Three Chinese astronauts have safely returned to Earth in the recently-launched Shenzhou-21 spacecraft after their own spacecraft was declared unsafe.
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Significant progress towards answering one of the Clay Mathematics Institute’s seven Millennium Prize Problems has been achieved using deep learning. The challenge is to establish whether or not the Navier-Stokes equation of fluid dynamics develops singularities. The work was done by researchers in the US and UK – including some at Google Deepmind. Some team members had already shown that simplified versions of the equation could develop stable singularities, which reliably form. In the new work, the researchers found unstable singularities, which form only under very specific conditions.
The Navier–Stokes partial differential equation was developed in the early 19th century by Claude-Louis Navier and George Stokes. It has proved its worth for modelling incompressible fluids in scenarios including water flow in pipes; airflow around aeroplanes; blood moving in veins; and magnetohydrodynamics in plasmas.
No-one has yet proved, however, whether smooth, non-singular solutions to the equation always exist in three dimensions. “In the real world, there is no singularity…there is no energy going to infinity,” says fluid dynamics expert Pedram Hassanzadeh of the University of Chicago. “So if you have an equation that has a singularity, it tells you that there is some physics that is missing.” In 2000, the Clay Mathematics Institute in Denver, Colorado listed this proof as one of seven key unsolved problems in mathematics, offering a reward of $1,000,000 for an answer.
Researchers have traditionally tackled the problem analytically, but in recent decades high-level computational simulations have been used to assist in the search. In a 2023 paper, mathematician Tristan Buckmaster of New York University and colleagues used a special type of machine learning algorithm called a physics-informed neural network to address the question.
“The main difference is…you represent [the solution] in a highly non-linear way in terms of a neural network,” explains Buckmaster. This allows it to occupy a lower-dimensional space with fewer free parameters, and therefore to be optimized more efficiently. Using this approach, the researchers successfully obtained the first stable singularity in the Euler equation. This is an analogy to the Navier-Stokes equation that does not include viscosity.
A stable singularity will still occur if the initial conditions of the fluid are changed slightly – although the time taken for them to form may be altered. An unstable singularity, however, may never occur if the initial conditions are perturbed even infinitesimally. Some researchers have hypothesized that any singularities in the Navier-Stokes equation must be unstable, but finding unstable singularities in a computer model is extraordinarily difficult.
“Before our result there hadn’t been an unstable singularity for an incompressible fluid equation found numerically,” says geophysicist Ching-Yao Lai of California’s Stanford University.
In the new work the authors of the original paper and others teamed up with researchers at Google Deepmind to search for unstable singularities in a bounded 3D version of the Euler equation using a physics-informed neural network. “Unlike conventional neural networks that learn from vast datasets, we trained our models to match equations that model the laws of physics,” writes Yongji Wang of New York University and Stanford on Deepmind’s blog. “The network’s output is constantly checked against what the physical equations expect, and it learns by minimizing its ‘residual’, the amount by which its solution fails to satisfy the equations.”
After an exhaustive search at a precision that is orders of magnitude higher than a normal deep learning protocol, the researchers discovered new families of singularities in the 3D Euler equation. They also found singularities in the related incompressible porous media equation used to model fluid flows in soil or rock; and in the Boussinesq equation that models atmospheric flows.
The researchers also gleaned insights into the strength of the singularities. This could be important as stronger singularities might be less readily smoothed out by viscosity when moving from the Euler equation to the Navier-Stokes equation. The researchers are now seeking to model more open systems to study the problem in a more realistic space.
Hassanzadeh, who was not involved in the work, believes that it is significant – although the results are not unexpected. “If the Euler equation tells you that ‘Hey, there is a singularity,’ it just tells you that there is physics that is missing and that physics becomes very important around that singularity,” he explains. “In the case of Euler we know that you get the singularity because, at the very smallest scales, the effects of viscosity become important…Finding a singularity in the Euler equation is a big achievement, but it doesn’t answer the big question of whether Navier-Stokes is a representation of the real world, because for us Navier-Stokes represents everything.”
He says the extension to studying the full Navier-Stokes equation will be challenging but that “they are working with the best AI people in the world at Deepmind,” and concludes “I’m sure it’s something they’re thinking about”.
The work is available on the arXiv pre-print server.
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Virgin Galactic says it remains on schedule to complete development of its next-generation suborbital spaceplane and begin commercial flights before the end of 2026.
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An Atlas 5 rocket sent Viasat’s second ViaSat-3 satellite toward geostationary orbit Nov. 13, bringing the U.S. broadband provider closer to operating a terabit-per-second giant it had hoped to debut six years ago.
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SAN FRANCISCO – Canada’s SBQuantum has won an €800,000 ($932,000) European Space Agency contract to deliver a prototype quantum magnetometer for space-based Earth observation. Under the 21-month contract, announced Nov. 14, SBQuantum will upgrade the quantum diamond magnetometer delivered to ESA for testing and evaluation in 2024. The new version of the sensor will be […]
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Blue Origin successfully launched a NASA Mars mission on the second flight of its New Glenn booster Nov. 13, landing the vehicle’s first stage in the process.
The post New Glenn launches NASA’s ESCAPADE Mars mission, lands booster appeared first on SpaceNews.
Skyloom Global is a Colorado-based provider of space-based optical communications terminals
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Project Kuiper has shed its seven-year-old code name, emerging as Amazon Leo Nov. 13 as the company nears the start of initial broadband services from the low Earth orbit constellation next year.
