FIRST ON FOX: The Department of Energy, the Department of the Interior and the Environmental Protection Agency are set to announce a bevy of new actions Tuesday afternoon that will "unleash" coal energy following President Donald Trump's expected signature on an executive order reinvigorating "America's beautiful clean coal industry," Fox News Digital learned. "The American people need more energy, and the Department of Energy is helping to meet this demand by unleashing supply of affordable, reliable, secure energy sources -- including coal," Department of Energy Secretary Chris Wright said in a Tuesday statement provided to Fox News Digital. "Coal is essential for generating 24/7 electricity generation that powers American homes and businesses, but misguided policies from previous administrations have stifled this critical American industry," he said. "With President Trump's leadership, we are cutting the red tape and bringing back common sense." Trump is expected to sign an executive order Tuesday afternoon that will cut through red tape surrounding the coal industry, including directing the National Energy Dominance Council to designate coal as a "mineral," end a current pause to coal leasing on federal lands, promote coal and coal technology exports, and encourage the use of coal to power artificial intelligence initiatives, Fox News Digital learned of the upcoming executive order.

If you thought robot dogs were the coolest animatronic animals out there, prepare to think again. Kawasaki Heavy Industries, a company better known for its high-end motorcycles, has unveiled a hydrogen-powered, ride-on robo-horse. The bizarre device was unveiled at the Osaka Kansai Expo on April 4 as part of Kawasaki's'Impulse to Move' project. Dubbed the CORLEO, this two-seater quadruped is capable of galloping over almost any terrain. The company calls it a'revolutionary off-road personal mobility vehicle' which swaps out the familiar wheels for four robotic legs. To steer, all you need to do is move your body and the machine's AI vision will pick out the best route to take.

Given two boundary distributions, the Schr\"odinger Bridge (SB) problem seeks the ``most likely`` random evolution between them with respect to a reference process. It has revealed rich connections to recent machine learning methods for generative modeling and distribution matching. While these methods perform well in Euclidean domains, they are not directly applicable to topological domains such as graphs and simplicial complexes, which are crucial for data defined over network entities, such as node signals and edge flows. In this work, we propose the Topological Schr\"odinger Bridge problem (TSBP) for matching signal distributions on a topological domain. We set the reference process to follow some linear tractable topology-aware stochastic dynamics such as topological heat diffusion. For the case of Gaussian boundary distributions, we derive a closed-form topological SB (TSB) in terms of its time-marginal and stochastic differential. In the general case, leveraging the well-known result, we show that the optimal process follows the forward-backward topological dynamics governed by some unknowns. Building on these results, we develop TSB-based models for matching topological signals by parameterizing the unknowns in the optimal process as (topological) neural networks and learning them through likelihood training. We validate the theoretical results and demonstrate the practical applications of TSB-based models on both synthetic and real-world networks, emphasizing the role of topology. Additionally, we discuss the connections of TSB-based models to other emerging models, and outline future directions for topological signal matching.

Visual-inertial odometry (VIO) is widely used for state estimation in autonomous micro aerial vehicles using onboard sensors. Current methods improve VIO by incorporating a model of the translational vehicle dynamics, yet their performance degrades when faced with low-accuracy vehicle models or continuous external disturbances, like wind. Additionally, incorporating rotational dynamics in these models is computationally intractable when they are deployed in online applications, e.g., in a closed-loop control system. We present HDVIO2.0, which models full 6-DoF, translational and rotational, vehicle dynamics and tightly incorporates them into a VIO with minimal impact on the runtime. HDVIO2.0 builds upon the previous work, HDVIO, and addresses these challenges through a hybrid dynamics model combining a point-mass vehicle model with a learning-based component, with access to control commands and IMU history, to capture complex aerodynamic effects. The key idea behind modeling the rotational dynamics is to represent them with continuous-time functions. HDVIO2.0 leverages the divergence between the actual motion and the predicted motion from the hybrid dynamics model to estimate external forces as well as the robot state. Our system surpasses the performance of state-of-the-art methods in experiments using public and new drone dynamics datasets, as well as real-world flights in winds up to 25 km/h. Unlike existing approaches, we also show that accurate vehicle dynamics predictions are achievable without precise knowledge of the full vehicle state.

Abstract--In this paper, we analyze the performance of the estimation of Laplacian matrices under general observatio n models. Laplacian matrix estimation involves structural c on-straints, including symmetry and null-space properties, a long with matrix sparsity. By exploiting a linear reparametriza tion that enforces the structural constraints, we derive closed -form matrix expressions for the Cram er-Rao Bound (CRB) specifically tailored to Laplacian matrix estimation. We further extend the derivation to the sparsity-constrained case, introduc ing two oracle CRBs that incorporate prior information of the suppo rt set, i.e. the locations of the nonzero entries in the Laplaci an matrix. We examine the properties and order relations betwe en the bounds, and provide the associated Slepian-Bangs formu la for the Gaussian case. We demonstrate the use of the new CRBs in three representative applications: (i) topology identi fication in power systems, (ii) graph filter identification in diffuse d models, and (iii) precision matrix estimation in Gaussian M arkov random fields under Laplacian constraints. The CRBs are eval - uated and compared with the mean-squared-errors (MSEs) of the constrained maximum likelihood estimator (CMLE), whic h integrates both equality and inequality constraints along with sparsity constraints, and of the oracle CMLE, which knows the locations of the nonzero entries of the Laplacian matrix . We perform this analysis for the applications of power syste m topology identification and graphical LASSO, and demonstra te that the MSEs of the estimators converge to the CRB and oracle CRB, given a sufficient number of measurements. Graph-structured data and signals arise in numerous applications, including power systems, communications, finance, social networks, and biological networks, for analysis and inference of networks [ 2 ], [ 3 ]. In this context, the Laplacian matrix, which captures node connectivity and edge weights, serves as a fundamental tool for clustering [ 4 ], modeling graph diffusion processes [ 5 ], [ 6 ], topology inference [ 6 ]-[ 12 ], anomaly detection [ 13 ], graph-based filtering [ 14 ]-[ 18 ], and analyzing smoothness on graphs [ 19 ]. M. Halihal and T. Routtenberg are with the School of Electric al and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel, e-mail: moradha@post.bgu.ac.il, tirzar@b gu.ac.il.

