Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing approaches typically approximate such features within continuous function spaces, often requiring increased model capacity and high-resolution data. In this work, we propose Cut-DeepONet, a two-stage training framework that explicitly models discontinuities while reducing learning complexity. Our approach reformulates the problem via a lifting strategy, partitioning the domain into smooth subregions while representing discontinuities as boundaries in a higher-dimensional space. This separation aligns the operator learning task with the inductive bias of neural networks and avoids directly approximating discontinuities. An additional network predicts input-dependent discontinuity locations for unseen inputs, which are then used to guide the neural operator in generating smooth components within each region. Experiments on benchmark PDEs show that Cut-DeepONet outperforms state-of-the-art methods, even when trained on low-resolution datasets. The method excels on problems with discontinuities and sharp transitions, while using fewer trainable parameters. Our results highlight the benefits of changing the representation of operator learning rather than increasing model complexity.

Standard generative models struggle with heavy-tailed data: Lipschitz architectures cannot produce power-law tails from Gaussian noise, and interpolating between heavy-tailed data and Gaussians is ill-posed. We propose a simple fix: apply the soft-log transform $ϕ(x) = \mathrm{sign}(x) \cdot \log(1 + |x|)$ coordinate-wise to data before training, then exponentiate samples after generation. A Hill diagnostic decides per-coordinate whether to transform, leaving light-tailed margins untouched at no added complexity. This compresses heavy tails into a range where standard flow matching succeeds, without heavy-tailed base distributions or architectural modifications. We provide theoretical intuition for why this works: the log-transform maps Pareto tails to exponentials, and the induced dynamics implement a form of tail annealing via power transformations. On a 144-configuration multivariate benchmark (3 copulas, $d$ up to 100, 4 tail indices), Log-FM dominates specialized baselines on $W_1$, CVaR$_{99}$, and extreme-quantile metrics, and is the only method with zero severe divergences across 2{,}880 runs.

What are Russia's gains from the Iran war? 'We are not losers; we are winners' More than 15,800 people killed in Russia's all-out war on Ukraine: UN The United Nations has said 15,850 people, including 791 children, have been killed in Ukraine since Russia's full-scale invasion of the neighbouring country in February 2022. The "actual figures are likely significantly higher", Kayoko Gotoh, Europe and Central Asia director of the UN's Department of Political and Peacebuilding Affairs (DPPA), told the UN Security Council on Tuesday. US President Donald Trump has attempted to mediate and announced the most recent three-day ceasefire earlier this month, but fighting has resumed. Tuesday's Russian attacks on Ukraine killed at least six people. A 15-year-old boy was among three people killed in a Russian ballistic missile attack on the city of Pryluky in north-central Ukraine's Chernihiv region on Tuesday morning, according to the State Emergency Service of Ukraine.

Estonia has said a Nato fighter jet shot down a drone, which it suspects was a Ukrainian projectile knocked off course by Russian electronic jamming, over its territory. Defence Minister Hanno Pevkur said a Romanian F-16 fired a missile and drone debris fell in a marshy area in central Estonia on Tuesday. Ukraine reacted by accusing Russia of deliberately redirecting Ukrainian drones launched at legitimate military targets in Russia, apologising to Estonia and all of our Baltic friends for such unintended incidents. Russia has not commented on the latest in a series of recent drone incursions over Nato members Estonia, Latvia and Lithuania. Last week, Latvian Prime Minister Evika Silina resigned following a political crisis over Russia-bound Ukrainian drones straying into Latvian territory.

The CEO of Google DeepMind tells WIRED that companies should use the productivity gains of AI to do more, not lay people off. Demis Hassabis, the CEO of Google DeepMind, is keen to talk about the coding skills of his company's newest model, Gemini 3.5 Flash. The model has been trained to perform complex agentic coding tasks: translate large code bases from one language to another; find and fix bugs lurking deep in knotty code; and even write entire operating systems from scratch. Hassabis does not, however, think this spells doom for software developers. "I have no idea why people are going around talking with certainty about that," Hassabis tells WIRED ahead of the new model reveal at today's Google's I/O event .

A long and bitter legal battle between tech billionaires Elon Musk and Sam Altman has culminated in victory for the OpenAI boss. Musk has vowed to appeal the verdict. But what did the trial reveal about big tech and the global AI race?

It is not only OpenAI but the AI race itself that was vindicated in the California courtroom last night . Even though Elon Musk essentially lost on a technicality, there's a clear signal from the verdict that making lots of money from AI and competing fiercely with rivals is simply business. The industry sometimes tries to display a united front, especially when it comes to safety, research and inclusivity. But this case served as a powerful reminder that none of the AI giants are charities and don't have to be, even if they once said otherwise. Cracks in the façade of industry collaboration for the sake of humanity have been exposed before.

The wars in Ukraine and Iran reveal a structural shift in modern warfare where the final ten percent of military degradation costs more than the first ninety percent.

Standard Chartered said it would cut 15% of its corporate function roles by 2030. Standard Chartered said it would cut 15% of its corporate function roles by 2030. Standard Chartered plans to cut more than 7,000 jobs over the next four years as it increasingly uses artificial intelligence. The London-headquartered lender is one of the first major global banks to lay out plans to cut thousands of jobs, citing AI as a driver to make its operations slimmer as it seeks to increase its profitability and tackle competition. StanChart said on Tuesday it would cut 15% of its back-office roles by 2030, which would result in about 7,800 redundancies out of its more than 52,000 staff in such roles.

What are Russia's gains from the Iran war? 'We are not losers; we are winners' A Russian attack has damaged port infrastructure in Ukraine's Danube River port city of Izmail, a vital grain-export hub, while Russian authorities said they had downed four Ukrainian drones headed towards Moscow, as peace efforts remain stalled and both sides continue reciprocal attacks. Izmail, in the Odesa region, is a frequently targeted logistical centre and was hit in the early hours of Tuesday. It is Ukraine's largest port on the Danube. The attack lasted from about 1am to 3am (22:00 to 00:00 GMT), with firefighters battling a blaze in a building with blown-out windows. This followed another Russian attack on port infrastructure in Izmail on the night of May 2. In Kharkiv, two people were rescued, and one may remain trapped under the rubble after a Russian drone attack, Mayor Ihor Terekhov said on Telegram.