find a formula for how to predict the occurrence of these maritime monsters. The new knowledge can make shipping safer.

Stories about monster waves, called rogue waves, have been the lore of sailors for centuries. But when a 26-metre-high rogue wave slammed into the Norwegian oil platform Draupner in 1995, digital instruments were there to capture and measure the North Sea monster. It was the first time that a rogue had been measured and provided scientific evidence that abnormal ocean waves really do exist.

Since then, these extreme waves have been the subject of much study. And now, researchers from the University of Copenhagen’s Niels Bohr Institute have used AI methods to discover a mathematical model that provides a recipe for how — and not least when — rogue waves can occur.

With the help of enormous amounts of big data about ocean movements, researchers can predict the likelihood of being struck by a monster wave at sea at any given time.

“Basically, it is just very bad luck when one of these giant waves hits. They are caused by a combination of many factors that, until now, have not been combined into a single risk estimate. In the study, we mapped the causal variables that create rogue waves and used artificial intelligence to gather them in a model which can calculate the probability of rogue wave formation,” says Dion Häfner.

Häfner is a former PhD student at the Niels Bohr Institute and first author of the scientific study, which has just been published in the journal Proceedings of the National Academy of Sciences (PNAS).

Rogue waves happen every day

In their model, the researchers combined available data on ocean movements and the sea state, as well as water depths and bathymetric information. Most importantly, wave data was collected from buoys in 158 different locations around US coasts and overseas territories that collect data 24 hours a day. When combined, this data — from more than a billion waves — contains 700 years’ worth of wave height and sea state information.

The researchers analyzed the many types of data to find the causes of rogue waves, defined as being waves that are at least twice as high as the surrounding waves — including extreme rogue waves that can be over 20 meters high. With machine learning, they transformed it all into an algorithm that was then applied to their dataset.

“Our analysis demonstrates that abnormal waves occur all the time. In fact, we registered 100,000 waves in our dataset that can be defined as rogue waves. This is equivalent around 1 monster wave occurring every day at any random location in the ocean. However, they aren’t all monster waves of extreme size,” explains Johannes Gemmrich, the study’s second author.

Artificial intelligence as a scientist

In the study, the researchers were helped by artificial intelligence. They used several AI methods, including symbolic regression which gives an equation as output, rather than just returning a single prediction as traditional AI methods do.

By examining more than 1 billion waves, the researchers’ algorithm has analyzed its own way into finding the causes of rogue waves and condensed it into equation that describes the recipe for a rogue wave. The AI learns the causality of the problem and communicates that causality to humans in the form of an equation that researchers can analyze and incorporate into their future research.

“Over decades, Tycho Brahe collected astronomical observations from which Kepler, with lots of trial and error, was able to extract Kepler’s Laws. Dion used machines to do with waves what Kepler did with planets. For me, it is still shocking that something like this is possible,” says Markus Jochum.

Phenomenon known since the 1700s

The new study also breaks with the common perception of what causes rogue waves. Until now, it was believed that the most common cause of a rogue wave was when one wave briefly combined with another and stole its energy, causing one big wave to move on.

However, the researchers establish that the most dominant factor in the materialization of these freak waves is what is known as “linear superposition.” The phenomenon, known about since the 1700s, occurs when two wave systems cross over each other and reinforce one another for a brief period of time.

“If two wave systems meet at sea in a way that increases the chance to generate high crests followed by deep troughs, the risk of extremely large waves arises. This is knowledge that has been around for 300 years and which we are now supporting with data,” says Dion Häfner.

Safer shipping

The researchers’ algorithm is good news for the shipping industry, which at any given time has roughly 50,000 cargo ships sailing around the planet. Indeed, with the help of the algorithm, it will be possible to predict when this “perfect” combination of factors is present to elevate the risk of a monster wave that could pose a danger for anyone at sea.

“As shipping companies plan their routes well in advance, they can use our algorithm to get a risk assessment of whether there is a chance of encountering dangerous rogue waves along the way. Based on this, they can choose alternative routes,” says Dion Häfner.

Both the algorithm and research are publicly available, as are the weather and wave data deployed by the researchers. Therefore, Dion Häfner says that interested parties, such as public authorities and weather services, can easily begin calculating the probability of rogue waves. And unlike many other models created using artificial intelligence, all of the intermediate calculations in the researchers’ algorithm are transparent.

“AI and machine learning are typically black boxes that don’t increase human understanding. But in this study, Dion used AI methods to transform an enormous database of wave observations into a new equation for the probability of rogue waves, which can be easily understood by people and related to the laws of physics,” concludes Professor Markus Jochum, Dion’s thesis supervisor and co-author.



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Early dark energy could resolve cosmology’s two biggest puzzles

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A new study by MIT physicists proposes that a mysterious force known as early dark energy could solve two of the biggest puzzles in cosmology and fill in some major gaps in our understanding of how the early universe evolved.

