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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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Online randomized interpolative decomposition with a posteriori error estimator for temporal PDE data reduction

Traditional low-rank approximation is a powerful tool for compressing large data matrices that arise in simulations of partial differential equations (PDEs), but suffers from high computational cost and requires several passes over the PDE data. The compressed data may also lack interpretability thus making it difficult to identify feature patterns from the original data. Here, to address these issues, we present an online randomized algorithm to compute the interpolative decomposition (ID) of large-scale data matrices in situ. Compared to previous randomized IDs that used the QR decomposition to determine the column basis, we adopt a streaming ridge leverage score-based column subset selection algorithm that dynamically selects proper basis columns from the data and thus avoids an extra pass over the data to compute the coefficient matrix of the ID. In particular, we adopt a single-pass error estimator based on the non-adaptive Hutch++ algorithm to provide real-time error approximation for determining the best coefficients. As a result, our approach only needs a single pass over the original data and thus is suitable for large and high-dimensional matrices stored outside of core memory or generated in PDE simulations. A strategy to improve the accuracy of the reconstructed data gradient, when desired, within the ID framework is also presented. We provide numerical experiments on turbulent channel flow and ignition simulations, and on the NSTX Gas Puff Image dataset, comparing our algorithm with the offline ID algorithm to demonstrate its utility in real-world applications.

Column subset selection↗
DOE OSTI2022

Different CT slice thickness and contrast‐enhancement phase in radiomics models on the differential performance of lung adenocarcinoma

Abstract Background To investigate the effects of computed tomography (CT) reconstruction slice thickness and contrast‐enhancement phase on the differential diagnosis performance of radiomic signature in lung adenocarcinoma. Methods A total of 187 patients who had been pathologically confirmed with lung adenocarcinoma and nonadenocarcinoma were divided into a training cohort ( n = 149) and validation cohort ( n = 38). All the patients underwent contrast‐enhanced CT and the images were reconstructed with different slice thickness. The radiomic features were extracted from different slice thickness and scan phase. The logistic regression (LR) algorithm was used to build a machine learning model for each group. The area under the curve (AUC) obtained from the receiver operating characteristic (ROC) curve and DeLong test was used to evaluate its discriminating performance. Results Finally, 34 image features and five semantic features were selected to establish a radiomics model. Based on the three contrast‐enhanced CT phases and four reconstruction slice thickness, 12 groups of radiomics models showed good discrimination ability with the AUCs range from 0.9287 to 0.9631, sensitivity range from 0.8349 to 0.9083, specificity range from 0.825 to 0.925 in the training group. Similar results were observed in the validation group. However, there was no statistical significance between the different CT scan phase groups and different slice thickness ( p > 0.05). Conclusions The radiomic analysis of contrast‐enhanced CT can be used for the differential diagnosis of lung adenocarcinoma. Moreover, different slice thickness and contrast‐enhanced scan phase did not affect the discriminating ability in the radiomics models.

Wang, Yang↗
DOE OSTI2025

Optimal Control of Differentially Private EV Charging: A Scalable Learning Approach Under Uncertainty

Internet of Things (IoT)-enabled electric vehicles (IoEVs) enable intelligent charging coordination that accounts for grid congestion. However, increased data exchange raises privacy concerns, as charging patterns can reveal sensitive driver behavior to grid operators. Here, we propose a differentially private (DP) EV charging framework that enables coordinated control while protecting driver data with theoretical privacy guarantees. Nevertheless, integrating DP inevitably introduces uncertainty into the control strategy for EVs, which can lead to infeasible solutions. To tackle this challenge, we develop a feasible and scalable control algorithm based on constrained reinforcement learning (CRL) and convex hulls. While our framework is designed to handle the uncertainty introduced by DP, it is general and also applicable to other sources of uncertainty in EV charging, such as the stochastic nature of driver behavior and renewable variability. This ensures feasible and privacy-preserving coordination of EV charging at scale. Our method constructs convex hulls within the action space to guarantee feasibility under stochastic constraints and incorporates constraint reduction techniques to improve scalability. Case studies based on IEEE benchmark systems demonstrate that the proposed approach effectively balances feasibility under uncertainty, scalability, and privacy in large-scale EV charging control.

