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On the Existence of Steady-State Solutions to the Equations Governing Fluid Flow in Networks
The steady-state solution of fluid flow in pipeline infrastructure networks driven by junction/node potentials is a crucial ingredient in various decision-support tools for system design and operation. While the nonlinear system is known to have a unique solution (when one exists), the absence of a definite result on the existence of solutions hobbles the development of computational algorithms, for it is not possible to distinguish between algorithm failure and non-existence of a solution. In this letter, we show that for any fluid whose equation of state is a scaled monomial, a unique solution exists for such nonlinear systems if the term solution is interpreted in terms of potentials and flows rather than pressures and flows. However, for gases following the CNGA equation of state, while the question of existence remains open, we construct an alternative system that always has a unique solution and show that the solution to this system is a good approximant of the true solution. Further, the existence result for flow of natural gas in networks also applies to other fluid flow networks such as water distribution networks or networks that transport carbon dioxide in carbon capture and sequestration. Most importantly, our result enables correct diagnosis of algorithmic failure, problem stiffness, and non-convergence in computational algorithms.
Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations
Here, we demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We conduct experiments on 38 cases from the PGLib-OPF library, showing that the LNC strengthen the SOC and CDF relaxations in 100% of the test cases, with average and maximum differences in the optimality gaps of 6.2% and 17.5% respectively. The NF relaxation is strengthened in 46.2% of test cases, with average and maximum differences in the optimality gaps of 1.3% and 17.3% respectively. We also study the trade-off between relaxation quality and solve time, demonstrating that the strengthened CDF relaxation outperforms the strengthened SOC formulation in terms of runtime and number of iterations needed, while the strengthened NF formulation is the most scalable with the lowest relaxation quality improvement due to these LNC.
Fast and Accurate Intersections on a Sphere
We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and numerical robustness over the ones traditionally implemented in geoscience software. We then show how algorithms based on the concept of error-free transformations (EFT) can be applied to evaluate this formula within a relative error bound that is on the order of machine precision. Here, we demonstrate that, with a vectorized and parallelized implementation, this enhanced accuracy is achieved with no compute time overhead compared to a direct calculation in hardware floating point, making our algorithm suitable for performance-sensitive applications like regridding of high-resolution climate data. In contrast, evaluating our formula using high-precision data types like quadruple precision and arbitrary precision, or using the robust intersection computation routines from the Computational Geometry Algorithms Library, leads to significant computational overhead, especially since these alternatives inhibit vectorization. More generally, our work demonstrates how EFT techniques can be combined and extended to implement nontrivial geometric calculations with high accuracy and speed.
New Time Integrators and Capabilities in SUNDIALS Versions 6.2.0-7.4.0
SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This article overviews several significant improvements and new features added over the last 3 years to support scientific simulations run on high-performance computing systems. Notably, three new classes of one-step methods have been implemented: low storage Runge–Kutta, symplectic partitioned Runge–Kutta, and operator splitting. In addition, we describe new timestep adaptivity support for multirate methods, adjoint sensitivity analysis capabilities for explicit Runge–Kutta methods, additional options for Anderson acceleration in nonlinear solvers, and improved error handling and logging.
Exascale Computing and Data Handling: Challenges and Opportunities for Weather and Climate Prediction
The emergence of exascale computing and artificial intelligence offer tremendous potential to significantly advance Earth system prediction capabilities. However, enormous challenges must be overcome to adapt models and prediction systems to use these new technologies effectively. A 2022 WMO report on exascale computing recommends “urgency in dedicating efforts and attention to disruptions associated with evolving computing technologies that will be increasingly difficult to overcome, threatening continued advancements in weather and climate prediction capabilities.” Further, the explosive growth in data from observations, model and ensemble output, and postprocessing threatens to overwhelm the ability to deliver timely, accurate, and precise information needed for decision-making. Artificial intelligence (AI) offers untapped opportunities to alter how models are developed, observations are processed, and predictions are analyzed and extracted for decision-making. Given the extraordinarily high cost of computing, growing complexity of prediction systems, and increasingly unmanageable amount of data being produced and consumed, these challenges are rapidly becoming too large for any single institution or country to handle. This paper describes key technical and budgetary challenges, identifies gaps and ways to address them, and makes a number of recommendations.
Model-predictive optimal control of ferrofluidic microrobots in three-dimensional space
Ferrofluid microrobots have emerged as promising tools for minimally invasive medical procedures. Their unique properties to navigate complex fluids and reach otherwise inaccessible regions of the human body have enabled new applications in targeted drug delivery, tissue engineering, and diagnostics. Here, this paper proposes a model-predictive controller for the external magnetic manipulation of ferrofluid microrobots in three dimensions (3D). The internal optimization routine of the controller determines appropriate changes in the applied electromagnetic field to minimize the deviation between the actual and desired trajectories of the microrobot. A linear system governing locomotion is derived and used as the equality constraints of the optimization problems associated with the feedback index. In addition to ferrofluid droplets, the controller presented in this work may be applied to other magnetically-pulled microrobots. Several experiments are performed to validate the controller and showcase its ability to adapt to changes in system parameters such as the desired tracking trajectory and the size, orientation, deformation, and velocity of the microrobot. The accuracy of the controller is analyzed for each experiment, and the average error is found to be within 0.25 mm for small velocities. An additional experiment is performed to demonstrate significant improvement over a PID controller that is optimally tuned using Bayesian optimization. The results presented in this paper suggest that the proposed control algorithm could enable new microrobotic capabilities in minimally invasive medical procedures, lab-on-a-chip applications, and microfluidics.
