Symmetric triangle quadrature rules for arbitrary functions
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97 MATHEMATICS AND COMPUTING↗
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Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions
Abstract The ability to efficiently load functions on quantum computers with high fidelity is essential for many quantum algorithms, including those for solving partial differential equations and Monte Carlo estimation. In this work, we introduce the Fourier series loader (FSL) method for preparing quantum states that exactly encode multi-dimensional Fourier series using linear-depth quantum circuits. Specifically, the FSL method prepares a (Dn)-qubit state encoding the 2 Dn -point uniform discretization of aD-dimensional function specified by aD-dimensional Fourier series. A free parameter,m, which must be less thann, determines the number of Fourier coefficients, 2 D ( m + 1 ) , used to represent the function. The FSL method uses a quantum circuit of depth at most 2 ( n − 2 ) + ⌈ log 2 ( n − m ) ⌉ + 2 D ( m + 1 ) + 2 − 2 D ( m + 1 ) , which is linear in the number of Fourier coefficients, and linear in the number of qubits (Dn) despite the fact that the loaded function’s discretization is over exponentially many (2 Dn ) points. The FSL circuit consists of at most D n + 2 D ( m + 1 ) + 1 − 1 single-qubit and D n ( n + 1 ) / 2 + 2 D ( m + 1 ) + 1 − 3 D ( m + 1 ) − 2 two-qubit gates; we present a classical compilation algorithm with runtime O ( 2 3 D ( m + 1 ) ) to determine the FSL circuit for a given Fourier series. The FSL method allows for the highly accurate loading of complex-valued functions that are well-approximated by a Fourier series with finitely many terms. We report results from noiseless quantum circuit simulations, illustrating the capability of the FSL method to load various continuous 1D functions, and a discontinuous 1D function, on 20 qubits with infidelities of less than 10 −6 and 10 −3 , respectively. We also demonstrate the practicality of the FSL method for near-term quantum computers by presenting experiments performed on the Quantinuum H1-1 and H1-2 trapped-ion quantum computers: we loaded a complex-valued function on 3 qubits with a fidelity of over 95 % , as well as various 1D real-valued functions on up to 6 qubits with classical fidelities ≈99%, and a 2D function on 10 qubits with a classical fidelity ≈94%.
Physics↗
Symmetric Triangle Quadrature Rules for Arbitrary Functions.
Abstract not provided.
Freno, Brian Andrew↗
Linear Velocity Problems Part 2: Thermodynamic Considerations
A compressible polytropic gas, in one dimensional planar, cylindrical, or spherical coordinate systems, is examined through four thermodynamic properties: mass density, pressure, specific internal energy (SIE), and entropy, under the assumptions that the fluid velocity is linearly proportional to the radial coordinate and that the Euler gas dynamics equations assert a self similar solution class. The behavior of the thermodynamics is almost entirely determined by an arbitrary function that results from the derivation of the density distribution. Through physical and other arguments, the arbitrary function can be plotted spatially with time profiles, providing a deeper understanding of the system and how the arbitrary function affects the behavior of the compressible gas.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Scale Invariance of the Homentropic Inviscid Euler Equations with Application to the Noh Problem
We investigate the inviscid compressible flow (Euler) equations constrained by an ”isentropic” equation of state (EOS), whose functional form in pressure is an arbitrary function of density alone. Under the aforementioned condition, we interrogate using symmetry methods the scale-invariance of the homentropic inviscid Euler equations. We find that under general conditions, we can reduce the inviscid Euler equations into a system of two coupled ordinary differential equations. To exemplify the utility of these results, we formulate two example scale-invariant, self-similar solutions. The first example includes a shock-free expanding bubble scenario, featuring a modified Tait EOS. The second example features the classical Noh problem, coupled to an arbitrary isentropic EOS. In this case, in order to satisfy the conditions set forth in the classical Noh problem, we find that the solution for the flow is given by a transcendental algebraic equation in the shocked density.