Engineering - Power transmission and distribution↗
DOE OSTI2021

Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control

Herein, we present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional sub-spaces whose basis functions are realizations of a sequence of neural networks. Here, the finite-dimensional subspaces are then used to define a standard Galerkin approximation of the variational equation. This approach enjoys a number of advantages, including: the sequential nature of the algorithm offers a systematic approach to enhancing the accuracy of a given approximation; the sequential enhancements provide a useful indicator for the error that can be used as a criterion for terminating the sequential updates; the basic approach is largely oblivious to the nature of the partial differential equation under consideration; and, some basic theoretical results are presented regarding the convergence (or otherwise) of the method which are used to formulate basic guidelines for applying the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Massively parallel modeling and inversion of electrical resistivity tomography data using PFLOTRAN

Abstract. Electrical resistivity tomography (ERT) is a broadly accepted geophysical method for subsurface investigations. Interpretation of field ERT data usually requires the application of computationally intensive forward modeling and inversion algorithms. For large-scale ERT data, the efficiency of these algorithms depends on the robustness, accuracy, and scalability on high-performance computing resources. In this regard, we present a robust and highly scalable implementation of forward modeling and inversion algorithms for ERT data. The implementation is publicly available and developed within the framework of PFLOTRAN, an open-source, state-of-the-art massively parallel subsurface flow and transport simulation code. The forward modeling is based on a finite-volume discretization of the governing differential equations, and the inversion uses a Gauss–Newton optimization scheme. To evaluate the accuracy of the forward modeling, two examples are first presented by considering layered (1D) and 3D earth conductivity models. The computed numerical results show good agreement with the analytical solutions for the layered earth model and results from a well-established code for the 3D model. Inversion of ERT data, simulated for a 3D model, is then performed to demonstrate the inversion capability by recovering the conductivity of the model. To demonstrate the parallel performance of PFLOTRAN's ERT process model and inversion capabilities, large-scale scalability tests are performed by using up to 131 072 processes on a leadership class supercomputer. These tests are performed for the two most computationally intensive steps of the ERT inversion: forward modeling and Jacobian computation. For the forward modeling, we consider models with up to 122 ×106 degrees of freedom (DOFs) in the resulting system of linear equations and demonstrate that the code exhibits almost linear scalability on up to 10 000 DOFs per process. On the other hand, the code shows superlinear scalability for the Jacobian computation, mainly because all computations are fairly evenly distributed over each process with no parallel communication.

58 GEOSCIENCES↗
DOE OSTI2025

RE-INTEGRATE EMT Simulation Software: Graph Convolutional Network for Sparse Matrix Pattern Detection

The increasing complexity of power networks, driven by proliferation of inverters, presents analytical challenges that simplified models often fail to capture, necessitating Electromagnetic Transient (EMT) simulations. EMT models are represented as discretized differential-algebraic equations (DAEs), forming a linear system Ax = b that is computationally intensive to solve. Due to inherent sparsity of adjacency matrix A, distinct patterns emerge that, when accurately identified, enable efficient solver selection to minimize computation time. However, identifying ideal pattern is complicated by numerous reordering algorithms and limited structural insights. To address this, we introduce a Graph Convolutional Network (GCN) model for classifying sparse matrix patterns common in power system analysis. The model, achieving 96% test accuracy, is validated using PV plant models of 125 MW capacities connected to New England 39-bus transmission system (TS), and further scaled to a 4,992-bus network with 384 PV plants, yielding 191, 616 × 191, 616 sized A matrix. For all cases, the GCN model accurately identifies the matrix’s intrinsic sparse pattern, demonstrating its potential to enhance solver performance in EMT analysis.

Hossain, Md Rifat [Florida International Universit↗
DOE OSTI2023

A new approach to color-coherent parton evolution

We present a simple parton-shower model that replaces the explicit angular ordering of the coherent branching formalism with a differentially accurate simulation of soft-gluon radiation by means of a non-trivial dependence of the splitting functions on azimuthal angles. We introduce a global kinematics mapping and provide an analytic proof that it satisfies the criteria for next-to leading logarithmic accuracy. In the new algorithm, initial and final state evolution are treated on the same footing. We provide an implementation for final-state evolution in the numerical code ALARIC and present a first comparison to experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Digital Twin Framework for PIP-II Linac: AI-Driven Multi-Scale Modeling from Ion Source to 800 MeV

The PIP-II linac will enable >1.2 MW beam power for DUNE, requiring unprecedented operational reliability across its warm front-end (RFQ, MEBT) and five distinct SRF sections operating at 162.5/325/650 MHz. We present a comprehensive digital twin framework uniquely combining a fully differentiable fast beam transport code with neural network surrogates trained on high-fidelity PIC simulations, capturing space charge and nonlinear dynamics beyond traditional envelope codes while achieving 10⁴ speedup at <1% accuracy. End-to-end differentiability enables gradient-based optimization across 500+ parameters simultaneously previously impossible with conventional tools while the model incorporates static/dynamic errors and serves as a virtual commissioning platform for diverse hardware integration. The framework facilitates reinforcement learning for pulsed/CW mode transitions, predictive maintenance through anomaly detection, and autonomous tuning algorithm development with real-time execution capability. Validation against physics simulations shows excellent agreement for the front-end, with initial results demonstrating potential for 30% commissioning time reduction and proactive fault mitigation, providing a scalable blueprint for operating next-generation high-intensity accelerators.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗
DOE OSTI2025