The post Project Kuiper becomes Amazon Leo ahead of LEO broadband service debut appeared first on SpaceNews.
On its third-quarter earnings call Nov. 12, Firefly executives highlighted the company’s alignment with the Pentagon’s planned “Golden Dome” missile defense initiative
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NASA’s Goddard Space Flight Center (GSFC) looks set to lose a big proportion of its budget as a two-decade reorganization plan for the centre is being accelerated. The move, which is set to be complete by March, has left the Goddard campus with empty buildings and disillusioned employees. Some staff even fear that the actions during the 43-day US government shutdown, which ended on 12 November, could see the end of much of the centre’s activities.
Based in Greenbelt, Maryland, the GSFC has almost 10 000 scientists and engineers, about 7000 of whom are directly employed by NASA contractors. Responsible for many of NASA’s most important uncrewed missions, telescopes, and probes, the centre is currently working on the Nancy Grace Roman Space Telescope, which is scheduled to launch in 2027, as well as the Dragonfly mission that is due to head for Saturn’s largest moon Titan in 2028.
The ability to meet those schedules has now been put in doubt by the Trump administration’s proposed budget for financial year 2026, which started in September. It calls for NASA to receive almost $19bn – far less than the $25bn it has received for the past two years. If passed, Goddard would lose more than 42% of its staff.
Congress, which passes the final budget, is not planning to cut NASA so deeply as it prepares its 2026 budget proposal. But on 24 September, Goddard managers began what they told employees was “a series of moves…that will reduce our footprint into fewer buildings”. The shift is intended to “bring down overall operating costs while maintaining the critical facilities we need for our core capabilities of the future”.
While this is part of a 20-year “master plan” for the GSFC that NASA’s leadership approved in 2019, the management’s memo stated that “all planned moves will take place over the next several months and be completed by March 2026″. A report in September by Democratic members of the Senate Committee on Commerce, Science, and Transportation, which is responsible for NASA, asserts that the cuts are “in clear violation of the [US] constitution [without] regard for the impacts on NASA’s science missions and workforce”.
On 3 November, the Goddard Engineers, Scientists and Technicians Association, a union representing NASA workers, reported that the GSFC had already closed over a third of its buildings, including some 100 labs. This had been done, it says, “with extreme haste and with no transparent strategy or benefit to NASA or the nation”. The union adds that the “closures are being justified as cost-saving but no details are being provided and any short-term savings are unlikely to offset a full account of moving costs and the reduced ability to complete NASA missions”.
Zoe Lofgren, the lead Democrat on the House of Representatives Science Committee, has demanded of Sean Duffy, NASA’s acting administrator, that the agency “must now halt” any laboratory, facility and building closure and relocation activities at Goddard. In a letter to Duffy dated 10 November, she also calls for the “relocation, disposal, excessing, or repurposing of any specialized equipment or mission-related activities, hardware and systems” to also end immediately.
Lofgren now wants NASA to carry out a “full accounting of the damage inflicted on Goddard thus far” by 18 November. Owing to the government shutdown, no GSFC or NASA official was available to respond to Physics World’s requests for a response.
Meanwhile, the Trump administration has renominated billionaire entrepreneur Jared Isaacman as NASA’s administrator. Trump had originally nominated Isaacman, who had flown on a private SpaceX mission and carried out spacewalk, on the recommendation of SpaceX founder Elon Musk. But the administration withdrew the nomination in May following concerns among some Republicans that Isaacman had funded the Democrat party.
The post NASA’s Goddard Space Flight Center hit by significant downsizing appeared first on Physics World.
Simi Valley, CA — [November 13, 2025] — ESI Motion, a leader in advanced motion and power solutions, proudly announces the release of its next-generation space-rated satellite battery, SatBat, engineered […]
The post ESI Motion Launches “SatBat,” a Revolutionary Space-Rated Battery Set to Redefine Power Systems in Low Earth Orbit appeared first on SpaceNews.
Like any major endeavour, designing and fabricating semiconductor chips requires compromise. As well as trade-offs between cost and performance, designers also consider carbon emissions and other environmental impacts.
In this episode of the Physics World Weekly podcast, Margaret Harris reports from the Heidelberg Laureate Forum where she spoke to two researchers who are focused on some of these design challenges.
Up first is Mariam Elgamal, who’s doing a PhD at Harvard University on the development of environmentally sustainable computing systems. She explains why sustainability goes well beyond energy efficiency and must consider the manufacturing process and the chemicals used therein.
Harris also chats with Andrew Gunter, who is doing a PhD at the University of British Columbia on circuit design for computer chips. He talks about the maths-related problems that must be solved in order to translate a desired functionality into a chip that can be fabricated.
The post Designing better semiconductor chips: NP hard problems and forever chemicals appeared first on Physics World.
The Middle East is no longer asking whether it should develop domestic space capabilities; it’s deciding with whom it will develop them. If the United States wants to be the country of choice ahead of China, it must create a joint space partnership agreement framework to align American and partner nations’ industry, government and financial […]
The post Countering China’s Space Silk Road: a U.S. partnership model for the Middle East appeared first on SpaceNews.
In this episode of Space Minds, host David Ariosto speaks with Jim Bridenstine, former NASA Administrator and U.S. Congressman, who oversaw the launch of the Artemis program—America’s renewed effort to return astronauts to the Moon.
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Lux Aeterna is attracting growing interest from across the U.S. government for heat shield technology designed to make satellites fully reusable, securing two partnership agreements since emerging from stealth in June.
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