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At least 361 records · Page 20

Evaluating convective parameterization closures using cloud‐resolving model simulation of tropical deep convection

Abstract Closure is an important component of a mass flux‐based convective parameterization scheme, and it determines the amount of convection with the aid of a large‐scale variable (closure variable) that is sensitive to convection. In this study, we have evaluated and quantified the relationship between commonly used closure variables and convection for a range of global climate model (GCM) horizontal resolutions, taking convective precipitation and mass flux at 600 hPa as measures for deep convection. We have used cloud‐resolving model simulation data to create domain averages representing GCM horizontal resolutions of 128 km, 64 km, 32 km, 16 km, 8 km, and 4 km. Lead‐lag correlation analysis shows that except moisture convergence and turbulent kinetic energy, none of the other closure variables evaluated in this study show any relationship with convection for the six subdomain sizes. It is found that the correlation between moisture convergence and convective precipitation is largest when moisture convergence leads convection. This correlation weakens as the subdomain size decreases to 8 km or smaller. Although convective precipitation and mass flux increase with moisture convergence at a given subdomain size, as the subdomain size increases, the rate at which they increase becomes smaller. This suggests that moisture convergence‐based closure should scale down the predicted mass flux for a given moisture convergence as GCM resolution increases.

Suhas, E.↗

A preconditioning technique for Schur complement systems arising in stochastic optimization

Deterministic sample average approximations of stochastic programming problems with recourse are suitable for a scenario-based parallelization. In this paper the parallelization is obtained by using an interior-point method and a Schur complement mechanism for the interior-point linear systems. However, the direct linear solves involving the dense Schur complement matrix are expensive, and adversely affect the scalability of this approach. We address this issue by proposing a stochastic preconditioner for the Schur complement matrix and by using Krylov iterative methods for the solution of the dense linear systems. The stochastic preconditioner is built based on a subset of existing scenarios and can be assembled and factorized on a separate process before the computation of the Schur complement matrix finishes on the remaining processes. The expensive factorization of the Schur complement is removed from the parallel execution flow and the scaling of the optimization solver is considerably improved with this approach. The spectral analysis indicates an exponentially fast convergence in probability to 1 of the eigenvalues of the preconditioned matrix with the number of scenarios incorporated in the preconditioner. Numerical experiments performed on the relaxation of a unit commitment problem show good performance, in terms of both the accuracy of the solution and the execution time.

99 GENERAL AND MISCELLANEOUS↗

Learning continuous models for continuous physics

Abstract Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.

97 MATHEMATICS AND COMPUTING↗

Stability of spherical converging shock wave

Based on Guderley's self-similar solution, stability of spherical converging shock wave is studied. A rigorous linear perturbation theory is developed, in which the growth rate of perturbation is given as a function of the spherical harmonic number ℓ and the specific heats ratio γ. Numerical calculation reveals the existence of a γ-dependent cut-off mode number ℓ{sub c}, such that all the eigenmode perturbations for ℓ > ℓ{sub c} are smeared out as the shock wave converges at the center. The analysis is applied to partially spherical geometries to give significant implication for different ignition schemes of inertial confinement fusion. Two-dimensional hydrodynamic simulations are performed to verify the theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Temporal Summary Images: An Approach to Narrative Visualization via Interactive Annotation Generation and Placement

Visualization is a powerful technique for analysis and communication of complex, multidimensional, and time-varying data. However, it can be difficult to manually synthesize a coherent narrative in a chart or graph due to the quantity of visualized attributes, a variety of salient features, and the awareness required to interpret points of interest (POIs). We present Temporal Summary Images (TSIs) as an approach for both exploring this data and creating stories from it. As a visualization, a TSI is composed of three common components: (1) a temporal layout, (2) comic strip-style data snapshots, and (3) textual annotations. To augment user analysis and exploration, we have developed a number of interactive techniques that recommend relevant data features and design choices, including an automatic annotations workflow. As the analysis and visual design processes converge, the resultant image becomes appropriate for data storytelling. For validation, we use a prototype implementation for TSIs to conduct two case studies with large-scale, scientific simulation datasets.

