Computational models in science and engineering are often assessed by checking whether the residual norm is consistent with the assumed noise level. This can be misleading in smoothing inverse problems: structured model errors may be attenuated in observation space, leaving residual magnitudes below practitioner discrepancy thresholds while coherent residual patterns remain. As a result, residual-norm diagnostics can accept fitted models that still give biased parameters, predictions, or quantities of interest. We propose a structure-sensitive sequential diagnostic based on e-processes. The method uses a portfolio of spatial residual-pattern experts, updates their likelihood-ratio wealth as observations are processed, and rejects the fitted model when the aggregate wealth crosses a prescribed threshold, giving anytime-valid type-I error control for a fixed fitted model. We compare the method with Morozov discrepancy checks, fixed-sample residual tests, and batch projection tests. Across three inverse problems (elliptic diffusion, two-dimensional Stokes flow, and a glaciological ice-stream inversion implemented in the community finite-element model icepack) we demonstrate how standard discrepancy checks accept misspecified fits that produce materially wrong quantities of interest. Structure-sensitive batch tests detect these failures using the full dataset, while the e-process detects them earlier from a fraction of the observations. After rejection, the expert wealth attributes the evidence to residual patterns in the chosen dictionary and provides a basis for exploratory model correction.

Battery, gas, and robotic mowers are on sale, from a $179 corded push mower to RTK robots that cut the lawn for you. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. All kinds of mowers are on sale. We may earn revenue from the products available on this page and participate in affiliate programs. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy .

This robotic surface skimmer offers an entirely different concept in pool cleaning. But does that translate to effective debris removal? Lack of solar charging makes it impractical for most pools, where skimming needs to be nonstop. Pool skimmers, which flit along the surface of the water, constitute a small but stable subsection of the pool robot world. While their effectiveness varies, all of them work more or less the same way, cruising around the pool on a catamaran-like body, scooping up leaves into a basket that sits between the two propeller-powered hulls.

With origins in the English countryside, The Cotswold Company is known for upscale furniture that evokes its bucolic backstory. It's a step-change for a business that's tracked the shift from mail-order catalogs and showrooms to websites. In its simplest form, AI means searching for items via chatbots, but agentic AI could one day see Cotswold's customers represented by bots picking and buying products like a personal shopper. "There is always first-mover advantage with these things," said Chief Executive Officer Ralph Tucker, who joined in 2020 and is AI-readying a business that did 80% of its £123 million ($163 million) in sales online in its latest fiscal year. "If our customers are there, we need to be there and we need to be brilliant at it." In a time of both misinformation and too much information, quality journalism is more crucial than ever.

We investigate a forecasting framework based on a simple discrete-time dynamic model with coefficients varying in time. The parameters of the model are recovered within a deep learning framework, which makes it possible to retain a transparent parametric structure while simultaneously accounting for complex and nonstationary patterns in the observed phenomenon. Our analysis covers two specifications of the noise process. Besides the standard Gaussian setting, we also consider Laplace-distributed noise, which can offer a more adequate description in the presence of heavier tails and sharper local fluctuations. For both cases, we formulate the predictive scheme of the model and analyze the associated uncertainty quantification, including the construction of prediction intervals. The results illustrate that a relatively simple model, when combined with time-dependent parameter estimation, can serve as a mathematically tractable and practically flexible tool for forecasting complex dynamics under different noise assumptions. The general model is stated for TVAR($p$), while the prediction-interval formulas and the numerical experiments are developed for the TVAR(1) case.

