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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗
DOE OSTI2025

A High-Efficiency Delayed Update Algorithm for Evaluating Slater Determinants in Quantum Monte Carlo

For quantum Monte Carlo simulations of molecular systems or supercells with thousands of electrons, matrix operations related to Slater determinants lead the computational cost. McDaniel et al. [J. Chem. Phys. 2017, 147, 174107] proposed a delayed update algorithm to increase computational efficiency by using matrix–matrix multiplication when updating the inverse matrices of Slater determinants. However, preparing intermediate matrices for applying the Sherman–Morrison–Woodbury formula remained a bottleneck. Here, in this work, we introduce an improved algorithm for CPUs and GPUs that (1) reduces this bottleneck by iteratively updating the intermediate matrices and (2) is efficient at any acceptance ratio, with no cost for rejected moves on CPUs and minimal cost on GPUs. We show the full scheme of integrating the delayed update algorithm into a single-electron move. The high efficiency of our algorithm is demonstrated on CPUs and GPUs for a 512 atom/6144 valence electron calculation, with 12× and 2× overall speed-up compared to traditional rank-1 update schemes in diffusion quantum Monte Carlo, respectively.

Luo, Ye [Argonne National Laboratory (ANL), Argonn↗
DOE OSTI2025

Cyber‐Resilient Distributed Energy Resource Control Algorithms for Smart Distribution Grids

ABSTRACT This paper focuses on the development of cyber‐resilient gradient‐based optimisation algorithms and theoretical proof for grid‐interactive distributed energy resource (DER) control to enable two grid services of virtual power plants (VPPs) dispatch and grid voltage regulation, considering the communication and security impacts. Firstly, the combined DER dispatch and voltage regulation as a real‐time gradient‐based optimisation problem is recapped. Thereafter, we consider a probabilistic traffic model to characterise packet delays and loss in a communication network, and study how the delays enter the process of information exchange among the grid measurement units, local DER controllers and the grid control centre that execute this control algorithm in a coordinated manner. Then, a strategy combining delay thresholds and message update rules is proposed to immunity the asynchrony resulting from the communications traffic and it avoids possible numerical instabilities and sensitivities of the power tracking and voltage regulation capabilities, resulting as cyber‐resilient DER control algorithms. Additionally, their convergence is theoretically proved. Effectiveness of proposed cyber‐resilient algorithms has been validated on the IEEE 37‐bus system in terms of convergence, VPP tracking and voltage regulation performance for smart distribution systems with high penetration of DERs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Active space selection with self-healing diffusion Monte Carlo algorithms for periodic solids

Multideterminant Diffusion Monte Carlo (DMC) displays improved accuracy over single determinant DMC. Self-Healing Diffusion Monte Carlo (SHDMC) is a DMC based method that iteratively improves a multideterminant trial wavefunction. Although configuration interaction or complete active space (CAS) methods are very accurate and computationally feasible for many systems, they are not optimal for application to solids. SHDMC is accurate and designed for application to solids, so developing SHDMC based active space selection algorithms is a worthy endeavor. Here, we present and compare active space selection algorithms that are designed for use in conjunction with SHDMC, without relying on external approaches. For benchmarking, we calculated the ground state energy of a small unit cell of graphene and compared the results with a complete basis set extrapolated selected CI and a reference SHDMC trajectory. We found that systematically expanding the active space using an “auto-branching” algorithm optimally balances accuracy with computational practicality. To the best of our knowledge, this is the first work that demonstrates completely self-contained DMC-based active space selection algorithms that do not depend on external methods for determinant selection.

Spanedda, Nicole [ORNL]↗
DOE OSTI2025

The track-length extension fitting algorithm for energy measurement of interacting particles in liquid argon TPCs and its performance with ProtoDUNE-SP data

This paper introduces a novel track-length extension fitting algorithm for measuring the kinetic energies of inelastically interacting particles in liquid argon time projection chambers (LArTPCs). The algorithm finds the most probable offset in track length for a track-like object by comparing the measured ionization density as a function of position with a theoretical prediction of the energy loss as a function of the energy, including models of electron recombination and detector response. The algorithm can be used to measure the energies of particles that interact before they stop, such as charged pions that are absorbed by argon nuclei. The algorithm's energy measurement resolutions and fractional biases are presented as functions of particle kinetic energy and number of track hits using samples of stopping secondary charged pions in data collected by the ProtoDUNE-SP detector, and also in a detailed simulation. Additional studies describe the impact of the dE/dx model on energy measurement performance. The method described in this paper to characterize the energy measurement performance can be repeated in any LArTPC experiment using stopping secondary charged pions.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Reducing measurement costs by recycling the Hessian in adaptive variational quantum algorithms

