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Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equations

arXiv.org Artificial Intelligence

The machine learning methods for data-driven identification of partial differential equations (PDEs) are typically defined for a given number of spatial dimensions and a choice of coordinates the data have been collected in. This dependence prevents the learned evolution equation from generalizing to other spaces. In this work, we reformulate the problem in terms of coordinate- and dimension-independent representations, paving the way toward what we call ``spatially liberated" PDE learning. To this end, we employ a machine learning approach to predict the evolution of scalar field systems expressed in the formalism of exterior calculus, which is coordinate-free and immediately generalizes to arbitrary dimensions by construction. We demonstrate the performance of this approach in the FitzHugh-Nagumo and Barkley reaction-diffusion models, as well as the Patlak-Keller-Segel model informed by in-situ chemotactic bacteria observations. We provide extensive numerical experiments that demonstrate that our approach allows for seamless transitions across various spatial contexts. We show that the field dynamics learned in one space can be used to make accurate predictions in other spaces with different dimensions, coordinate systems, boundary conditions, and curvatures.


AMD's shares surge on deal to supply AI chips to OpenAI

Al Jazeera

AMD's shares surge on deal to supply AI chips to OpenAI United States chipmaker AMD will supply artificial intelligence chips to OpenAI in a multi-year deal that would bring in tens of billions of dollars in annual revenue and give the ChatGPT creator the option to buy up to roughly 10 percent of the company. Shares of the chipmaker surged more than 34 percent on Monday when the deal was announced, putting them on track for their biggest one-day gain in more than nine years and adding roughly $80bn to the company's market value. "We view this deal as certainly transformative, not just for AMD, but for the dynamics of the industry," AMD executive vice president Forrest Norrod told the Reuters news agency. The agreement closely ties the startup at the centre of the AI boom to AMD, one of the strongest rivals of Nvidia, which recently agreed to make substantial investments in OpenAI. Analysts said it was a significant vote of confidence in AMD's AI chips and software but is unlikely to dent Nvidia's dominance, as the market leader continues to sell every AI chip it can make.


The Most Reviled Tech CEO in New York Confronts His Haters

The Atlantic - Technology

Avi Schiffmann says he's enjoying the angry reaction to the Friend AI pendant. I f you haven't already heard of Friend, the company that makes a $129 wearable AI companion--a plastic disk, containing a microphone, on a necklace--you probably also have not seen Friend's recent ad campaign. Late this past summer, Friend paid $1 million to plaster more than 10,000 white posters throughout the New York City subway system with messages such as I'll binge the entire series with you . Across the city, the ads are covered in graffiti criticizing the pendant ( it doesn't have eyes, bruh; CRINGE) as well as the idea of AI altogether ( AI wouldn't care if you lived or died); some vandals invite you to befriend a senior citizen instead of a chatbot, or volunteer with a community garden--you will meet cool people! Many of the ads have been ripped and torn.


OpenAI Wants ChatGPT to Be Your Future Operating System

WIRED

At OpenAI's Developer Day, CEO Sam Altman showed off apps that run entirely inside the chat window--a new effort to turn ChatGPT into a platform. On Monday, OpenAI unveiled a new way to embed third-party apps directly into ChatGPT. At the company's annual developer conference in San Francisco, CEO Sam Altman said the move would "enable a new generation of apps that are adaptive, interactive, and personalized, that you can chat with." Starting today, some developers will be able to use a preview version of a new Apps software development kit (SDK) to build apps within ChatGPT using open standards. The ability to distribute these apps is currently limited to a handful of big partners.


OpenAI's Blockbuster AMD Deal Is a Bet on Near-Limitless Demand for AI

WIRED

OpenAI's Blockbuster AMD Deal Is a Bet on Near-Limitless Demand for AI OpenAI's latest move in the race to build massive data centers in the US shows it believes demand for AI will keep surging--even as skeptics warn of a bubble. Sam Altman, CEO of OpenAI, Lisa Su, CEO of Advanced Micro Devices, and Michael Intrator, CEO of CoreWeave, arrive to testify during the Senate on Thursday, May 8, 2025.Photograph: Tom Williams; Getty Images Save this storyOpenAI announced on Monday that it will acquire several data centers' worth of chips from AMD in a blockbuster deal that could also give OpenAI the option to acquire a roughly 10 percent stake in the chipmaker. It's another bold bet from OpenAI that demand for generative artificial intelligence will continue rising--bubble be damned. "Excited to partner with AMD to use their chips to serve our users!" OpenAI CEO Sam Altman said on X, adding that the company will also ramp up its investments in Nvidia chips. He added: "The world needs much more compute " OpenAI said in a blog post this morning that it would commit to purchasing 6 gigawatts' worth of AMD chips over the next several years.


I Got Laid Off. A.I. Wrote My New Cover Letter. It Was Surprisingly Good--Except for One Alarming Mistake.