97 MATHEMATICS AND COMPUTING↗
Octofitter: Fast, Flexible, and Accurate Orbit Modeling to Detect Exoplanets
As next-generation imaging instruments and interferometers search for planets closer to their stars, they must contend with increasing orbital motion and longer integration times. These compounding effects make it difficult to detect faint planets but also present an opportunity. Increased orbital motion makes it possible to move the search for planets into the orbital domain, where direct images can be freely combined with the radial velocity and proper motion anomaly, even without a confirmed detection in any single epoch. In this paper, we present a fast and differentiable multimethod orbit-modeling and planet detection code called Octofitter. This code is designed to be highly modular and allows users to easily adjust priors, change parameterizations, and specify arbitrary function relations between the parameters of one or more planets. Octofitter further supplies tools for examining model outputs including prior and posterior predictive checks and simulation-based calibration. We demonstrate the capabilities of Octofitter on real and simulated data from different instruments and methods, including HD 91312, simulated JWST/NIRISS aperture masking interferometry observations, radial velocity curves, and grids of images from the Gemini Planet Imager. We show that Octofitter can reliably recover faint planets in long sequences of images with arbitrary orbital motion. This publicly available tool will enable the broad application of multiepoch and multimethod exoplanet detection, which could improve how future targeted ground- and space-based surveys are performed. Finally, its rapid convergence makes it a useful addition to the existing ecosystem of tools for modeling the orbits of directly imaged planets.
79 ASTRONOMY AND ASTROPHYSICS↗
Hamiltonian formulations for perturbed dissipationless plasma equations
The Hamiltonian formulations for the perturbed Vlasov–Maxwell equations and the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms of the perturbation derivative ∂ F / ∂ ϵ ≡ [ F , S ] of an arbitrary functional F [ ψ ] of the Vlasov–Maxwell fields ψ = ( f , E , B ) or the ideal MHD fields ψ = ( ρ , u , s , B ) , which are assumed to depend continuously on the (dimensionless) perturbation parameter ϵ . In this study, [ , ] denotes the functional Poisson bracket for each set of plasma equations and the perturbation action functional S is said to generate dynamically accessible perturbations of the plasma fields. The new Hamiltonian perturbation formulation introduces a framework for functional perturbation methods in plasma physics and highlights the crucial roles played by polarization and magnetization in Vlasov–Maxwell and ideal MHD perturbation theories. One application considered in this paper is a formulation of plasma stability that guarantees dynamical accessibility and leads to a natural generalization to higher-order perturbation theory.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Optimization techniques in self-similar compressible flow
We investigate the one-dimensional (1D) inviscid compressible flow equations for an ideal gas through the lens of optimization techniques. It is the case that, to our knowledge, optimization analysis applied to the so-called “linear velocity” solutions of the Euler compressible flow equations has not been previously conducted. Through both gradient-based and variational techniques, new variants of well-studied flow scenarios, i.e., self-similar, 1D, linear velocity solution class to idealized inviscid compressible flow equations, are determined, as encoded in both the kinematic and thermodynamic properties of this self-similar solution class. With the kinematics of the said solutions being driven by a self-similar “scale radius” and the thermodynamics being driven separately through the appearance of an arbitrary function, a myriad of new solution classes is possible. Acting as a guide to more realistic physical circumstances as well as discovery, it is the hope that the presented cases serve as the framework for future investigations into the intersection of self-similarity and optimization techniques. Fields of study that may find this work to be of interest include aerodynamic design, flow control, inertial confinement fusion, physics-informed neural networks, and other related areas of interest.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Energy density and spectrum of single-cycle and sub-cycle electromagnetic pulses
Based on the exact solution of the Maxwell equations in the form of a collapsing spherical vector wave specified by an arbitrary function of time, we have calculated the maximum energy density that can be achieved when focusing extremely short pulses of various shapes. It is shown that our earlier formula expressing the maximum energy density in terms of the spectrum parameters for Gaussian quasi-monochromatic pulses is approximately (with an accuracy of ±40 %) valid for the main types of extremely short pulses. (extremely short laser pulses)
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Metric DBSCAN
SAND2025-11725O Metric DBSCAN is an implementation of the popular DBSCAN clustering algorithm that works in general metric spaces. DBSCAN is a clustering algorithm, a fundamental building block in machine learning. It takes a set of objects and, given some notion of distance, identifies coherent groups of objects. With Metric DBSCAN, users can provide an arbitrary function to compute distance. Nearly all existing implementations of DBSCAN restrict distance to one of a few formulations. Metric DBScan accomplishes this cleanly and efficiently. The Python source code is on Github. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
Dalbey, Keith↗
End-to-End Differentiable Modeling and Management of the Environment
Focal Area: (2) Data acquisition and assimilation enabled by machine learning, AI, and advanced methods including experimental/network design/optimization. We emphasize the importance of leveraging optimization techniques from AI/machine learning (ML) to solve challenging problems in Earth system modeling. Science Challenge: Automatic differentiation has had a transformative effect on ML by allowing the calculation of gradients of arbitrary functions in an incredibly large class of models. We can potentially realize similar improvements in parameter estimation and control for Earth system models (ESMs) by reimplementing them in computational frameworks from ML. Practitioners working with large (>10 7 parameters) models in ML and AI can obtain good predictive performance in a range of spatiotemporal tasks by making use of optimization via stochastic gradient descent and incorporating prior knowledge at multiple levels. We propose writing ESMs in open-source computational frameworks such as Torch, Tensorflow, and JAX to greatly expand the scope of environmental forecasting and management challenges, which can be addressed by leveraging automatic differentiation and gradient descent-like algorithms. We do not call for a wholesale replacement of physical models with data-driven surrogates, but rather advocate for interleaving physical and empirical equations in a manner that is most faithful to the extent of our scientific knowledge and observational data. Central to this topic is the merging of differentiable physical simulations with differentiable optimization layers, which are now both beginning to come to the forefront.