Digital Twin Framework for PIP-II Linac: AI-Driven Multi-Scale Modeling from Ion Source to 800 MeV

The PIP-II linac will enable >1.2 MW beam power for DUNE, requiring unprecedented operational reliability across its warm front-end (RFQ, MEBT) and five distinct SRF sections operating at 162.5/325/650 MHz. We present a comprehensive digital twin framework uniquely combining a fully differentiable fast beam transport code with neural network surrogates trained on high-fidelity PIC simulations, capturing space charge and nonlinear dynamics beyond traditional envelope codes while achieving 10⁴× speedup at <1% accuracy. End-to-end differentiability enables gradient-based optimization across 500+ parameters simultaneously—previously impossible with conventional tools—while the model incorporates static/dynamic errors and serves as a virtual commissioning platform for diverse hardware integration. The framework facilitates reinforcement learning for pulsed/CW mode transitions, predictive maintenance through anomaly detection, and autonomous tuning algorithm development with real-time execution capability. Validation against physics simulations shows excellent agreement for the front-end, with initial results demonstrating potential for 30% commissioning time reduction and proactive fault mitigation, providing a scalable blueprint for operating next-generation high-intensity accelerators.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗
DOE OSTI2022

Project Report: High Frequency Axion LDRD - A Multiport Approach to Thermal Noise and Scattering Parameter Simulation of Cryogenic Experiments

In this report, a simple algorithm for detailed system-level thermal noise analysis is developed, demonstrated, and verified. This method uses noise-wave theory and noise covariance matrices to cascade noise and scattering parameters of multiport devices at different temperatures. This method addresses the effects of return loss, multiport isolation/coupling, and static temperature differentials between components, and will work in cases where the noise temperature is at or near the quantum noise limit. An ideal multidevice network will first be demonstrated to show that this method’s results are consistent with the Friis cascade when component parameters such as return loss and isolation are ideal. Following the ideal multidevice example, a cryogenic experiment is conducted to demonstrate that the proposed simulation method is successful when real data are used.

42 ENGINEERING↗
DOE OSTI2024

Multiphysics Time-Integration for Turbulent Combustion at the Exascale

Turbulent reacting flow systems are often modeled with coupled time-dependent partial differential equations (PDEs). Solving such equations can easily tax the world's largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This generic operator-splitting strategy leads to a set of ordinary differential equations (ODEs) that need to be solved as part of an "outer-loop" time-stepping approach. In many combustion applications, the ODEs to be solved can be very stiff, exhibiting timescales that span many orders of magnitude. The SUNDIALS library provides a plethora of robust time integration algorithms for solving these ODEs on exascale-capable computing hardware, yet for many complex applications (such multicomponent fuels or emissions predictions), the chemical models remain too complex to solve using reasonable resources. The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of the simulations. In this talk, I will discuss the use of the SUDIALS library of ODE solvers together with automatic code generation tools to solve complex turbulent reacting flow problems using QSSA models.

chemistry↗
DOE OSTI2025

Accelerating multilevel Markov Chain Monte Carlo using machine learning models

Here, this work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian inference often substitute computationally expensive high-fidelity models with machine learning models, thereby introducing approximation errors, our approach offers a computationally efficient alternative by augmenting high-fidelity models with low-fidelity ones within a hierarchical framework. The multilevel approach utilizes the low-fidelity machine learning model (MLM) for inexpensive evaluation of proposed samples thereby improving the acceptance of samples by the high-fidelity model. The hierarchy in our multilevel algorithm is derived from geometric multigrid hierarchy. We utilize an MLM to accelerate the coarse level sampling. Training machine learning model for the coarsest level significantly reduces the computational cost associated with generating training data and training the model. We present an MCMC algorithm to accelerate the coarsest level sampling using MLM and account for the approximation error introduced. We provide theoretical proofs of detailed balance and demonstrate that our multilevel approach constitutes a consistent MCMC algorithm. Additionally, we derive the expression for cost reduction due to machine learning model to facilitate cost analysis of the hierarchical sampling algorithm. Our technique is demonstrated on a standard benchmark inference problem in groundwater flow, where we estimate the probability density of a quantity of interest using a four-level MCMC algorithm. Our proposed algorithm accelerates multilevel sampling by a factor of two while achieving similar accuracy compared to sampling using the standard multilevel algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

GP-BayesOpInf

SAND2025-01851O GP-BayesOpInf is a software tool that uses algorithms to combine Gaussian process regression, principal component analysis, and linear Bayesian inference to produce a probabilistic reduced-order model for time-dependent systems. Numerical examples include the compressible Euler equations for an ideal gas, a heat diffusion process with a nonlinear reaction term, and a set of ordinary differential equations describing a compartmental model in epidemiology. 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.