One puzzle in question is the “Hubble tension,” which refers to a mismatch in measurements of how fast the universe is expanding. The other involves observations of numerous early, bright galaxies that existed at a time when the early universe should have been much less populated.

Now, the MIT team has found that both puzzles could be resolved if the early universe had one extra, fleeting ingredient: early dark energy. Dark energy is an unknown form of energy that physicists suspect is driving the expansion of the universe today. Early dark energy is a similar, hypothetical phenomenon that may have made only a brief appearance, influencing the expansion of the universe in its first moments before disappearing entirely.

Some physicists have suspected that early dark energy could be the key to solving the Hubble tension, as the mysterious force could accelerate the early expansion of the universe by an amount that would resolve the measurement mismatch.

The MIT researchers have now found that early dark energy could also explain the baffling number of bright galaxies that astronomers have observed in the early universe. In their new study, reported in the Monthly Notices of the Royal Astronomical Society, the team modeled the formation of galaxies in the universe’s first few hundred million years. When they incorporated a dark energy component only in that earliest sliver of time, they found the number of galaxies that arose from the primordial environment bloomed to fit astronomers’ observations.

You have these two looming open-ended puzzles,” says study co-author Rohan Naidu, a postdoc in MIT’s Kavli Institute for Astrophysics and Space Research. “We find that in fact, early dark energy is a very elegant and sparse solution to two of the most pressing problems in cosmology.”

The study’s co-authors include lead author and Kavli postdoc Xuejian (Jacob) Shen, and MIT professor of physics Mark Vogelsberger, along with Michael Boylan-Kolchin at the University of Texas at Austin, and Sandro Tacchella at the University of Cambridge.

Big city lights

Based on standard cosmological and galaxy formation models, the universe should have taken its time spinning up the first galaxies. It would have taken billions of years for primordial gas to coalesce into galaxies as large and bright as the Milky Way.

But in 2023, NASA’s James Webb Space Telescope (JWST) made a startling observation. With an ability to peer farther back in time than any observatory to date, the telescope uncovered a surprising number of bright galaxies as large as the modern Milky Way within the first 500 million years, when the universe was just 3 percent of its current age.

“The bright galaxies that JWST saw would be like seeing a clustering of lights around big cities, whereas theory predicts something like the light around more rural settings like Yellowstone National Park,” Shen says. “And we don’t expect that clustering of light so early on.”

For physicists, the observations imply that there is either something fundamentally wrong with the physics underlying the models or a missing ingredient in the early universe that scientists have not accounted for. The MIT team explored the possibility of the latter, and whether the missing ingredient might be early dark energy.

Physicists have proposed that early dark energy is a sort of antigravitational force that is turned on only at very early times. This force would counteract gravity’s inward pull and accelerate the early expansion of the universe, in a way that would resolve the mismatch in measurements. Early dark energy, therefore, is considered the most likely solution to the Hubble tension.

Galaxy skeleton

The MIT team explored whether early dark energy could also be the key to explaining the unexpected population of large, bright galaxies detected by JWST. In their new study, the physicists considered how early dark energy might affect the early structure of the universe that gave rise to the first galaxies. They focused on the formation of dark matter halos — regions of space where gravity happens to be stronger, and where matter begins to accumulate.

“We believe that dark matter halos are the invisible skeleton of the universe,” Shen explains. “Dark matter structures form first, and then galaxies form within these structures. So, we expect the number of bright galaxies should be proportional to the number of big dark matter halos.”

The team developed an empirical framework for early galaxy formation, which predicts the number, luminosity, and size of galaxies that should form in the early universe, given some measures of “cosmological parameters.” Cosmological parameters are the basic ingredients, or mathematical terms, that describe the evolution of the universe.

Physicists have determined that there are at least six main cosmological parameters, one of which is the Hubble constant — a term that describes the universe’s rate of expansion. Other parameters describe density fluctuations in the primordial soup, immediately after the Big Bang, from which dark matter halos eventually form.

The MIT team reasoned that if early dark energy affects the universe’s early expansion rate, in a way that resolves the Hubble tension, then it could affect the balance of the other cosmological parameters, in a way that might increase the number of bright galaxies that appear at early times. To test their theory, they incorporated a model of early dark energy (the same one that happens to resolve the Hubble tension) into an empirical galaxy formation framework to see how the earliest dark matter structures evolve and give rise to the first galaxies.

“What we show is, the skeletal structure of the early universe is altered in a subtle way where the amplitude of fluctuations goes up, and you get bigger halos, and brighter galaxies that are in place at earlier times, more so than in our more vanilla models,” Naidu says. “It means things were more abundant, and more clustered in the early universe.”

“A priori, I would not have expected the abundance of JWST’s early bright galaxies to have anything to do with early dark energy, but their observation that EDE pushes cosmological parameters in a direction that boosts the early-galaxy abundance is interesting,” says Marc Kamionkowski, professor of theoretical physics at Johns Hopkins University, who was not involved with the study. “I think more work will need to be done to establish a link between early galaxies and EDE, but regardless of how things turn out, it’s a clever — and hopefully ultimately fruitful — thing to try.”

