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At least 19 records

A Practical Solver for Scalar Data Topological Simplification

This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of “signal” persistence pairs to maintain, our approaches produces an output field g that is close to f and which optimizes (i) the cancellation of “non-signal” pairs, while (ii) preserving the “signal” pairs. In contrast to pre-existing simplification algorithms, our approach is not restricted to persistence pairs involving extrema and can thus address a larger class of topological features, in particular saddle pairs in three-dimensional scalar data. Our approach leverages recent generic persistence optimization frameworks and extends them with tailored accelerations specific to the problem of topological simplification. Extensive experiments report substantial accelerations over these frameworks, thereby making topological simplification optimization practical for real-life datasets. Our approach enables a direct visualization and analysis of the topologically simplified data, e.g., via isosurfaces of simplified topology (fewer components and handles). We apply our approach to the extraction of prominent filament structures in three-dimensional data. Specifically, we show that our pre-simplification of the data leads to practical improvements over standard topological techniques for removing filament loops. Here, we also show how our approach can be used to repair genus defects in surface processing. Finally, we provide a C++ implementation for reproducibility purposes.

97 MATHEMATICS AND COMPUTING

Application of Fuel Depletion Chain Simplification to Experiment Analysis in the Advanced Test Reactor

An irradiation experiment analysis can be informed by high-fidelity reactor engineering depletion results, but this comes at a computational cost. Applying depletion chain simplification to the advanced test reactor driver fuel before performing experiment depletions permits their programmatic parameters to be calculated faster, with a small penalty to accuracy. Here, this work contrasts the results of two irradiation experiments with different neutronic characteristics. Overall, the simplified nuclide library produced using a simple one-group microscopic cross-section library for a pressurized water reactor in the depletion chain simplification process performed comparably in terms of accuracy and runtime to the simplified nuclide library produced using a three-group microscopic cross-section library generated specifically for the advanced test reactor experiments being modeled. This is attributed to the additional nuclides and transmutation pathways preserved in the one-group cross-section library, which has data for 297 nuclides, compared to the three-group cross-section library, which has data for 217 nuclides. This indicates that a cross-section library with more nuclides is better than a cross-section library with fewer nuclides for the depletion chain simplification process, even if the cross-section library with fewer nuclides better represents the flux spectrum of the system being considered.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Adaptive continuity-preserving simplification of street networks

Street network data is widely used to study human-based activities and urban structure. Often, these data are geared towards transportation applications, which require highly granular, directed graphs that capture the complex relationships of potential traffic patterns. While this level of network detail is critical for certain fine-grained mobility models, it represents a hindrance for studies concerned with the morphology of the street network. For the latter case, street network simplification — the process of converting a highly granular input network into its most simple morphological form — is a necessary, but highly tedious preprocessing step, especially when conducted manually. In this manuscript, we develop and present a novel adaptive algorithm for simplifying street networks that is both fully automated and able to mimic results obtained through a manual simplification routine. The algorithm — available in the neatnet Python package — outperforms current state-of-the-art procedures when comparing those methods to manually, human-simplified data, while preserving network continuity.

Python

Adaptive continuity-preserving simplification of street networks

While street network data are nearly universally available, their representation is usually transportation-based. However, for many types of analyses, e.g., urban morphology or network science, unprocessed transportation-based street network data is unsuitable, making a cumbersome manual simplification process necessary. To address this challenge, in this paper we propose an algorithm for simplification of street networks, based on the detection of network portions that need to be simplified, and continuity-preserving heuristics that generate new geometries. The algorithm, released in the open-source Python package neatnet, facilitates the generation of morphological networks and generalises to various geographical contexts without a need to alter the parameters, while offering better performance than other available solutions.