Abstract Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with Adaptive Derivative-Assembled Problem-Tailored variational quantum eigensolver (ADAPT-VQE), an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variational parameter, and where all parameters acquired thus far are optimized in each iteration. In ADAPT-VQE and other adaptive VQAs that followed it, it has been shown that initializing parameters to their optimal values from the previous iteration speeds up convergence and avoids shallow local traps in the parameter landscape. However, no other data from the optimization performed at one iteration is carried over to the next. In this work, we propose an improved quasi-Newton optimization protocol specifically tailored to adaptive VQAs. The distinctive feature in our proposal is that approximate second derivatives of the cost function are recycled across iterations in addition to optimal parameter values. We implement a quasi-Newton optimizer where an approximation to the inverse Hessian matrix is continuously built and grown across the iterations of an adaptive VQA. The resulting algorithm has the flavor of a continuous optimization where the dimension of the search space is augmented when the gradient norm falls below a given threshold. We show that this inter-optimization exchange of second-order information leads the approximate Hessian in the state of the optimizer to be consistently closer to the exact Hessian. As a result, our method achieves a superlinear convergence rate even in situations where the typical implementation of a quasi-Newton optimizer converges only linearly. Our protocol decreases the measurement costs in implementing adaptive VQAs on quantum hardware as well as the runtime of their classical simulation.

Ramôa, Mafalda (ORCID:0000000302187801)↗
DOE OSTI2026

Evaluating multistation phase picking algorithm phase neural operator (PhaseNO) on local seismic networks

Reliable automatic phase picking is important for many seismic applications. With the development of machine learning approaches, many algorithms are proposed, evaluated and applied to different areas. Many of these algorithms are single station based, while recent proposed methods start to combine surrounding stations into consideration in the problem of phase picking. Among these algorithms, the phase neural operator (PhaseNO) shows promising results on regional data sets comparing to existing algorithms. But there are many use cases for the local seismic networks in our community, therefore in this paper we evaluate the performance of PhaseNO on four different local data sets and compare the results to PhaseNet and EQTransformer. We used both individual phase picking metrics as well as association metrics to illustrate the performance of PhaseNO. By manually reviewing the newly detected events, we find that the PhaseNO model outperforms the single station-based approaches in the local-scale use cases due to its consideration of coherent signals from multiple stations. We also explored PhaseNO’s behaviours when only using one station, as well as gradually increasing the number of stations in the seismic network to better understand its behaviour. Overall, using the off-the-shelf machine learning based phase pickers, PhaseNO demonstrated its good performance on local-scale seismic networks.

58 GEOSCIENCES↗
DOE OSTI2025

Least H 2 norm updating of quadratic interpolation models for derivative-free trust-region algorithms

One particular class of derivative-free optimization algorithms is trust-region algorithms based on quadratic models given by the under-determined interpolation. Different techniques in updating the quadratic model from iteration to iteration will give different interpolation models. We propose a new way to update the quadratic model by minimizing the $H^{2}$ norm of the difference between neighboring quadratic models. The motivation for applying the $H^{2}$ norm is given. The theoretical properties of our new updating technique are also presented. We propose the projection in the sense of $H^{2}$ norm and the interpolation error analysis of our model function. We obtain the coefficients of the quadratic model function using the Karush–Kuhn–Tucker (KKT) conditions. Numerical results show the advantages of our model on the test set considered, and the derivative-free algorithms based on our least $H^{2}$ norm updating quadratic model functions can solve test problems with fewer function evaluations than the algorithm based on the least Frobenius norm updating model and the other compared methods.

derivative-free optimization↗
DOE OSTI2025

Stochastic relativistic viscous hydrodynamics from the Metropolis algorithm

We propose an algorithm for simulating stochastic relativistic fluid dynamics based on Metropolis updates. Each step of the algorithm begins with an update based on ideal hydrodynamics. This is followed by proposing random (spatial) momentum transfers between fluid cells, keeping the total energy fixed. These proposals are then accepted or rejected using the change in entropy as a statistical weight. The algorithm reproduces relativistic viscous hydrodynamics in the “density frame,” which is a formulation of viscous hydrodynamics we review and clarify here. This formulation is first order in time and requires no auxiliary dynamical fields such as Π 𝜇⁢𝜈 . The only parameters are the shear and bulk viscosities and the equation of state. Here, by adopting the 3+1 split of general relativity, we extend the Metropolis algorithm to general space-time coordinates, such as Bjorken coordinates, which are commonly used to simulate heavy-ion collisions.