Challenges of COVID-19 Case Forecasting in the US, 2020–2021
During the COVID-19 pandemic, forecasting COVID-19 trends to support planning and response was a priority for scientists and decision makers alike. In the United States, COVID-19 forecasting was coordinated by a large group of universities, companies, and government entities led by the Centers for Disease Control and Prevention and the US COVID-19 Forecast Hub ( https://covid19forecasthub.org ). We evaluated approximately 9.7 million forecasts of weekly state-level COVID-19 cases for predictions 1–4 weeks into the future submitted by 24 teams from August 2020 to December 2021. We assessed coverage of central prediction intervals and weighted interval scores (WIS), adjusting for missing forecasts relative to a baseline forecast, and used a Gaussian generalized estimating equation (GEE) model to evaluate differences in skill across epidemic phases that were defined by the effective reproduction number. Overall, we found high variation in skill across individual models, with ensemble-based forecasts outperforming other approaches. Forecast skill relative to the baseline was generally higher for larger jurisdictions (e.g., states compared to counties). Over time, forecasts generally performed worst in periods of rapid changes in reported cases (either in increasing or decreasing epidemic phases) with 95% prediction interval coverage dropping below 50% during the growth phases of the winter 2020, Delta, and Omicron waves. Ideally, case forecasts could serve as a leading indicator of changes in transmission dynamics. However, while most COVID-19 case forecasts outperformed a naïve baseline model, even the most accurate case forecasts were unreliable in key phases. Further research could improve forecasts of leading indicators, like COVID-19 cases, by leveraging additional real-time data, addressing performance across phases, improving the characterization of forecast confidence, and ensuring that forecasts were coherent across spatial scales. In the meantime, it is critical for forecast users to appreciate current limitations and use a broad set of indicators to inform pandemic-related decision making.
A Novel Framework to Evaluate the Costs and Potential of Bioenergy in Decarbonization of the U.S. Economy
The long-term strategy of the United States targets reaching economy-wide net-zero emissions by 2050 and a carbon-neutral electricity grid by 2035 (U.S. Department of State and U.S. Executive Office of the President, 2021). Meeting these targets would require considerable changes to the energy system. Some key characteristics of illustrative net-zero energy systems include increased penetration of renewable energy and carbon sources, use of CO2 capture and storage (CCS) in hard-to-abate sectors, and a greater role for energy carriers such as electricity and hydrogen (Davis et al, 2018). Another common feature of such energy systems is the need for carbon dioxide removal (CDR) approaches (Horowitz et al, 2022). Across all these characteristics of net-zero energy systems, bioenergy and biomass feedstock is anticipated to play an important role. Biomass feedstock serves as a renewable carbon source. This can enable conversion of such feedstock into fuels and energy carriers for hard-to-abate sectors such as aviation. Indeed, the U.S. Government has a target to meet all jet fuel demand by 2050 from sustainable aviation fuel (SAF), where biofuel pathways are likely to have an important role (EERE, 2020). Bioenergy is also highly versatile with the possibility to convert feedstock into electricity, hydrogen, liquid fuels, heat or high-value products, based on biomass type, demand and technology availability (Clarke et al, 2022). Combination of bioenergy with CCS can also nominally deliver CDR (Fuhrman et al, 2023). As such, the share of bioenergy is expected to grow by at least five time across scenarios studied for the long-term strategy of the U.S. between 2020 and 2050 (Horowitz et al, 2022). Notwithstanding the role of bioenergy in the energy systems, its deployment, costs and scalability are influenced by a number of factors. Some of these factors pertain to policy interventions such as imposition of a binding decarbonization target either at an economy-wide level or the sectoral level. Resource availability and type of biomass feedstock also varies considerably across regions. From a technological perspective, the readiness of bioenergy conversion pathways is subject to high variability. This influences the costs of deployment. Moreover, the sourcing of feedstock, grid carbon intensity, and co-product handling approaches all affect the life cycle efficacy of bioenergy. The latter, in turn, is particularly important in determining the extent to which bioenergy with CCS or BECCS can effectively deliver CDR (Fajardy and Mac Dowell, 2017).
Influenza Vaccination Timing
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Reimagining DOE Lab-University Partnership for the AI Era
This report describes observations and suggestions from a workshop on needs for partnerships between national laboratories and universities in the AI era. The workshop took place over two days in March of 2024 at Texas A&M University’s Bush School of Government and Public Service Washington, D.C., teaching site. Through good fortune this happened to be at the peak of cherry blossom season and the weather was beautiful. In attendance were professors and leadership from universities across the nation, members of four national laboratories, and a representative of the Office of Critical and Emerging Technologies in Department of Energy (DOE). This group spanned a broad range of disciplines—applied mathematics, materials science, nuclear security, intelligence, and more. The workshop also had the benefit of insights from Charlie McMillan, former director of Los Alamos National Laboratory, and retired Air Force Lieutenant General Jack Shanahan, who led AI efforts at the Pentagon.
BB-CVXOPT: Basic Block Execution Count Estimation and Extrapolation using Constrained Convex Optimization
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Pathways to instability in models of fire propagation
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Adventures in Nonlinearity
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Improving Performance and Cost of Direct Air Capture in Dynamic Conditions through Modeling and System Design
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Xenon Signal Denoising via Supervised, Semi-Supervised, and Unsupervised Models (arXiv:2603.27005)
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S&TR July August 2026 Density Functional Theory issue
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