Slate

After sending out more than 100 applications, I learned the robots are no longer satisfied with taking our jobs--they also want to prevent us from getting new ones. I got laid off five months ago. Every morning I drink a pot of coffee while I write cover letters, tweak my rรฉsumรฉ, and submit job applications into the abyss, knowing they will likely never be seen by human eyes--only crawled by the cold, lifeless algorithms of an artificial intelligence. I feel like General Zod from, floating off into space trapped inside a two-dimensional phantom zone, screaming in silence about my job qualifications and core competencies. The job market is a mess.


WIRED Roundup: The New Fake World of OpenAI's Social Video App

WIRED

On this episode of, we break down some of the week's best stories, covering everything from Peter Thiel's obsession with the Antichrist to the launch of OpenAI's new Sora 2 video app. All products featured on WIRED are independently selected by our editors. However, we may receive compensation from retailers and/or from purchases of products through these links. In today's episode, Zoรซ Schiffer is joined by WIRED's senior culture editor Manisha Krishnan to run through five of the best stories we published this week--from how federal workers are being told to blame Democrats for the government shutdown to Peter Thiel's ongoing obsession with the Antichrist. Then, Zoรซ and Manisha break down the news of OpenAI launching a new social app for AI-generated videos. Write to us at uncannyvalley@wired.com . You can always listen to this week's podcast through the audio player on this page, but if you want to subscribe for free to get every episode, here's how: If you're on an iPhone or iPad, open the app called Podcasts, or just tap this link . Today on the show, we're bringing you five stories that you need to know about this week. Including our scoop of how OpenAI just launched a social app dedicated completely to AI-generated videos. I'm joined today by our Senior Culture Editor, Manisha Krishnan. Our first story is about the thing that I feel like our whole newsroom is talking about, possibly the whole country is talking about.


OpenAI wants to buy 10% of AMD. That should make PC gamers nervous

PCWorld

When you purchase through links in our articles, we may earn a small commission. If AMD turns to the cloud, does that mean less love for the PC market? In the ongoing war of AI investment, OpenAI has secured itself a new ally: AMD. The chip maker will trade millions of its upcoming Instinct MI450 GPUs for an investment by the AI company, worth up to 10 percent of its stock. The numbers, though, remain vague.


I've seen AI try to ESCAPE labs. The apocalypse is already here... and our children will be the first victims

Daily Mail - Science & tech

America's richest real estate tycoon disowns son with shockingly icy 12-word statement after'man cave' plans went terribly wrong Horrific stab wounds suffered by grease truck driver, 69, 'stabbed by Mark Sanchez' with NFL star facing up to six years in prison Taylor Swift makes surprise confession on her song'about ex Joe Alwyn' as she insists fans have'always had the wrong idea' about it Sinister notes that are plaguing remote county explodes as fears mount over creepy messages: 'What else could they do?' Key North Atlantic current is on the brink of COLLAPSING - plunging Europe into a'Little Ice Age', scientists warn Visionary billionaire died in a suspicious house fire. Then a mysterious will emerged... CBS staff in panic as anti-woke firebrand Bari Weiss takes control with no-nonsense show on America's most divisive issues Trump's war room plots savage bloodbath as countdown enters final hours: Live updates Trump sends Navy officers wild with powerful message to liberals claiming he's'unwell' We got hopelessly hooked on a trendy'wellness' tonic. We thought it was harmless but our descent into addiction left us depressed, in debt... and in rehab Judge speaks out after her $1.5m mansion'exploded' in suspected arson attack after she defied Trump order Mark Sanchez's alleged victim's family breaks silence as grim photos emerge after violent attack So many women suffer bloated, uncomfortable guts, says DR EMILY LEEMING. Here's the 7 simple cures I give my patients - you won't have read these before My son made a horrifying accusation about me in therapy... it's destroyed our relationship: DEAR JANE Ex-NFL star Mark Sanchez'thought he'd been shot and pounded on window of pub to get help', bartender reveals Nicole Kidman's friends tear into Keith Urban over bombshell split: 'Total 180 on who he is' Real Housewives of Atlanta vet Porsha Williams reveals she is dating a woman... after ex Simon was deported by ICE US billionaire retail estate tycoon is ordered to sell off his'exceptional' ยฃ36million London mansion in bitter divorce battle with ex-wife My husband works in Dubai and has cheated on me at least three times so far.


OpenAI signs multibillion-dollar chip deal with AMD

The Guardian

OpenAI and the chipmaker AMD announced on Monday that they had signed a multibillion-dollar chip deal that would also give the ChatGPT creator the option to buy a large stake in the chipmaker. The deal offers OpenAI an opportunity to buy 10% in AMD and marks a major vote of confidence in the company's AI chips and software. Shares of AMD surged more than 30% and added about $80bn to its market capitalization after the announcement. "We view this deal as certainly transformative, not just for AMD, but for the dynamics of the industry," said Forrest Norrod, AMD's executive vice-president. The latest deal, among a string of investment commitments, is a testament to OpenAI and the broader AI industry's voracious appetite for computing power as companies race toward developing AI technology that meets or exceeds human intelligence.