Fleischmann, Martin [Charles University, Prague, C

M&C 2025: Application of Fuel Depletion Chain Simplification to Experiment Analysis in the Advanced Test Reactor

Irradiation experiment analysis can be informed by high-fidelity reactor engineering depletion results, but it comes at a computational cost. Applying depletion chain simplification to the Advanced Test Reactor driver fuel before performing experiment depletions permits their programmatic parameters to be calculated faster, with a small penalty to accuracy. This work contrasts the results of two irradiation experiments with different neutronic characteristics and provides general recommendations.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Thermo-hydraulic steam pipe models for district heating simulations: Simplifications to balance accuracy and simulation speed

Steam piping networks are essential for optimizing performance in industrial processes and district heating systems. However, dynamic models that balance thermo-hydraulic accuracy with computational efficiency remain limited. In response, this paper presents a new discretized steam pipe model based on the plug flow approach, capturing key thermo-hydraulic behaviors while simplifying steam phase change processes. Implemented in Modelica, the model accurately calculates temperature and pressure distributions along steam pipelines. To improve computational efficiency for district-scale simulations, five model simplifications are introduced: lumped thermo-hydraulic functions, empirical correlations, fluid state approximations, steady-state dynamics and inclusion of flow derivatives. These simplified models achieve 85%-98% accuracy in predicting pressure drop and condensation losses, including dynamic condensate behavior during pipe warm-up—a factor often overlooked in existing models. The models support diverse network configurations, scaling effectively to systems with multiple distribution pipes and connected building loads. Discrete models provide detailed insights but exhibit a cubic increase in simulation time as the network scales by N connected building O(N 2.42 ). In contrast, lumped models simulate 10–28 times faster than discrete, offering quadratic scaling of simulation time O(N 1.73 ). However, they still require 6 times more computation time than a lossless network, highlighting the inherent computational challenges of modeling compressible fluid flow. In conclusion, the steady-state lumped variant, with its near-linear scalability in computational time O(N 1.01 ), emerges as an efficient solution for preliminary design evaluations and extensive parametric studies.

15 GEOTHERMAL ENERGY

Extremely Scalable Distributed Computation of Contour Trees via Pre-Simplification

Contour trees offer an abstract representation of the level set topology in scalar fields and are widely used in topological data analysis and visualization. However, applying contour trees to large-scale scientific datasets remains challenging due to scalability limitations. Recent developments in distributed hierarchical contour trees have addressed these challenges by enabling scalable computation across distributed systems. Building on these structures, advanced analytical tasks—such as volumetric branch decomposition and contour extraction—have been introduced to facilitate large-scale scientific analysis. Despite these advancements, such analytical tasks substantially increase memory usage, which hampers scalability. In this paper, we propose a pre-simplification strategy to significantly reduce the memory overhead associated with analytical tasks on distributed hierarchical contour trees. We demonstrate enhanced scalability through strong scaling experiments, constructing the largest known contour tree—comprising over half a trillion nodes with complex topology—in under 15 minutes on a dataset containing 550 billion elements.

Li, Mingzhe [University of Utah]

Simplification of the Grid Model and its Impact on the Analysis of Electrical Power Systems

Here, this paper analyzes the impact of the use of Kron reduction on the state variables of a three-phase electrical system, even when it does not meet the necessary conditions for its application. Reduction is applied to a power line model to eliminate the equation corresponding to the neutral conductor of the line. The ATP program is used to model and simulate the behavior of an electrical system considering different degrees of disequilibrium as a reference for the comparison of results. The results show that under certain conditions of disequilibrium the Kron reduction can lead to significant errors in the state variables of the system.

Electric Power Systems

Shorter function summaries for finite state machine-based high consequence systems using logic synthesis and tautologies (Final Report LDRD 24-1302)

Computer programs are often viewed as collections of functions – each function has parameters (inputs) and computes a return value, and each has potential side effects that modify program state (outputs). In this research, a Sandia symbolic execution tool designed to support “human-in-the-loop” analysis was modified to automatically create “function summaries,” and a new tool, “diaboolical,” was created to support enhancing readability of the summary using a novel approach to bit-vector simplification that leverages logic synthesis and tautologies. For this effort, students at Auburn University created several finite state machines (FSMs) to serve as exemplars for high-consequence systems. Function summaries for each of the machines were obtained, and then portions of the summaries were simplified using both diaboolical and the simplification procedure of a popular SMT solver. A comparison of the results shows that diaboolical can often produce smaller function summaries, with expression length improvements over the unsimplified function summaries ranging from 0% to 90% for diaboolical and 0% to 65% for the SMT solver, though diaboolical had a significantly greater cost in time. Diaboolical was evaluated against a collection of “arbitrary” C-code as well as FSM exemplars, and for both datasets it achieved an approximately 10% improvement in expression length compared to simplifications that could be obtained using existing techniques. Function summaries can assist assurance efforts that evaluate existing systems and their executable code. A smaller function summary is likely easier for humans to understand and could thus increase the ability and efficacy of assurance practices centered around the analysis of executable artifacts.