97 MATHEMATICS AND COMPUTING↗

Development of a Method for Shape Optimization for a Gas Turbine Fuel Injector Design Using Metal-Additive Manufacturing

Adjoint shape optimization has enabled physics-based optimal designs for aerodynamic surfaces. Additive manufacturing (AM) makes it possible to manufacture complex shapes. However, there has been a gap between optimal and manufacturable surfaces due to the inherent limitations of commercial computational fluid dynamics (CFD) codes to implement geometric constraints during adjoint computation. In such cases, the design sensitivities are exported and used to perform constrained shape modifications using parametric information stored in computer aided design (CAD) files to satisfy manufacturability constraints. However, modifying the design using adjoint methods in CFD solvers and performing constrained shape modification in CAD can lead to inconsistencies due to different shape parameterization schemes. This paper describes a method to enable the simultaneous optimization of the fluid domain and impose AM manufacturability constraints, resolving one of the key issues of geometry definition for isogeometric analysis. Similar to a grid convergence study, the proposed method verifies the consistencies between shape parameterization techniques present within commercial CAD and CFD software during mesh movement as a part of the adjoint shape optimization routine. By identifying the appropriate parameters essential to a shape optimization study, the error metric between the different parameterization techniques converges to demonstrate sufficient consistencies for justifiable exchange of data between CAD and CFD. For the identified shape optimization parameters, the error metric to measure the deviation between the two parameterization schemes lies within the AM laser-powder bed fusion (L-PBF) process tolerance. Additionally, comparison for subsequent objective function calculations between iterations of the optimization loop showed acceptable differences within 1% variation between the modified geometries obtained using the two parameterization schemes. This method provides justification for the use of multiphysics guided adjoint design sensitivities computed in CFD software to perform shape modifications in CAD to incorporate AM manufacturability constraints during the shape optimization loop such that optimal designs are also additively manufacturable.

33 ADVANCED PROPULSION SYSTEMS↗

Large Language Model for Validation, Optical Calibration, and Learning (VOCAL) Distributed Temperature Sensing Interface

Distributed temperature sensing (DTS) using fiber optic sensors (FOS) offers a promising method for temperature measurements in advanced reactors, such as sodium fast reactors and molten salt cooled reactors. To support the calibration and validation of DTS measurements, Argonne National Laboratory developed the Validation, Optical Calibration, and Learning (VOCAL) software package. This report describes the integration of a local large language model (LLM) with a retrieval-augmented generation (RAG) system into the VOCAL interface to serve as an interactive user assistant. The LLM framework enhances the VOCAL platform’s accessibility to users by explaining interface components, clarifying inputs and outputs, and answering user queries dynamically in real-time. The accuracy of the LLM assistant performance was evaluated with 20 queries regarding the interface and its parameters using experimental data from the Thermal Hydraulic Experimental Test Article (THETA) facility. Results demonstrate that the LLM achieved a 95% accuracy rate, with a BERTScore of 0.8816 and SBERT value of 0.7417. Furthermore, validation of the RAG system within the LLM framework showed optimal accuracy with k-values between 1 and 2 using the k-refinement convergence test. The prompt perturbation analysis demonstrated good initial consistency for the RAG system, exhibiting the highest accuracy under punctuation variations and the greatest sensitivity under query reordering. Notably, the model’s errors were limited to data retrieval failures rather than factual hallucinations, reinforcing its baseline reliability. The integration of LLM provides a highly accurate, userfriendly enhancement to the VOCAL platform without disrupting its core computational capabilities for FOS calibration and validation.

Hong, Evan↗

Inferring the Contribution of Microbial Taxa and Organic Matter Molecular Formulas to Ecological Assembly