Kornelius Raeth 1 Nicole Ludwig 1 2 Abstractscoring rules distribute the training gradient in proportion to Sample-based generative models are increasingly data density, with no awareness of the decision maker's cost structure. The model's limited capacity is allocated globused for probabilistic forecasting in high-stakes ally, leaving decision-critical regions of the output space decision settings, yet their training objectives are potentially underserved. These models are commonly trained with strictly proper Given a forecast, a decision maker with cost function c(a,y), scoring rules, such as the energy score, which al-of action aand outcome y, selects the action that minimises locate their training signal in proportion to dataexpected cost under the forecast distribution; a point forecast density, with no awareness of where forecast eris insufficient to evaluate this expectation. A good forecast rors are most costly for downstream decisions. Crucially, the energy score objective with a differentiable deci-observed cost of the optimal action is itself a proper scoring sion loss that directly penalises the cost incurredrule (Hartline et al., 2025; Kleinberg et al., 2023), placing by acting on the model's forecast. This combinedit in the same family as the energy score which licenses loss is theoretically grounded, as the decision losstheir combination as a theoretically well-founded training is itself a proper scoring rule. Introduction score acts as that anchor, preventing the model from collapsing outside cost-sensitive regions. Our method is theo-tion based on a temperature forecast, balancing asset loss against the cost of intervention. In the weather domain, retically grounded and leads to better downstream decisions state-of-the-art forecasting systems (Lang et al., 2024; Pricewhile retaining full probabilistic forecasts, as validated on et al., 2023) are trained with strictly proper scoring rulessynthetic and real-world forecasting tasks. A gradient analysis showing which regions benefitscore reduces to the continuous ranked probability score from the decision loss and why, based on the cost (CRPS), widely used in meteorological forecast verificafunction structure. Both model classes introduced above are commonly trained by minimising strictly proper sion calibration.

Autoencoders (AEs) have emerged as powerful tools for non-linear dimensionality reduction, often surpassing traditional linear methods such as Proper Orthogonal Decomposition (POD) in scenarios characterized by slowly decaying Kolmogorov $n$-widths. In the realm of Reduced-Order Modelling (ROM), these models are increasingly utilized to learn low-dimensional representations of solution manifolds associated with parametric Partial Differential Equations (PDEs). However, the high expressivity of AEs presents a challenge: although trained networks typically minimize reconstruction error, they often struggle to capture the essential properties necessary for building accurate and robust ROMs. Recent works by arXiv:2307.15288v2 and arXiv:2506.11641v1 have tackled this challenge in fully connected AEs by proposing representation-consistent architectures, which preserve some of the properties belonging to POD. This study builds upon that concept by extending representation consistency for convolutional layers. We introduce a novel class of symmetric Convolutional AutoEncoders (CAEs) designed to embody the primary properties of manifold parametrization mappings. When integrated into a ROM framework, this architecture demonstrates significantly improved predictive capabilities. Specifically, we compared the performance of the ROMs based on classical and symmetric CAEs on three one dimensional academic test cases, namely the Linear Advection, the Viscous Burger and the Kuramoto Sivashinsky equation. Numerical results demonstrate that our proposed symmetric approach consistently yields more accurate latent trajectories, lower reconstruction errors, and enhanced model robustness.

More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Temperatures can still drop below freezing at night in Yellowstone, even during the summer. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy . A massive heat dome blanketing more than half of the United States is subjecting millions of people to some of the hottest summer temperatures in over a decade.

People participate in a march to protest against the opening of AI datacentres in Vancouver, Canada, on 27 June 2026. People participate in a march to protest against the opening of AI datacentres in Vancouver, Canada, on 27 June 2026. We can live without AI, but can we live without clean water? Readers respond to an article about Erin Brockovich's battle against datacentres and voice their fears for the environment What are the benefits obtained from AI's massive use of electricity and water ( 'We're up against forces that have all the money in the world': Erin Brockovich on her battle against AI datacentres, 29 June)? Analysis shows that the top four uses of AI are "therapy/companionship", "technical assistance and troubleshooting", "fun and nonsense", and "fan fiction and storytelling". AI use for therapy, and due to loneliness, appears not to reduce loneliness.

The sun's violent death could look like this A white dwarf and an unusual exoplanet hint that'stellar death is not the end.' More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy . The sun still has a long life ahead of it, say five billion years or so.