Hydrodynamic noise↗
DOE OSTI2025

Stochastic noise can be helpful for variational quantum algorithms

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided, for example, by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle-points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms. Published by the American Physical Society 2025

Liu, Junyu↗
DOE OSTI2025

Metriplectic four-bracket algorithm for constructing thermodynamically consistent dynamical systems

A unified thermodynamic algorithm is presented for constructing thermodynamically consistent dynamical systems, i.e., systems that have Hamiltonian and dissipative parts that conserve energy while producing entropy. The algorithm is based on the metriplectic 4-bracket given in Morrison and Updike [Phys. Rev. E 109, 045202 (2024)]. A feature of the unified thermodynamic algorithm is the force-flux relation 𝐉 𝛼 =−𝐿 𝛼⁢𝛽 𝛁(𝛿⁢𝐻⁡/𝛿⁢𝜉 𝛽 ) for phenomenological coefficients 𝐿 𝛼⁢𝛽 , Hamiltonian 𝐻, and dynamical variables 𝜉 𝛽 . The algorithm is applied to the Navier-Stokes-Fourier, the Cahn-Hilliard-Navier-Stokes, and Brenner-Navier-Stokes-Fourier systems, and significant generalizations of these systems are obtained.

Multiphase flows↗
DOE OSTI2025

Nonvariational ADAPT algorithm for quantum simulations

We explore a nonvariational quantum state preparation approach combined with the ADAPT operator selection strategy in the application of preparing the ground state of a desired target Hamiltonian. In this algorithm, energy gradient measurements determine both the operators and the gate parameters in the quantum circuit construction. We compare this nonvariational algorithm with ADAPT-VQE and with feedback-based quantum algorithms in terms of the rate of energy reduction, the circuit depth, and the measurement cost in molecular simulation. We find that, despite using deeper circuits, this new algorithm reaches chemical accuracy at a similar measurement cost to ADAPT-VQE. Since it does not rely on a classical optimization subroutine, it may provide robustness against circuit parameter errors due to imperfect control or gate synthesis.

Tang'S, Ho Lun [Virginia Polytechnic Inst. and Sta↗
DOE OSTI2025

A Polynomial-Time Classical Algorithm for Noisy Quantum Circuits

We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g., the computational basis). Our approach is based upon the intuition that noise exponentially damps nonlocal correlations relative to local correlations. This enables one to classically simulate a noisy quantum circuit by keeping track of only the dynamics of local quantum information. Our algorithm also enables sampling from the output distribution of a circuit in quasipolynomial time, so long as the distribution anticoncentrates. A number of implications are discussed, including a fundamental limit on the efficacy of noise mitigation strategies: For constant noise rates, any quantum circuit for which error mitigation succeeds in polynomial-time on most input states can also be classically simulated in polynomial-time on most input states. Our algorithms scale exponentially in the inverse noise rate, which is fundamental and makes them impractical for current quantum devices.

decoherence↗
DOE OSTI2026

RADAI: A Large-Scale Realistic Dataset for Radiation Detection Algorithm Development

Open, realistic datasets are essential for developing and benchmarking radiation detection algorithms, yet they remain scarce. The Radiological Anomaly Detection and Identification (RADAI) project was develop to create datasets that meet the training and testing needs for sophisticated radiation detection algorithms. The RADAI dataset is a large-scale synthetic resource that integrates high-fidelity Monte Carlo simulations with realistic urban scenarios to capture both background variability and source signatures. RADAI models construction-material NORM, people and vehicles, urban clutter, and dynamic environmental effects such as cosmic-ray and rain-induced transients, and they provide list-mode detector data with motion and response modeling suitable for algorithm training and evaluation. The RADAI project resulted in three publicly-released complementary datasets together with an online scoring portal for standardized performance assessment and an open software toolkit that supports data access, augmentation, model development, and evaluation. These resources enable reproducible comparisons across methods and promote rigorous studies at the scale required by contemporary machine learning. By grounding algorithm development in realistic, well-documented conditions, RADAI supports progress toward more robust detection, identification, and localization in complex urban environments.

Ghawaly, James M. [Division of Computer Science an↗
DOE OSTI2025

Surrogate-Based Autotuning for Randomized Sketching Algorithms in Regression Problems

Algorithms from Randomized Numerical Linear Algebra (RandNLA) are known to be effective in handling high-dimensional computational problems, providing high-quality empirical performance as well as strong probabilistic guarantees. However, their practical application is complicated by the fact that the user needs to set various algorithm-specific tuning parameters which are different from those used in traditional NLA. This paper demonstrates how a surrogate-based autotuning approach can be used to address fundamental problems of parameter selection in RandNLA algorithms. In particular, we provide a detailed investigation of surrogate-based autotuning for sketch-and-precondition (SAP)-based randomized least squares methods, which have been one of the great success stories in modern RandNLA. Empirical results show that our surrogate-based autotuning approach can achieve near-optimal performance with much less tuning cost than a random search (up to about 7.6x fewer trials of different parameter configurations). Moreover, while our experiments focus on least squares, our results demonstrate a general-purpose autotuning pipeline applicable to any kind of RandNLA algorithm.