We demonstrated the potential of early dark energy as a unified solution to the two major issues faced by cosmology. This might be an evidence for its existence if the observational findings of JWST get further consolidated,” Vogelsberger concludes. “In the future, we can incorporate this into large cosmological simulations to see what detailed predictions we get.”

This research was supported, in part, by NASA and the National Science Foundation.



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Plant-derived secondary organic aerosols can act as mediators of plant-plant interactions

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A new study published in Science reveals that plant-derived secondary organic aerosols (SOAs) can act as mediators of plant-plant interactions. This research was conducted through the cooperation of chemical ecologists, plant ecophysiologists and atmospheric physicists at the University of Eastern Finland.

It is well known that plants release volatile organic compounds (VOCs) into the atmosphere when damaged by herbivores. These VOCs play a crucial role in plant-plant interactions, whereby undamaged plants may detect warning signals from their damaged neighbours and prepare their defences. “Reactive plant VOCs undergo oxidative chemical reactions, resulting in the formation of secondary organic aerosols (SOAs). We wondered whether the ecological functions mediated by VOCs persist after they are oxidated to form SOAs,” said Dr. Hao Yu, formerly a PhD student at UEF, but now at the University of Bern.

The study showed that Scots pine seedlings, when damaged by large pine weevils, release VOCs that activate defences in nearby plants of the same species. Interestingly, the biological activity persisted after VOCs were oxidized to form SOAs. The results indicated that the elemental composition and quantity of SOAs likely determines their biological functions.

“A key novelty of the study is the finding that plants adopt subtly different defence strategies when receiving signals as VOCs or as SOAs, yet they exhibit similar degrees of resistance to herbivore feeding,” said Professor James Blande, head of the Environmental Ecology Research Group. This observation opens up the possibility that plants have sophisticated sensing systems that enable them to tailor their defences to information derived from different types of chemical cue.

“Considering the formation rate of SOAs from their precursor VOCs, their longer lifetime compared to VOCs, and the atmospheric air mass transport, we expect that the ecologically effective distance for interactions mediated by SOAs is longer than that for plant interactions mediated by VOCs,” said Professor Annele Virtanen, head of the Aerosol Physics Research Group. This could be interpreted as plants being able to detect cues representing close versus distant threats from herbivores.

The study is expected to open up a whole new complex research area to environmental ecologists and their collaborators, which could lead to new insights on the chemical cues structuring interactions between plants.



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Folded or cut, this lithium-sulfur battery keeps going

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Most rechargeable batteries that power portable devices, such as toys, handheld vacuums and e-bikes, use lithium-ion technology. But these batteries can have short lifetimes and may catch fire when damaged. To address stability and safety issues, researchers reporting in ACS Energy Letters have designed a lithium-sulfur (Li-S) battery that features an improved iron sulfide cathode. One prototype remains highly stable over 300 charge-discharge cycles, and another provides power even after being folded or cut.

Sulfur has been suggested as a material for lithium-ion batteries because of its low cost and potential to hold more energy than lithium-metal oxides and other materials used in traditional ion-based versions. To make Li-S batteries stable at high temperatures, researchers have previously proposed using a carbonate-based electrolyte to separate the two electrodes (an iron sulfide cathode and a lithium metal-containing anode). However, as the sulfide in the cathode dissolves into the electrolyte, it forms an impenetrable precipitate, causing the cell to quickly lose capacity. Liping Wang and colleagues wondered if they could add a layer between the cathode and electrolyte to reduce this corrosion without reducing functionality and rechargeability.

The team coated iron sulfide cathodes in different polymers and found in initial electrochemical performance tests that polyacrylic acid (PAA) performed best, retaining the electrode’s discharge capacity after 300 charge-discharge cycles. Next, the researchers incorporated a PAA-coated iron sulfide cathode into a prototype battery design, which also included a carbonate-based electrolyte, a lithium metal foil as an ion source, and a graphite-based anode. They produced and then tested both pouch cell and coin cell battery prototypes.

After more than 100 charge-discharge cycles, Wang and colleagues observed no substantial capacity decay in the pouch cell. Additional experiments showed that the pouch cell still worked after being folded and cut in half. The coin cell retained 72% of its capacity after 300 charge-discharge cycles. They next applied the polymer coating to cathodes made from other metals, creating lithium-molybdenum and lithium-vanadium batteries. These cells also had stable capacity over 300 charge-discharge cycles. Overall, the results indicate that coated cathodes could produce not only safer Li-S batteries with long lifespans, but also efficient batteries with other metal sulfides, according to Wang’s team.

The authors acknowledge funding from the National Natural Science Foundation of China; the Natural Science Foundation of Sichuan, China; and the Beijing National Laboratory for Condensed Matter Physics.



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