The Chinese supercomputer LineShine was ranked as the fastest in the world, despite not using any GPUs. China now has the world's fastest supercomputer, overtaking the United States. The system, known as LineShine and installed at the National Supercomputing Center in Shenzhen, displaced the US system El Capitan from the top spot in the TOP500 ranking in terms of computing power. The breakthrough comes amid an intense competition between Beijing and Washington for technological supremacy, marked by high tariffs and restrictions on a wide range of hardware components and software. Since 1993, the TOP500 ranking has identified the world's most powerful supercomputers every six months through a series of standardized benchmarks that evaluate each system's performance, taking into account both its theoretical speed and its real-world performance, as well as its energy efficiency.

China beats U.S. with world's fastest supercomputer, but race not geared for AI work Workers at Elon Musk's xAI facility, which houses a large supercomputer known as Colossus, used for Artificial Intelligence (AI) data processing, in Memphis, Tennessee, on Sept. 11, 2025 | REUTERS SAN FRANCISCO - China has overtaken the U.S. to win the top spot on a list of the world's fastest supercomputers, but the results may say more about Beijing's desire to show self-sufficiency in computing systems than its standing in the global AI race, experts said. The LineShine system at the National Supercomputing Center in Shenzhen, China, uses domestically designed chips and won the top spot on the TOP500, a biannual global ranking of supercomputers, with the country's first listing in three years. The ranking comes as the U.S. and China are increasingly competing in advanced computing, with U.S. President Donald Trump on Monday signing an executive order that aims to put the U.S. ahead of China in the emerging field of quantum computing. In the June 2026 edition of TOP500, LineShine beat out the previous titleholder, El Capitan, a supercomputer housed at Lawrence Livermore National Laboratory that the U.S. government uses to develop and maintain its nuclear weapons stockpile. But technology and policy experts said the results do not mean that China has the world's fastest computer for AI work because of changes in the computing industry in recent years and the methods used to compile the list.

This paper investigates approximation-theoretic aspects of the in-context learning capability of the transformers in representing a family of noisy linear dynamical systems. Our first theoretical result establishes an upper bound on the approximation error of multi-layer transformers with respect to an L2-testing loss uniformly defined across tasks. This result demonstrates that transformers with logarithmic depth can achieve error bounds comparable with those of the least-squares estimator. In contrast, our second result establishes a non-diminishing lower bound on the approximation error for a class of single-layer linear transformers, which suggests a depth-separation phenomenon for transformers in the in-context learning of dynamical systems.

Generative models are spearheading recent progress in deep learning, showcasing strong promise for trajectory sampling in dynamical systems as well. However, whereas latent space modeling paradigms have transformed image and video generation, similar approaches are more difficult for most dynamical systems. Such systems - from chemical molecule structures to collective human behavior - are described by interactions of entities, making them inherently linked to connectivity patterns, entity conservation, and the traceability of entities over time. Our approach, LAM-SLIDE (Latent Space Modeling of Spatial Dynamical Systems via Linked Entities), bridges the gap between: (1) keeping the traceability of individual entities in a latent system representation, and (2) leveraging the efficiency and scalability of recent advances in image and video generation, where pre-trained encoder and decoder enable generative modeling directly in latent space. The core idea of LAM-SLIDE is the introduction of identifier representations (IDs) that enable the retrieval of entity properties and entity composition from latent system representations, thus fostering traceability. Experimentally, across different domains, we show that LAM-SLIDE performs favorably in terms of speed, accuracy, and generalizability.

State-space models (SSMs) are the standard formalism for Bayesian treatment of dynamical systems, with natural applications in statistics, signal processing, and machine learning. Despite their importance in both theory and application, dynamical systems have proven difficult to incorporate in modern probabilistic programming languages (PPLs), making state-of-the-art methods less accessible to practitioners and introducing friction in following the "Bayesian workflow." We introduce dynestyx, a probabilistic programming library with first-class support for SSMs, including state-of-the-art methods in the estimation of both states and parameters. Through a single, unified interface, users may specify arbitrary priors for discrete-time or continuous-time dynamical systems, perform inference over mixed-effect data, and make state and parameter estimates with principled uncertainty quantification.

Forecasting the evolution of complex dynamical systems remains a fundamentally challenging task, primarily due to pronounced nonlinear interactions, high-dimensional state spaces, and the concomitant requirement for rigorous and reliable uncertainty quantification. Contemporary reduced-order modelling (ROM) frameworks frequently exhibit inherent trade-offs among predictive accuracy, numerical stability, and interpretability, and thus often fail to achieve an optimal balance among these competing objectives. To address these limitations, we propose a framework for forecasting complex dynamical systems via a kernel autonomous ordinary differential equation approach based on Gaussian Processes and Quadratic Order Model Reduction. Our base method, the Gaussian Process Ordinary Differential Equations model, allows accurate short-term forecasting with uncertainty quantification, and it provably converges to the real autonomous equation in the smooth case. We integrate it with quadratic order reduced-order modelling and sphere projection for learning the latent dynamics efficiently while preserving stability. Numerical experiments demonstrate that our full model outperforms ROM forecasting methods such as Extended Dynamic Mode Decomposition, Bagging Optimised Dynamic Mode Decomposition and Linear and Nonlinear Disambiguation Optimisation in terms of accuracy or computational costs. These results demonstrate the potential of the framework as a robust and stable tool for forecasting complex dynamical systems with rigorous uncertainty quantification.

Understanding how grid cells perform path integration calculations remains a fundamental problem. In this paper, we conduct theoretical analysis of a general representation model of path integration by grid cells, where the 2D self-position is encoded as a higher dimensional vector, and the 2D self-motion is represented by a general transformation of the vector. We identify two conditions on the transformation. One is a group representation condition that is necessary for path integration. The other is an isotropic scaling condition that ensures locally conformal embedding, so that the error in the vector representation translates conformally to the error in the 2D self-position. Then we investigate the simplest transformation, i.e., the linear transformation, uncover its explicit algebraic and geometric structure as matrix Lie group of rotation, and explore the connection between the isotropic scaling condition and a special class of hexagon grid patterns. Finally, with our optimization-based approach, we manage to learn hexagon grid patterns that share similar properties of the grid cells in the rodent brain. The learned model is capable of accurate long distance path integration.

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as geometric graphs, i.e., graphs with nodes positioned in the Euclidean space given an arbitrarily chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as Galilean invariance. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their relationship with statistical learning is largely unexplored. We formalize a framework to learn the Koopman operator from finite data trajectories of the dynamical system. We consider the restriction of this operator to a reproducing kernel Hilbert space and introduce a notion of risk, from which different estimators naturally arise. We link the risk with the estimation of the spectral decomposition of the Koopman operator. These observations motivate a reduced-rank operator regression (RRR) estimator. We derive learning bounds for the proposed estimator, holding both in i.i.d. and non i.i.d.

It generally takes 18 to 36 months to build a hyperscale AI site - such as, presumably, one of the world's most powerful supercomputers. It generally takes 18 to 36 months to build a hyperscale AI site - such as, presumably, one of the world's most powerful supercomputers. From press release to scrap metal site: the Essex'supercomputer' that's still a scaffolding yard Nscale's AI project still in use as depot ahead of pledged completion date - with planning permission filed after Guardian's inquiries Revealed: UK's multibillion AI drive is built on'phantom investments' T he press releases announcing a gleaming supercomputer on the outskirts of north London depict a glass and concrete building, rising from a tree-lined street. Accompanied by images of glowing blue robot faces, it looks like the centre of a technological revolution. By the end of this year, that artist's impression is supposed to be a reality.