54 ENVIRONMENTAL SCIENCES↗
Stochastic Approaches for Calculating and Aggregating Detection Probabilities for Nuclear Material Diversion
The authors built and tested a stochastic simulation to estimate achieved detection probabilities (DPs) on a stratum basis, over a tailorable range of diverted amounts from 0 to 2 significant quantities (SQ), using typical International Atomic Energy Agency (IAEA) inspection data: i.e., SQ in stratum, number of items, number of gross/partial/bias defect measurements conducted, and realistic relative standard deviation (RSD) values for typical IAEA verification measurements. For bulk strata, the model calculates achieved DP at 0.01 SQ diversion increments; for item strata, the model calculates DP using the smallest realistic diversion increment (e.g., a plate, pin, or coupon). After successfully benchmarking against IAEA deterministic models, the simulation was used to test the sensitivity of DP to certain standard assumptions and selected input parameters. First, the equal defect assumption was tested; the results suggest significant complexity in the effectiveness of partial defect measurements. Next, the authors explored the sensitivity of DP to the assumed RSD of attribute tests. Then, the authors compared non-normal models for instrument performance (e.g., logistic, step, or arbitrary functions) to the typical results from a normal distribution (characterized by RSD). This last comparison was supplemented with experimentally derived performance data for an HM-5 gamma spectrometer. The HM-5 was used to make enrichment measurements on both LEU and HEU MTR fuel elements as plates were removed, and the results fit with logistic and step curves and applied in the simulation. These stochastic DP results were compared to DP estimates from a deterministic model assuming a normal curve and typical RSD, yielding insights that could improve effectiveness in the field. These early results illustrate the potential of stochastic models to better understand achieved DP and to improve safeguards effectiveness.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
Optimization Through Multi-Fidelity Modeling
We present a novel method for optimizing parameter selection for simulations with an evaluation budget. We start with an existing method for building a multi-fidelity model out of many low-fidelity simulations and few high-fidelity simulations. We propose a novel method to simplify parameter selection without sacrificing performance. We verify these results and compare with existing literature. Next, we propose a novel algorithm which uses this difference model to suggest new points in the parameter design space to simulate. We add each point we simulate to the model to improve its quality for the next iteration. The algorithm trades off reducing the uncertainty of the existing model with optimization of the objective. The first is more useful when a large fraction of the computation budget remains. The second is more useful when a small fraction of the computation budget remains. Our method converges to the optimum by using a high-fidelity evaluation for just 16 of the 427 points. Our method is general enough to work if there is no low-fidelity model. Furthermore, it is agnostic to the underlying physics of the problem. Therefore, both the low-fidelity and high-fidelity models can be generated by any arbitrary function, including simulations and physical experiments.