Cho, Younghyun↗
DOE OSTI2025

Proton pulse charge calculation algorithm in Beam Power Limiting System at Spallation Neutron Source

A proton pulse charge calculation algorithm in the Beam Power Limiting System (BPLS) at the Spallation Neutron Source (SNS) was developed and implemented in an FPGA. The algorithm calculates one-minute running average of the pulse charges and issues a fault to the Personal Protection System (PPS) and the Machine Protection System (MPS) when a limit is reached. A bit-accurate model of the algorithm was first developed and tested in Matlab® and then implemented and simulated in VHDL using Vivado® design environment. Finally, the algorithm was verified on a µTCA-based hardware platform.

Bobrek, Miljko [ORNL] (ORCID:0000000332763451)↗
DOE OSTI2025

Improving ICARUS Track Reconstruction Algorithms

The ICARUS experiment is part of the Short-Baseline Neutrino (SBN) program at Fermilab. The main goal of the experiment is to investigate the possibility of sterile neutrinos in the O(1 eV) mass region and provide clarification of the anomaly detected from the Liquid Scintillator Neutrino Detector (LSND) and MiniBooNE experiments. The ICARUS-T600 detector is a Liquid Argon Time Projection Chamber (LAr-TPC), that can provide excellent 3D imaging and calorimetric reconstruction of any ionizing particles. This detection technique allows a detailed study of neutrino interactions, spanning a wide energy spectrum (from a few keV to several hundreds of GeV). The detector consists of two identical adjacent modules, filled with a total of 760 tons of ultra-pure liquid argon. Each module houses two LAr-TPCs separated by a common cathode with a maximum drift distance of 1.5 m, equivalent to about 1 ms drift time for the nominal $500$ V/m electric drift field. The anode is made of three parallel wire planes positioned 3 mm apart, where the stainless-steel wires are oriented on each plane at a different angle with respect to the horizontal direction ($+60^\degree$,$-60^\degree$,$0^\degree$). The first two planes (Induction 1 and Induction 2) provide a non-destructive charge measurement, whereas the ionization charge is fully collected by the last collection plane. In total, 53248 wires with a 3 mm pitch and length up to 9 m are installed in the detector. In the first stage of the reconstruction, segments of waveforms corresponding to physical signals (hits) are searched for in the deconvolved wire waveform with a threshold-based hit-finding algorithm. Each hit is then fitted with a Gaussian, whose area is proportional to the number of drift electrons generating the signal. In the second stage of the reconstruction, hits are passed as input to Pandora, a framework software composed of different pattern recognition algorithms, that performs a 3D reconstruction of the full image recorded in the collected event, including the identification of interaction vertices and tracks and showers inside the TPC. These are organized into a hierarchical structure (called slice) of particles generated starting from a primary interaction vertex. In some cases, related to the inefficiencies in the hit detection or excessive deflection of the particle trajectory, Pandora breaks the particle's track into two or more smaller pieces and considers each piece as an independent track. We studied this phenomenon focusing on primary muons from ν_μ CC interactions contained in a single module with a track at least 20 cm long, to exclude delta rays. The study determined that about $7-8\%$ of the muon tracks are broken. Approximately $80\%$ of the times, Pandora assigns all segments of the track to the same slice (intra-slice track split), while in the remaining $20\%$ of the cases, one of the segments is associated with another slice (extra-slice track split). To mitigate this phenomenon, we designed an algorithm that detects and stitches the tracks broken by Pandora for the intra-slice split. In Monte Carlo simulations, the algorithm showed an efficiency exceeding $80\%$ and a purity exceeding $93\%$.

Ricci, Alessandro Maria [Pisa U.; INFN, Pisa] (ORC↗
DOE OSTI2026

Grid Topology Discovery Algorithm Evaluation of Suitability for Utility Deployment (CRADA 606 Final Report)

This work presents the results of a field-informed demonstration aimed at evaluating the practical suitability of a topology discovery algorithm for utility environments. We demonstrated an algorithm that uses a graph-theory-informed state estimation approach for model selection. In collaboration with Survalent and Peninsula Light Co., the algorithm was applied to real feeder models and field measurements from supervisory control and data acquisition (SCADA) and advanced metering infrastructure (AMI) systems to identify the operational topology of a power distribution system. The demonstration assessed the algorithm’s performance under realistic data conditions, including sparse and noisy measurements, and examined its ability to identify the most likely network configurations. The results confirmed that the approach can effectively narrow down feasible topologies, providing operators with improved situational awareness of network status. Key lessons learned emphasize the need for systematic data validation and strategic sensor placement to enhance observability. These insights inform future deployment strategies and guide refinements for broader adoption in utility operations.

24 POWER TRANSMISSION AND DISTRIBUTION↗