97 MATHEMATICS AND COMPUTING

Directional finite difference method for directly solving 3D gyrokinetic field equations with enhanced accuracy

The gyrokinetic (GK) field equation is a three-dimensional (3D) elliptic equation, but it is often simplified to a set of two-dimensional (2D) equations by assuming that the field does not vary along a specific direction. However, this simplification can introduce inevitable 0th-order numerical errors, as nonlinear mode coupling in toroidal geometry can produce undesirable harmonic modes that violate the assumption. In this work, we propose a novel directional finite difference method (FDM) with a local coordinate transformation to better resolve the target field of interest. The directional FDM can accurately solve 3D GK field equations without simplifications, which can overcome the limitations of conventional methods. The accuracy and efficiency of different FDMs are analyzed in great detail for a variety of geometries, from simple 2D Cartesian coordinates to realistic 3D curvilinear coordinates. The 0th-order numerical errors of simplified 2D GK equations were found to be more problematic for low-harmonic modes and low aspect ratio geometries such as spherical tokamaks. On the other hand, the directional 3D FDM can accurately resolve a much wider range of harmonic modes aligned to the direction of interest, including the low-harmonic modes. In conclusion, we demonstrate that the directional 3D FDM is a highly effective algorithm for solving the 3D GK field equations, achieving accuracy improvements of 10 to 100 times or more, particularly for low-harmonic modes in spherical tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Data for Impact of Vertical and Seasonal Variation in Leaf Traits on Simulating Soybean Canopy Photosynthesis via 1D and 3D Modeling

Accurate modeling of photosynthesis is crucial for predicting crop productivity and quantifying the carbon cycle in agroecosystems. Leaf traits are essential inputs for modeling canopy photosynthesis. Yet, many existing models still use fixed plant functional type (PTF)-based values to parameterize leaf traits under a big-leaf or two-big-leaf assumption, neglecting their vertical profiles and seasonal changes. This simplification may introduce significant uncertainties in estimating gross primary productivity (GPP). In this study, we simulated soybean GPP and tested the effects of vertical and seasonal variation in three key leaf photosynthetic traits: the maximum carboxylation rate at 25 °C (Vcmax25), leaf chlorophyll content (LCC), and leaf mass per area (LMA) in the 1D-SCOPE and 3D-Helios models. Weekly field measurements were conducted during the growing season of 2024 to support the simulation. We designed ten leaf trait parameterization schemes by incorporating different combinations of vertical profiles and seasonal changes, while assuming homogeneous canopy architecture in both models. Our results revealed that Vcmax25 vertical and seasonal variation had the strongest influence on simulated GPP in both 1D and 3D models, while LCC and LMA effects were minimal. Particularly, the scheme with an empirically parameterized Vcmax25 profile achieved comparable performance to the scheme with the measured Vcmax25 profile. Both 1D-SCOPE and 3D-Helios accurately modeled GPP (SCOPE: R2 = 0.87, Bias = 0.55 µmol m⁻² s⁻¹; Helios: R2 = 0.9, Bias = 0.22 µmol m⁻² s⁻¹) under the most complex scheme, and their responses to vertical and seasonal variation in leaf traits were consistent, demonstrating the robustness of our findings. Based on our findings, we propose a scalable framework for parameterizing leaf traits to improve GPP simulations. This study contributes to improving the representation of leaf trait dynamics in canopy-level photosynthesis models, potentially enhancing our ability to predict crop productivity and understand agroecosystem carbon dynamics.