Generation planning approaches face challenges in managing the incompatible mathematical structures between stochastic production simulations for reliability assessment and optimization models for generation planning, which hinders the integration of reliability constraints. This study proposes an approach to embedding reliability verification constraints into generation expansion planning by leveraging a weighted oblique decision tree (WODT) technique. For each planning year, a generation mix dataset, labeled with reliability assessment simulations, is generated. An WODT model is trained using this dataset. Reliability-feasible regions are extracted via depth-first search technique and formulated as disjunctive constraints. These constraints are then transformed into mixed-integer linear form using a convex hull modeling technique and embedded into a unit commitment-integrated generation expansion planning model. The proposed approach is validated through a long-term generation planning case study for the Electric Reliability Council of Texas (ERCOT) region, demonstrating its effectiveness in achieving reliable and optimal planning solutions.

Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches often do not generalize readily to a broader class of linear models. In this work, we propose a novel algorithmic framework for solving a general class of non-negative linear regression models with an entropy-regularized OT datafit term, based on Sinkhorn-like scaling iterations. Our framework accommodates convex penalty functions on the weights (e.g. squared-$\ell_2$ and $\ell_1$ norms), and admits additional convex loss terms between the transported marginal and target distribution (e.g. squared error or total variation). We derive simple multiplicative updates for common penalty and datafit terms. This method is suitable for large-scale problems due to its simplicity of implementation and straightforward parallelization.

A new AI weather prediction system, developed by a team of researchers from the University of Cambridge, can deliver accurate forecasts which use less computing power than current AI and physics-based forecasting systems. The system, Aardvark Weather, has been supported by the Alan Turing Institute, Microsoft Research and the European Centre for Medium Range Weather Forecasts. It provides a blueprint for a new approach to weather forecasting with the potential to improve current practices. The results are reported in the journal Nature. "Aardvark reimagines current weather prediction methods offering the potential to make weather forecasts faster, cheaper, more flexible and more accurate than ever before, helping to transform weather prediction in both developed and developing countries," said Professor Richard Turner from Cambridge's Department of Engineering, who led the research.

While most modern machine learning methods offer speed and accuracy, few promise interpretability or explainability -- two key features necessary for highly sensitive industries, like medicine, finance, and engineering. Using eight datasets representative of one especially sensitive industry, nuclear power, this work compares a traditional feedforward neural network (FNN) to a Kolmogorov-Arnold Network (KAN). We consider not only model performance and accuracy, but also interpretability through model architecture and explainability through a post-hoc SHAP analysis. In terms of accuracy, we find KANs and FNNs comparable across all datasets, when output dimensionality is limited. KANs, which transform into symbolic equations after training, yield perfectly interpretable models while FNNs remain black-boxes. Finally, using the post-hoc explainability results from Kernel SHAP, we find that KANs learn real, physical relations from experimental data, while FNNs simply produce statistically accurate results. Overall, this analysis finds KANs a promising alternative to traditional machine learning methods, particularly in applications requiring both accuracy and comprehensibility.

Complex systems with intricate causal dependencies challenge accurate prediction. Effective modeling requires precise physical process representation, integration of interdependent factors, and incorporation of multi-resolution observational data. These systems manifest in both static scenarios with instantaneous causal chains and temporal scenarios with evolving dynamics, complicating modeling efforts. Current methods struggle to simultaneously handle varying resolutions, capture physical relationships, model causal dependencies, and incorporate temporal dynamics, especially with inconsistently sampled data from diverse sources. We introduce Temporal-SVGDM: Score-based Variational Graphical Diffusion Model for Multi-resolution observations. Our framework constructs individual SDEs for each variable at its native resolution, then couples these SDEs through a causal score mechanism where parent nodes inform child nodes' evolution. This enables unified modeling of both immediate causal effects in static scenarios and evolving dependencies in temporal scenarios. In temporal models, state representations are processed through a sequence prediction model to predict future states based on historical patterns and causal relationships. Experiments on real-world datasets demonstrate improved prediction accuracy and causal understanding compared to existing methods, with robust performance under varying levels of background knowledge. Our model exhibits graceful degradation across different disaster types, successfully handling both static earthquake scenarios and temporal hurricane and wildfire scenarios, while maintaining superior performance even with limited data.