Diffusion-based samplers -- Score Based Diffusions, Bridge Diffusions and Path Integral Diffusions -- match a target at terminal time, but the real leverage comes from choosing the schedule that governs the intermediate-time dynamics. We develop a path-wise schedule -- selection gramework for Harmonic PID with a time-varying stiffness, exploiting Piece-Wise-Constant(PWC) parametrizations and a simple hierarchical refinement. We introduce schedule-sensitive Quality-of-Sampling (QoS) diagnostics. Assuming a Gaussian-Mixture (GM) target, we retain closed-form Green functions' ration and numerically stable, Neural-Network free oracles for predicted-state maps and score. Experiments in 2D show that QoS driven PWC schedules consistently improve early-exit fidelity, tail accuracy, conditioning of the dynamics, and speciation (label-selection) timing at fixed integration budgets.

Only five millimeters of this experimental material called MOCHI can shield your hand from a flame. Breakthroughs, discoveries, and DIY tips sent every weekday. A well-placed window can brighten a room with natural light and offer scenic views of the outside world. Buildings consume around 40 percent of society's energy production, and much of that energy is wasted due to poor insulation in the winter and too much heat retention during the summer. Even the most eco-friendly windows inevitably add to this energy drain.

Engadget has been reviewing the latest devices for over two decades, adding well over 100 in-depth product tests to our tally every year. For 2025, we have compiled a list of the best gear we reviewed this year based on the highest review scores in each category. From Pixel to iPad, and Switch 2 to Sony WH-1000XM6, our reviews team has spent thousands of hours testing new products this year to discover the best of the best. Now it's your turn to rediscover the best gadgets of 2025, including explanations from our editors as to why these products were rated so highly.

"We really can't do this research without collaboration." Wąsala collaborates with atmospheric scientists from SRON (Space Research Organisation Netherlands) on machine learning models that detect large greenhouse gas emissions from space. There is too much data to review manually, and such models offer a solution. How much greenhouse gas do humans emit? The machine learning method Wąsala refers to detects emissions in the form of a point source: plumes.

If a major disaster like Fukushima or Chernobyl ever happens again, the world would know almost straight away, thanks to an array of government and DIY radiation-monitoring programs running globally.

Startups flush with cash are building AI-assisted laboratories to find materials far faster and more cheaply, but are still waiting for their ChatGPT moment. The microwave-size instrument at Lila Sciences in Cambridge, Massachusetts, doesn't look all that different from others that I've seen in state-of-the-art materials labs. Inside its vacuum chamber, the machine zaps a palette of different elements to create vaporized particles, which then fly through the chamber and land to create a thin film, using a technique called sputtering. What sets this instrument apart is that artificial intelligence is running the experiment; an AI agent, trained on vast amounts of scientific literature and data, has determined the recipe and is varying the combination of elements. Later, a person will walk the samples, each containing multiple potential catalysts, over to a different part of the lab for testing. Another AI agent will scan and interpret the data, using it to suggest another round of experiments to try to optimize the materials' performance. For now, a human scientist keeps a close eye on the experiments and will approve the next steps on the basis of the AI's suggestions and the test results. But the startup is convinced this AI-controlled machine is a peek into the future of materials discovery--one in which autonomous labs could make it far cheaper and faster to come up with novel and useful compounds. Flush with hundreds of millions of dollars in new funding, Lila Sciences is one of AI's latest unicorns.

Many problems in science and engineering involve time-dependent, high dimensional datasets arising from complex physical processes, which are costly to simulate. In this work, we propose WeldNet: Windowed Encoders for Learning Dynamics, a data-driven nonlinear model reduction framework to build a low-dimensional surrogate model for complex evolution systems. Given time-dependent training data, we split the time domain into multiple overlapping windows, within which nonlinear dimension reduction is performed by auto-encoders to capture latent codes. Once a low-dimensional representation of the data is learned, a propagator network is trained to capture the evolution of the latent codes in each window, and a transcoder is trained to connect the latent codes between adjacent windows. The proposed windowed decomposition significantly simplifies propagator training by breaking long-horizon dynamics into multiple short, manageable segments, while the transcoders ensure consistency across windows. In addition to the algorithmic framework, we develop a mathematical theory establishing the representation power of WeldNet under the manifold hypothesis, justifying the success of nonlinear model reduction via deep autoencoder-based architectures. Our numerical experiments on various differential equations indicate that WeldNet can capture nonlinear latent structures and their underlying dynamics, outperforming both traditional projection-based approaches and recently developed nonlinear model reduction methods.

What is in the 28-point US plan for Ukraine? 'Ukraine is running out of men, money and time' Can the US get all sides to end the war? Why is Europe opposing Trump's peace plan? Two people were killed in a Ukrainian drone strike on the Russian city of Saratov, regional Governor Roman Busargin said in a statement on Telegram. An unspecified number of people were also injured in the attack.

Things to Do in L.A. Tap to enable a layout that focuses on the article. Ex-Trump DOJ lawyers say'fraudulent' UC antisemitism probes led them to quit Data centers for AI could nearly triple San José's energy use. This is read by an automated voice. Please report any issues or inconsistencies here . The county seat of Santa Clara is touting its partnership with Pacific Gas & Electric, claiming the city is "the West Coast's premier destination for data center development."

Fears about AI data centers' water use have exploded. Experts say the reality is far more complicated than people think. Last month, journalist Karen Hao posted a Twitter thread in which she acknowledged that there was a substantial error in her blockbuster book Empire of AI. Hao had written that a proposed Google data center in a town near Santiago, Chile, could require "more than one thousand times the amount of water consumed by the entire population"--a figure which, thanks to a unit misunderstanding, appears to have been off by a magnitude of 1,000. In the thread, Hao thanked Andy Masley, the head of an effective altruism organization in Washington, DC, for bringing the correction to her attention. Masley has spent the past several months questioning some of the numbers and rhetoric common in popular media about water use and AI on his Substack.