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Results for “Algorithmic differentiation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The Locus Algorithm II: A robust software system to maximise the quality of fields of view for Differential Photometry

We present the software system developed to implement the Locus Algorithm, a novel algorithm designed to maximise the performance of differential photometry systems by optimising the number and quality of reference stars in the Field of View with the target. Firstly, we state the design requirements, constraints and ambitions for the software system required to implement this algorithm. Then, a detailed software design is presented for the system in operation. Next, the data design including file structures used and the data environment required for the system are defined. Finally, we conclude by illustrating the scaling requirements which mandate a high-performance computing implementation of this system, which is discussed in the other papers in this series.

Nolan, Kevin↗
DOE OSTI2020

Machine learning and serving of discrete field theories

A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the learned discrete field theory to predict new observations of the field for new boundary and initial conditions. The approach of learning discrete field theories overcomes the difficulties associated with learning continuous theories by artificial intelligence. The serving algorithm of discrete field theories belongs to the family of structure-preserving geometric algorithms, which have been proven to be superior to the conventional algorithms based on discretization of differential equations. The effectiveness of the method and algorithms developed is demonstrated using the examples of nonlinear oscillations and the Kepler problem. In particular, the learning algorithm learns a discrete field theory from a set of data of planetary orbits similar to what Kepler inherited from Tycho Brahe in 1601, and the serving algorithm correctly predicts other planetary orbits, including parabolic and hyperbolic escaping orbits, of the solar system without learning or knowing Newton’s laws of motion and universal gravitation. The proposed algorithms are expected to be applicable when the effects of special relativity and general relativity are important.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A high-order WENO-limited finite-volume algorithm for atmospheric flow using the ADER-differential transform time discretization

A high-order-accurate weighted essentially non-oscillatory (WENO) limited upwind finite-volume scheme is detailed for the compressible, nonhydrostatic, inviscid Euler equations using an arbitrary derivatives (ADER) time-stepping scheme based on differential transforms (DTs). A second-order-accurate alternating Strang dimensional splitting is compared against multidimensional simulation with 2D transport using solid body rotation of various data. The two were found to give nearly identical accuracy in orthogonal, Cartesian coordinates. Orders of convergence are demonstrated at up to ninth-order accuracy with 2D transport. 1D transport is used to confirm that error decreases monotonically with increasing order of accuracy with WENO limiting even for discontinuous data. Further, WENO limiting always decreased the error compared with simulation without limiting in the L 1 norm. A series of standard 2D compressible nonhydrostatic Euler equation test cases were validated against previous results from literature. Finally, it was demonstrated that increasing the order of accuracy led to better resolved features and increased power for kinetic energy at small wavelengths.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

An explicitly solvable energy-conserving algorithm for pitch-angle scattering in magnetized plasmas

In this work, we develop an Explicitly Solvable Energy-Conserving (ESEC) algorithm for the Stochastic Differential Equation (SDE) describing the pitch-angle scattering process in magnetized plasmas. The Cayley transform is used to calculate both the deterministic gyromotion and stochastic scattering, affording the algorithm to be explicitly solvable and exactly energy conserving. An unusual property of the SDE for pitch-angle scattering is that its coefficients diverge at the zero velocity and do not satisfy the global Lipschitz condition. Consequently, when standard numerical methods, such as the Euler-Maruyama (EM), are applied, numerical convergence is difficult to establish. For the proposed ESEC algorithm, its energy-preserving property enables us to overcome this obstacle. We rigorously prove that the ESEC algorithm is order 1/2 strongly convergent. This result is confirmed by detailed numerical studies. For the case of pitch-angle scattering in a magnetized plasma with a constant magnetic field, the numerical solution is benchmarked against the analytical solution, and excellent agreements are found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

The Locus Algorithm III: A Grid Computing system to generate catalogues of optimised pointings for Differential Photometry

This paper discusses the hardware and software components of the Grid Computing system used to implement the Locus Algorithm to identify optimum pointings for differential photometry of 61,662,376 stars and 23,799 quasars. The scale of the data, together with initial operational assessments demanded a High Performance Computing (HPC) system to complete the data analysis. Grid computing was chosen as the HPC solution as the optimum choice available within this project. The physical and logical structure of the National Grid computing Infrastructure informed the approach that was taken. That approach was one of layered separation of the different project components to enable maximum flexibility and extensibility.

Creaner, Oisń↗
DOE OSTI2025

ESD: Ethernet Signal Differentiator [Poster]

Can Machine Learning Algorithms be trained to interpret and decode passively observed Automative Ethernet full-duplex signals without access to the original signals transmitted by either endpoint?