97 MATHEMATICS AND COMPUTING↗
Evaluating Safeguards Statistical Assumptions via Stochastic Simulation
Herein, the authors built and tested a stochastic simulation to estimate achieved detection probabilities (DPs) on a stratum basis, over a tailorable range of diverted amounts from 0 to 2 SQ, using typical IAEA inspection data: i.e., SQ in stratum, number of items, number of gross/partial/bias defect measurements conducted, and realistic relative standard deviation (RSD) values for typical IAEA verification measurements. For bulk strata, the model calculates achieved DP at 0.01 SQ diversion increments; for item strata, the model calculates DP using the smallest realistic diversion increment (e.g., a plate, pin, or coupon). After successfully benchmarking against IAEA deterministic models, the simulation was used to test the sensitivity of DP to certain standard assumptions and selected input parameters. First, the equal defect assumption was tested; the results suggest significant complexity in the effectiveness of partial defect measurements. Next, the authors explored the sensitivity of DP to the assumed RSD of attribute tests. Then, the authors compared non-normal models for instrument performance (e.g., logistic, step, or arbitrary functions) to the typical results from a normal distribution (characterized by RSD). This last comparison was supplemented with experimentally derived performance data for an HM-5. The HM-5 was used to make enrichment measurements on both LEU and HEU MTR fuel elements as plates were removed, and the results fit with logistic and step curves and applied in the simulation. These stochastic DP results were compared to DP estimates from a deterministic model assuming a normal curve and typical RSD, yielding insights that could improve effectiveness in the field. These early results illustrate the potential of stochastic models to better understand achieved DP and to improve safeguards effectiveness.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
Method and system for in situ cross-linking of materials to produce three-dimensional features via electron beams from mobile accelerators
A method and system for in situ cross-linking of polymers, Bitumen, and other materials to produce arbitrary functional or ornamental three-dimensional features using electron beams provided by mobile accelerators comprises defining a desired pattern for imparting on a target area, mapping the target area, defining at least one discrete voxel in the target area according to the desired pattern to be imparted on the target area, assigning an irradiation value to each of the at least one discrete voxels, and delivering a dose of irradiation to each of the at least one discrete voxels according to the assigned irradiation value.
43 PARTICLE ACCELERATORS↗
Method and system for in situ cross-linking of materials to produce three-dimensional features via electron beams from mobile accelerators
A method and system for in situ cross-linking of polymers, Bitumen, and other materials to produce arbitrary functional or ornamental three-dimensional features using electron beams provided by mobile accelerators comprises defining a desired pattern for imparting on a target area, mapping the target area, defining at least one discrete voxel in the target area according to the desired pattern to be imparted on the target area, assigning an irradiation value to each of the at least one discrete voxels, and delivering a dose of irradiation to each of the at least one discrete voxels according to the assigned irradiation value.
Sauers, Aaron↗
Euler-Rodrigues Parameters: A Quantum Circuit to Calculate Rigid-Body Rotations
The use of vectorial parameterization to create geometrical representations in computational models has a large number of applications. One particular application is the calculation of the 3D rotational motion of rigid bodies, that could be used for the spatial location estimation from objects. Provided the algebraic nature of this problem, it could benefit from Quantum Computing, in particular several vectors could be superposed to be transformed with a single operation, providing a quantum processing advantage. In this article, we propose an implementation of a Quantum Computing algorithm to compute Euler-Rodrigues Parameters to model rigid body rotations to transform arbitrary functions, rotating multiple vectors in superposition. We developed this algorithm using Qiskit, taking into account the limitations imposed by the current Noisy Intermediate Scale Quantum (NISQ) devices, such as the reduced number of qubits available and the limited coherence time.
Pelaez, Emilio↗
The MOOSE fluid properties module
The fluid properties module in MOOSE~\cite{lindsay2022moose} serves a variety of fluid simulation applications based on MOOSE, including the MOOSE Navier Stokes module~\cite{moose_ns}, Pronghorn~\cite{pgh}, the MOOSE thermal hydraulics module, SAM~\cite{sam}, RELAP-7~\cite{relap7}, Sockeye~\cite{sockeye}, Pronghorn-subchannel~\cite{subchannel} and the MOOSE porous flow module~\cite{porous}. These applications are used to solve coarse mesh multi-dimensional thermal-hydraulics~\cite{pgh}, 1D systems analysis~\cite{sam,relap7} in nuclear reactor analysis, heat pipe modeling~\cite{sockeye} and porous flow simulations~\cite{porous} for underground gas storage and water seepage. The use of consistent fluid properties across fluid flow applications facilitates coupled flow simulations~\cite{anl_sam_pgh,osti_1889653}. Each application has historically driven the implementation of several fluid properties, which were later extended to be compatible with other applications. The unique diversity of applications of the module, due to its presence in MOOSE, has driven its expansion to new fluids, such as advanced nuclear reactor coolants and, more recently, arbitrary functions or tables-based property definitions, as detailed in section~\ref{content}, as well as numerous thermophysical properties and variable sets, as detailed in subsection~\ref{sec:prop}. The need for different discretizations of flow equations based on the compressibility of the fluid has motivated support for both primitive (pressure- and temperature-based) and conservative (internal energy- and specific volume-based) flow variables in the module. Thermodynamic relations are used to convert between these two formulations, as needed. The module serves a dual purpose of providing fluid properties for direct use in flow simulations and facilitating the implementation of user-specific fluid properties. Contributions of new properties for existing fluids or new fluids are strongly encouraged.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