SciDAC↗
DOE OSTI2026

Kinetic Model of HoxEFU reduction by NADH [SWR-26-087]

This repository is used to release code generated for manuscripts on the Photosynthetic Energy Transduction core program. This code simulates the reduction of HoxEFU by NADH. The electro transfer rate constants for the simulation are specified in the .csv files. The two .csv files correspond tot he two models described in Dawson et al. Cell. Rep. Phys. Sci. 2026. The code utilizes a chemical master equation, a set of differential equations, defining the time evolution of the oxidation and reduction kinetics of NAD+, NADH, a FMN flavin, and a set of iron sulfur clusters. The kinetics of HoxEFU reduction by NADH are evaluated by numerical integration of the chemical master equation using a variable-time-step Runge-Kutta algorithm.

Dahl, Peter [National Laboratory of the Rockies (N↗
DOE OSTI2020

Identification of hot water end-use process of electric water heaters from energy measurements

This paper presents an algorithm for the identification of parameters for a stochastic hot water end-use process that drives a homogeneous population of thermostatically controlled electric water heaters (EWH). Usually, only metered interval consumption data (kWh) is collected and the hot water end-use process is unobservable to utility and aggregators. However, the availability of EWHs for demand response (DR) is closely coupled with the hot water end-use process. In this context, the hot water end-use process is modeled as a two-state Markov chain (Use / No use), which causes the thermostatic ON-OFF switching process to behave as a Markov renewal process (MRP). A set of first passage-time problems is developed to obtain the moments of the transition probability densities of the MRP. These problems are addressed by establishing a system of coupled partial differential equations characterizing the temperature evolution of the EWH population. A key quantity in the methodology for estimating the parameters is the total time an EWH is ON within a period of interest. It is referred to as the total busy time. Total busy time in this approach is a random variable for which analytical expressions of the moments are developed as a function of the metered window length. The latter expressions become the basis of a hot water demand model identification algorithm which is validated using agent-based simulations of EWHs.

42 ENGINEERING↗
DOE OSTI2024

Towards the Flexibility of HVDC-Interconnected Systems: A Novel Emergency Freqeuncy Response Model

In this paper, we propose a novel multi-time scale emergency frequency response model by unlocking the flexibility of High Voltage Direct Current (HVDC) systems. Unlike assigning power ramping rates for FACTS to regulate frequency in traditional methods, this paper designs a step-change electromagnetic power frequency response (EPFR) scheme, by leveraging the temporal over/under DC voltage capability of HVDC. Wherein the Kullback-Leibler Divergence is adopted to convexify the modified swing equation after integrating the step-change power. Further, to avoid the complicated differential equations, we equivalently reformulate the duration limits of DC voltage deviation into the HVDC decreasing power ramping rates, which participate in the system primary frequency response. Finally, the new steady-state operation level of HVDC is involved with the secondary frequency response. As a result, an improved three-level algorithm is developed to solve the model, wherein the instant step-change, primary, and secondary frequency response are coordinated together. After applying the proposed frequency response scheme on the test system, the EPFR is validated to effectively provide the most instantaneous supports when faced with bulk power loss due to extreme contingencies, and the resilience is ensured within acceptable expenditures.

Jiang, Sufan↗
DOE OSTI2020

Axionic dark matter halos in the gravitational field of baryonic matter

We consider a dark matter halo (DMH) of a spherical galaxy as a Bose–Einstein condensate (BEC) of the ultra-light axions (ULA) interacting with the baryonic matter. In the mean-field (MF) limit, we have derived the integro-differential equation of the Hartree–Fock type for the spherically symmetrical wave function of the DMH component. This equation includes two independent dimensionless parameters: (i) β is the ratio of baryon and axion total mases and (ii) ξ is the ratio of characteristic baryon and axion spatial parameters. We extended our “dissipation algorithm” for studying numerically the ground state of the axion halo in the gravitational field produced by the baryonic component. We calculated the characteristic size, x c of DMH as a function of β and ξ and obtained an analytical approximation for x c .

79 ASTRONOMY AND ASTROPHYSICS↗