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Differentiation and classification of bacterial endotoxins based on surface enhanced Raman scattering and advanced machine learning

Bacterial endotoxin, a major component of the Gram-negative bacterial outer membrane leaflet, is a lipopolysaccharide shed from bacteria during their growth and infection and can be utilized as a biomarker for bacterial detection. Here, the surface enhanced Raman scattering (SERS) spectra of eleven bacterial endotoxins with an average detection amount of 8.75 pg per measurement have been obtained based on silver nanorod array substrates, and the characteristic SERS peaks have been identified. With appropriate spectral pre-processing procedures, different classical machine learning algorithms, including support vector machine, k-nearest neighbor, random forest, etc., and a modified deep learning algorithm, RamanNet, have been applied to differentiate and classify these endotoxins. It has been found that most conventional machine learning algorithms can attain a differentiation accuracy of >99%, while RamanNet can achieve 100% accuracy. Such an approach has the potential for precise classification of endotoxins and could be used for rapid medical diagnoses and therapeutic decisions for pathogenic infections.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

A physical basis for cosmological correlators from cuts

Significant progress has been made in our understanding of the analytic structure of FRW wavefunction coefficients, facilitated by the development of efficient algorithms to derive the differential equations they satisfy. Moreover, recent findings indicate that the twisted cohomology of the associated hyperplane arrangement defining FRW integrals overestimates the number of integrals required to define differential equations for the wave-function coefficient. We demonstrate that the associated dual cohomology is automatically organized in a way that is ideal for understanding and exploiting the cut/residue structure of FRW integrals. Utilizing this understanding, we develop a systematic approach to organize compatible sequential residues, which dictates the physical subspace of FRW integrals for any n -site, ℓ-loop graph. In particular, the physical subspace of tree-level FRW wavefunction coefficients is populated by differential forms associated to cuts/residues that factorize the integrand of the wavefunction coefficient into only flat space amplitudes. After demonstrating the validity of our construction using intersection theory, we develop simple graphical rules for cut tubings that enumerate the space of physical cuts and, consequently, differential forms without any calculation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.

Applied Dynamical Systems↗
DOE OSTI2021

Stiff neural ordinary differential equations

Neural Ordinary Differential Equations (ODEs) are a promising approach to learn dynamical models from time-series data in science and engineering applications. This work aims at learning neural ODEs for stiff systems, which are usually raised from chemical kinetic modeling in chemical and biological systems. We first show the challenges of learning neural ODEs in the classical stiff ODE systems of Robertson’s problem and propose techniques to mitigate the challenges associated with scale separations in stiff systems. We then present successful demonstrations in stiff systems of Robertson’s problem and an air pollution problem. The demonstrations show that the usage of deep networks with rectified activations, proper scaling of the network outputs as well as loss functions, and stabilized gradient calculations are the key techniques enabling the learning of stiff neural ODEs. The success of learning stiff neural ODEs opens up possibilities of using neural ODEs in applications with widely varying time-scales, such as chemical dynamics in energy conversion, environmental engineering, and life sciences.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Degradation of performance in ICF implosions due to Rayleigh–Taylor instabilities: A Hamiltonian perspective

The Rayleigh–Taylor instability (RTI) is an ubiquitous phenomenon that occurs in inertial-confinement-fusion (ICF) implosions and is recognized as an important limiting factor of ICF performance. To analytically understand the RTI dynamics and its impact on ICF capsule implosions, we develop a first-principle variational theory that describes an imploding spherical shell undergoing RTI. The model is based on a thin-shell approximation and includes the dynamical coupling between the imploding spherical shell and an adiabatically compressed fluid within its interior. Using a quasilinear analysis, we study the degradation trends of key ICF performance metrics (e.g., stagnation pressure, residual kinetic energy, and areal density) as functions of initial RTI parameters (e.g., the initial amplitude and Legendre mode), as well as the 1D implosion characteristics (e.g., the convergence ratio). We compare analytical results from the theory against nonlinear results obtained by numerically integrating the governing equations of this reduced model. Our findings emphasize the need to incorporate polar flows in the calculation of residual kinetic energy and demonstrate that higher convergence ratios in ICF implosions lead to significantly greater degradation of key performance metrics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

An implementation of a high-order generalized finite difference method for solving the time-harmonic cold plasma wave equation in toroidal geometry

A high-order physics-informed meshless finite difference numerical technique is introduced for solving the time-harmonic cold plasma wave equation in toroidal geometries, presenting a novel application of the generalized finite difference (GFD) method to plasma wave simulations. The algorithm employs an irregular distribution of computational points, with local point density informed by the shortest wavelength derived from the cold plasma dispersion relation. Numerical stability and robustness are addressed using regularization techniques. The algorithm, implemented for two spatial dimensions, solves for the wave electric field and is demonstrated to achieve convergence rates of $\mathcal{O}$($\mathcal{h}$ $\mathcal{P}$ )⁠. Verification tests reproduce plane wave solutions, and example simulations of ion cyclotron resonance heating and electron cyclotron resonance heating demonstrate its capability, approaching realistic tokamak plasma scenarios. This work contributes to laying a foundation for the GFD method to be used in more sophisticated, optimized, and physically realistic full-wave simulations in time-harmonic plasma wave research.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Jacobian sparsity detection using Bloom filters

Determining Jacobian sparsity structure is an important step in the efficient computation of sparse Jacobians. We introduce a new method for determining Jacobian sparsity patterns by combining bit vector probing with Bloom filters. In conclusion, we further refine Bloom filter probing by combining it with hierarchical probing to yield a highly effective strategy for Jacobian sparsity pattern determination.

Bloom filter↗
DOE OSTI2025

Characterization of Pinhole Collimators for High-Resolution Gamma Imaging of Irradiated Fuel

Post-irradiation examination (PIE) of nuclear fuels requires imaging tools capable of resolving isotopic and spatial features with high throughput. This project contributes to a proof-of-concept effort aimed at advancing gamma emission tomography (GET) by evaluating novel fine-aperture pinhole collimators. Two Rose’s metal collimators, 100 µm (20° acceptance angle) and 350 µm (30° acceptance angle), were prototyped and characterized for their effectiveness in transporting gamma rays through the pinhole aperture. To support data collection, a Python-based data acquisition system was developed to coordinate a rotation stage, linear stage, and CZT detector, reducing latency in high-rate gamma event logging to one second per acquisition. Queue-based file writing enabled seamless real-time data capture for count rates up to 35,000 counts per second (cps). List-mode parsing algorithms were implemented to differentiate single and simultaneous gamma interactions for future tomographic reconstruction. Detector response was evaluated in both spectroscopy and list mode acquisition methods across varying source distances to confirm absolute and collimator efficiencies. Preliminary efficiency figures suggest effective collimation of gamma-rays with energies below 700 keV, with ~4% residual intensity through the aperture for Cs-137. The impact of collimator geometry on image quality is currently being evaluated. This groundwork supports the ongoing development of a sub mm resolution cone-beam CT system for imaging fuel phantoms, an essential step toward improving GET efficiency and accelerating nuclear fuel qualification efforts.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗
DOE OSTI2022

Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer

Many eigenvalue problems arising in practice are often of the generalized form A x = λ B x . One particularly important case is symmetric, namely A , B are Hermitian and B is positive definite. The standard algorithm for solving this class of eigenvalue problems is to reduce them to Hermitian eigenvalue problems. For a quantum computer, quantum phase estimation is a useful technique to solve Hermitian eigenvalue problems. In this work, we propose a new quantum algorithm for symmetric generalized eigenvalue problems using ordinary differential equations. The algorithm has lower complexity than the standard one based on quantum phase estimation. Moreover, it works for a wider case than symmetric: B is invertible, B - 1 A is diagonalizable and all the eigenvalues are real.

Science & Technology - Other Topics↗
DOE OSTI2020

SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations

Data-driven discovery of differential equations has been an emerging research topic. We propose a novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers. The subsampling technique is used for improving the accuracy of the Bayesian learning algorithm. It has two parameters: subsampling size and the number of subsamples. When the subsampling size increases with fixed total sample size, the accuracy of our algorithm goes up and then down. When the number of subsamples increases, the accuracy of our algorithm keeps going up. We demonstrate how to use our algorithm step by step and compare our algorithm with threshold sparse Bayesian regression (TSBR) for the discovery of differential equations. We show that our algorithm produces better results. We also discuss the merits of discovering differential equations from data and demonstrate how to discover models with random initial and boundary condition as well as models with bifurcations. The numerical examples are: (1) predator-prey model with noise, (2) shallow water equations with outliers, (3) heat diffusion with random initial and boundary condition, and (4) fish-harvesting problem with bifurcations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Efficient numerical algorithm for multi-level ionization of high-atomic-number gases

An efficient numerical algorithm for laser driven multi-level ionization of high-atomic-number gases is proposed and implemented in an electromagnetic particle-in-cell code SPACE. The algorithm is based on analytical solutions to the system of differential equations describing ionization evolution. Using analytical solutions resolves the multiscale issue of ionization due to different characteristic time scales of ionization processes and the main code time step. Algorithm efficiency and memory requirements are significantly improved by using a locally reduced system of differential equations. The algorithm also assigns proper orbital quantum numbers and their projections to ionization states. The algorithm is verified and validated using experimental data.

Cheng, A. (ORCID:000000021945282X)↗
DOE OSTI2024

Reduced-order modeling on a near-term quantum computer

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems of equations as well as systems of linear ordinary differential equations (ODEs) and partial differential equations (PDEs). Reducedorder modeling (ROM) algorithms for studying fluid dynamics have shown success in identifying linear operators that can describe flowfields, where dynamic mode decomposition (DMD) is a particularly useful method in which a linear operator is identified from data. In this work, DMD is reformulated as an optimization problem to propagate the state of the linearized dynamical system on a quantum computer. This reformulation was chosen as a means of facilitating implementation on a near-term quantum computer. Quadratic unconstrained binary optimization (QUBO), a technique for optimizing quadratic polynomials in binary variables, allows for quantum annealing algorithms to be applied. A quantum circuit model (quantum approximation optimization algorithm, QAOA) is utilized to obtain predictions of the state trajectories. Results are shown for the quantum-ROM predictions for flow over a 2D cylinder at Re = 220 and flow over a NACA0009 airfoil at Re = 500 and α = 15°. The quantum-ROM predictions are found to depend on the number of bits utilized for a fixed point representation and the truncation level of the DMD model. Comparisons with DMD predictions from a classical computer algorithm are made, as well as an analysis of the computational complexity and prospects for future, more fault-tolerant quantum computers.

97 MATHEMATICS AND COMPUTING↗