Photosynthesis

Learning the simplicity of scattering amplitudes

The simplification and reorganization of complex expressions lies at the core of scientific progress, particularly in theoretical high-energy physics. This work explores the application of machine learning to a particular facet of this challenge: the task of simplifying scattering amplitudes expressed in terms of spinor-helicity variables. We demonstrate that an encoder-decoder transformer architecture achieves impressive simplification capabilities for expressions composed of handfuls of terms. Lengthier expressions are implemented in an additional embedding network, trained using contrastive learning, which isolates subexpressions that are more likely to simplify. The resulting framework is capable of reducing expressions with hundreds of terms—a regular occurrence in quantum field theory calculations—to vastly simpler equivalent expressions. Starting from lengthy input expressions, our networks can generate the Parke-Taylor formula for five-point gluon scattering, as well as new compact expressions for five-point amplitudes involving scalars and gravitons.

Cheung, Clifford [California Institute of Technolo

Small-scale Assessment of Simplified Ceramic Waste Form Processing

The feasibility of directly processing glass-bonded sodalite ceramic waste form materials by heating a mixture of Zeolite 4A, chloride salt, and sodium borosilicate binder glass was demonstrated by generating laboratory-scale materials. This direct processing method eliminates pre-setting the moisture content of the Zeolite 4A, eliminates the step of occluding salt in the prepared Zeolite 4A prior to processing, and can be conducted using larger particle sizes of crushed Zeolite 4A and crushed borosilicate glass than those called for in the current method. These simplifications are expected to facilitate material transfer and handling in a hot cell or controlled atmosphere environment and be more readily implemented at large scale than the current method. Most materials made to assess these simplifications were directly processed at 925 °C for two hours in an argon atmosphere glovebox, but one material was processed at 925 °C for four hours and one material was processed at 880 °C for two hours. Sodalite was generated and became microencapsulated by the binder glass in all materials. The microstructures were uniform throughout each product, were similar in all products, and were similar to the microstructures of materials made previously using the pressureless consolidation or hot isostatic pressing methods. Various formulations showed the efficiency of sodalite generation was not sensitive to the salt-to-Zeolite 4A ratio or salt-to-glass mass ratio, although a greater relative mass of glass is required to encapsulate sodalite generated from large particles of aggregated Zeolite 4A. The upper limit of salt loadings that can be effectively processed remains to be determined. The effectiveness of direct processing provided new insights into the conversion mechanism. The salt was likely dissolved into the glass that transported NaCl into the Zeolite 4A aggregates and sodalite was generated in situ as NaCl migrated from the outside of the aggregate inward. Other salt cations (e.g., potassium, strontium, cesium, and probably lithium) remain dissolved in the glass encapsulating the zeolite/sodalite domains. When the glass solidifies during cooling, small halite inclusion phases form in glass within sodalite domains and large mixed salt inclusions form in glass surrounding the sodalite due to the low solubility of chloride in the (solid) glass. Other salt cations were oxidized during processing and formed inclusions in the bulk glass (e.g., neodymium). Initial degradation tests show the dissolution behavior of directly processed CWF (SCWF) materials is similar to CWF materials made using different methods.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W

The impact of simplified window and exhaust fan assumptions on indoor air quality in multifamily buildings

In residential buildings, the indoor air quality can be significantly affected by ventilation measures initiated by occupants, including the operation of windows and in-unit exhaust fans in kitchens and bathrooms. Many simulations simplify these factors by disregarding window opening behaviors and using fixed schedules for exhaust fan operation across all residential units. To estimate the impact of these simplifications in the U.S. context, this study used coupled CONTAM and EnergyPlus models to simulate airflow and contaminant transport in multifamily buildings. The coupled models parametrically varied climate zone, building airtightness, and mechanical ventilation system types. The study conducted a sensitivity analysis on two key occupant behaviors: (1) operating kitchen and bathroom exhausts on different schedules in individual dwelling units, and (2) scheduling open windows on ground and top floors. The simplified assumptions (i.e. uniform in-unit exhaust fan operation and window operation) had a minimal impact on inter-unit air flow and contaminant transport simulations across a broad range of building air leakage and mechanical ventilation system types. These findings suggest that for buildings with tight construction it is reasonable for most modelling and simulation efforts to ignore the effects of non-uniform exhaust fan operation and window opening.