Understanding the mechanisms underlying the assembly of communities has long been the goal of many ecological studies. While several studies have evaluated community wide ecological assembly, fewer have focused on investigating the impacts of individual members within a community or assemblage on ecological assembly. Here, we adapted a previous null model β-nearest taxon index (βNTI) to measure the contribution of individual features within an ecological community to overall assembly. This new metric, called feature-level βNTI (βNTI feat ), enables researchers to determine whether ecological features (e.g., individual microbial taxa) contribute to divergence, convergence, or have insignificant impacts across spatiotemporally resolved metacommunities or meta-assemblages. Using βNTI feat , we revealed that unclassified microbial lineages often contributed to community divergence while diverse groups (e.g., Crenarchaeota, Alphaproteobacteria, and Gammaproteobacteria) contributed to convergence. We also demonstrate that βNTI feat can be extended to other ecological assemblages such as organic molecules comprising organic matter (OM) pools. OM had more inconsistent trends compared to the microbial community though CHO-containing molecular formulas often contributed to convergence, while nitrogen and phosphorus-containing formulas contributed to both convergence and divergence. A network analysis was used to relate βNTI feat values from the putatively active microbial community and the OM assemblage and examine potentially common contributions to ecological assembly across different communities/assemblages. This analysis revealed that P-containing formulas often contributed to convergence/divergence separately from other ecological features and N-containing formulas often contributed to assembly in coordination with microorganisms. Additionally, members of Family Geobacteraceae were often observed to contribute to convergence/divergence in conjunction with both N- and P-containing formulas, suggesting a coordinated ecological role for family members and the nitrogen/phosphorus cycle. Overall, we show that βNTI feat offers opportunities to investigate the community or assemblage members, which shape the phylogenetic or functional landscape, and demonstrate the potential to evaluate potential points of coordination across various community types.

59 BASIC BIOLOGICAL SCIENCES↗

Accumulated approximation: A new method for structural optimization by iterative improvement

A new method for the solution of non-linear mathematical programming problems in the field of structural optimization is presented. It is an iterative scheme which for each iteration refines the approximation of objective and constraint functions by accumulating the function values of previously visited design points. The method has proven to be competitive for a number of well-known examples of which one is presented here. Furthermore because of the accumulation strategy, the method produces convergence even when the sensitivity analysis is inaccurate.

Rasmussen, John↗

Convergence acceleration of an aeroelastic Navier-Stokes solver

New capabilities have been added to a Navier-Stokes solver to perform steady-state simulations more efficiently. The flow solver for solving the Navier-Stokes equations is completely rewritten with a combination of the LU-SGS (Lower-Upper factored Symmetric Gauss-Seidel) implicit method and the modified HLLE (Harten-Lax-van Leer-Einfeldt) upwind scheme. A pseudo-time marching method is used for the directly coupled structural equations to improve overall convergence rates for static aeroelastic analysis. Results are demonstrated for transonic flows over rigid and flexible wings.

Obayashi, S.↗

An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.

Deng, Qingping↗

A Non-Linear Approach to Spacecraft Trajectory Control in the Vicinity of a Libration Point

An expanding interest in mission design strategies that exploit libration point regions demands the continued development of enhanced, efficient, control algorithms for station-keeping and formation maintenance. This paper discusses the development of a non-linear, station-keeping, control algorithm for trajectories in the vicinity of a libration point. The control law guarantees exponential convergence, based on a Lyaponov analysis. Controller performance is evaluated using FreeFlyer(R) and MATLAB(R) for a spacecraft stationed near the L2 libration point in the Earth-Moon system, tracking a pre-defined reference trajectory. Evaluation metrics are fuel usage and tracking accuracy. Simulation results are compared with a linear-based controller for a spacecraft tracking the same reference trajectory. Although the analysis is framed in the context of station-keeping, the control algorithm is equally applicable to a formation flying problem with an appropriate definition of the reference trajectory.

Luquette, Richard J.↗

A Non-Linear Approach to Spacecraft Formation Control in the Vicinity of a Collinear Libration Point

An expanding interest in mission design strategies that exploit libration point regions demands the continued development of enhanced, efficient, control algorithms for station-keeping and formation maintenance. This paper discusses the development of a non-linear, formation maintenance, control algorithm for trajectories in the vicinity of a libration point. However, the formulation holds for any trajectory governed by the equations of motion for the restricted three body problem. The control law guarantees exponential convergence, based on a Lyaponov analysis. FreeFlyer and MATLAB provide the simulation environment for controller performance evaluation. The simulation, modeled after the MAXIM Pathfinder mission, maintains the relative position of a "follower" spacecraft with respect to a "leader" spacecraft, stationed near the L2 libration point in the Sun-Earth system. Evaluation metrics are fuel usage and tracking accuracy.

Luquette, Richard J.↗

Numerical Solution of Multi-Dimensional Hyperbolic Conservation Laws on Unstructured Meshes

The lecture material will discuss the application of one-dimensional approximate Riemann solutions and high order accurate data reconstruction as building blocks for solving multi-dimensional hyperbolic equations. This building block procedure is well-documented in the nationally available literature. The relevant stability and convergence theory using positive operator analysis will also be presented. All participants in the minisymposium will be asked to solve one or more generic test problems so that a critical comparison of accuracy can be made among differing approaches.

Barth, Timothy J.↗

Guidelines for Computing Longitudinal Dynamic Stability Characteristics of a Subsonic Transport

A systematic study is presented to guide the selection of a numerical solution strategy for URANS computation of a subsonic transport configuration undergoing simulated forced oscillation about its pitch axis. Forced oscillation is central to the prevalent wind tunnel methodology for quantifying aircraft dynamic stability derivatives from force and moment coefficients, which is the ultimate goal for the computational simulations. Extensive computations are performed that lead in key insights of the critical numerical parameters affecting solution convergence. A preliminary linear harmonic analysis is included to demonstrate the potential of extracting dynamic stability derivatives from computational solutions.

Thompson, Joseph R.↗

Application of Simplified Pn Approximation to Angular Distribution of Neutron Source in MOC Calculations

Concept of the simplified Pn approximation is applied to represent angular distribution of anisotropic scattering source in order to decrease number of angular flux moments stored during transport sweeps. In practical design calculations, anisotropic scattering is usually taken into account through transport correction. Though the transport correction yields a reasonable result for many cases, detail treatment of anisotropic scattering is desirable in high fidelity neutronics calculations, e.g., a direct heterogeneous transport calculation in three dimensional geometry. Direct treatment of anisotropic scattering has been established, which commonly utilizes the series expansion by the spherical harmonics functions. The expansion by the spherical harmonics functions requires (L + 1){sup 2} angular flux moments when up to L-th order anisotropy is taken into account. The previous studies suggested that consideration up to P3 anisotropic scattering yields converged results in many neutronics analysis for LWR. In this case, (3 + 1){sup 2} = 16 angular flux moments should be stored and retained in each flux region of each energy group. This storage requirement would be significant in a large scale calculation with many flux regions and energy groups. Chao et al. proposed an explicit angular flux representation based on the simplified Pn (SPn) method. Number of angular flux moments required in a SPn calculation is (L + 1) when L-th order angular distribution is considered. Since the SPn method adopts the physical picture of 'locally 1D system' along particular direction, required number of angular flux moments is much smaller than that based on the spherical harmonics functions. In the present study, concept of the SPn method is applied to describe angular distribution of anisotropic scattering source. By adopting the SPn approximation, as described above, number of angular flux moments can be significantly reduced. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Geometry-aware training of factorized layers in tensor Tucker format

Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during train and inference of large networks. Given its easy implementation and flexibility, one promising approach is layer factorization, which reshapes weight tensors into a matrix format and parameterizes it as the product of two rank-r matrices. However, this family of approaches often requires an initial full-model warm-up phase, prior knowledge of a feasible rank, and it is sensitive to parameter initialization.In this work, we introduce a novel approach to train the factors of a Tucker decomposition of the weight tensors. Our training proposal proves to be optimal in locally approximating the original unfactorized dynamics and stable for the initialization. Furthermore, the rank of each mode is dynamically updated during training.We provide a theoretical analysis of the algorithm, showing convergence, approximation and local descent guarantees. The method's performance is further illustrated through a variety of experiments, showing remarkable training compression rates and comparable or even better performance than the full baseline and alternative layer factorization strategies.

Zangrando, Emanuele [Gran Sasso Science Institute ↗

Minimization of thermal deformation in crystal optics for high repetition-rate FEL

Minimizing thermal deformation in X-ray crystal optics is crucial for preserving coherence and wavefront in high-repetition-rate free-electron lasers (FELs). This study presents two approaches to reduce pulse-by-pulse transient thermal deformation in diamond crystals used in cavity-based X-ray FELs (CBXFELs): (1) cryogenic cooling with liquid nitrogen (LN₂), and (2) second-order correction via focusing optics. We revisit the temperature-dependent thermal-mechanical properties of diamond and silicon, implement a finite-element analysis (FEA) method to accelerate convergence to a quasisteady-state regime. Results show that LN₂-cooled diamond crystals meet the stringent deformation requirement of less than 15 pm RMS for the pulse at mJ scale at 1 MHz repetition frequency, and up to 1.5 mJ for 100 kHz. Second-order correction by using focusing elements within the cavity can reduce the impact of thermal deformation for both liquid nitrogen and water cooling.

free electron laser↗