Occupant behavior

Global symmetry and integral constraint on superconformal lines in four dimensions

We study properties of point-like impurities preserving flavor symmetry and supersymmetry in four-dimensional 𝒩 = 2 field theories. At large distances, such impurities are described by half-BPS superconformal line defects. By working in the AdS 2 × S 2 conformal frame, we develop a novel and simpler way of deriving the superconformal Ward identities relating the various two-point functions of flavor current multiplet operators in the presence of the defect. We use these relations to simplify a certain integrated two-point function of flavor current multiplet operators that, in Lagrangian theories, can be computed using supersymmetric localization. The simplification gives an integral constraint on the two-point function of the flavor current multiplet superconformal primary with trivial integration measure in the AdS 2 × S 2 conformal frame. We provide several consistency checks on our Ward identities.

extended supersymmetry

Relations between anomalous dimensions in the Regge limit

We extend the recent formalism developed for computing rapidity anomalous dimension of form factors using unitarity to the problem of high-energy near forward scattering. By combining the factorization of 2 → 2 scattering in the effective field theory (EFT) for Glauber operators with definite signature amplitudes, we derive an expression that relates anomalous dimensions (including Regge trajectories) to cut amplitudes, leading to significant computational simplifications. We demonstrate this explicitly by computing the one and two-loop Regge trajectories. Our formalism can also be used to bootstrap anomalous dimensions of operators not related by symmetries. As an example, we show that the full anomalous dimensions (including both the Regge pole and cut pieces) of the two Glauber exchange anti-symmetric octet operator, can be determined from the anomalous dimension of the single Glauber exchange operator. Many other such relations exist between other color channels at each order in α.

Effective Field Theories

Circles and triangles, the NLSM and Tr(Φ 3 )

A surprising connection has recently been made between the amplitudes for Tr(Φ 3 ) theory and the non-linear sigma model (NLSM). A simple shift of kinematic variables naturally suggested by the associahedron/stringy representation of Tr(Φ 3 ) theory yields pion amplitudes at all loops. In this note we provide an elementary motivation and proof for this link going in the opposite direction, starting from the non-linear sigma model and discovering its formulation as a sum over triangulations of surfaces with simple numerator factors. This uses an ancient connection between “circles” and “triangles”, interpreting the equation y = $\sqrt{1 – x^2}$ both as parametrizing points a circle as well as generating the number of triangulations of polygons. A further simplification of the numerator factors exposes them as arising from the kinematically shifted Tr(Φ3) theory, and gives rise to novel tropical representations of NLSM amplitudes. The connection to Tr(Φ 3 ) theory defines a natural notion of “surface-soft limit” intrinsic to curves on surfaces. Remarkably, with this definition, the soft limit of pion amplitudes vanishes directly at the level of the integrand, via obvious pairwise cancellations. We also give simple, explicit expressions for the multi-soft factors for tree and loop-level integrands in the limit as any number of pions are taken “surface-soft”.

Scattering Amplitudes

Extracting the asymptotic behavior of S-matrix elements from their phases

The asymptotic kinematic limits of S-matrices are dominated by large logarithms which, roughly speaking, fall into two categories: those which are controlled by a renormalization group (RG) scale, which we may think of as logs involving ratios of invariant mass scales, and those which are functions of ratios of rapidities, so called “rapidity logs”. It has been pointed out by Caron-Huot and Wilhlem [1] that RG anomalous dimension can be extracted from the phase of the S-matrix, which can greatly simplify calculations via unitarity methods. In this paper we generalize the results of [1] to show that the phase can be used to reconstruct rapidity anomalous dimensions, by performing a special type of complex boost. The methodology introduced allows one to calculate without the need for a rapidity regulator which can lead to significant simplifications. We demonstrate the use of this method to derive the rapidity anomalous dimensions in the Sudakov form factor and the two parton soft function at two loops order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS