Variational Approaches to Surrogate Modeling and Information Processing
Explore the source record for details and available documents.
Gruber, Anthony David [Sandia National Laboratorie↗
SEARCH · Search NASA
Results for “Variational approach”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Efficient Berry phase calculation via adaptive variational quantum computing approach
We present an adaptive variational quantum algorithm to estimate the Berry phase accumulated by a nondegenerate ground state under cyclic, adiabatic evolution of a time-dependent Hamiltonian. Our method leverages cyclic adiabatic evolution of the Hamiltonian and employs adaptive variational quantum algorithms for state preparation and evolution, optimizing circuit efficiency while maintaining high accuracy. We benchmark our approach on dimerized Fermi–Hubbard chains with four sites, demonstrating precise Berry phase simulations in both noninteracting and interacting regimes. Our results show that circuit depths reach up to 106 layers for noninteracting systems and increase to 279 layers for interacting systems due to added complexity. In addition, we demonstrate the robustness of our scheme across a wide range of parameters governing adiabatic evolution and variational algorithms. These findings highlight the potential of adaptive variational quantum algorithms for advancing quantum simulations of topological materials and computing geometric phases in strongly correlated systems.
Mootz, Martin [Ames Laboratory (AMES), Ames, IA (U↗
Variational neural network approach to QFT in the field basis
We present a variational neural network approach for solving quantum field theories in the field basis, focusing on the free Klein-Gordon model formulated in momentum space. While recent studies have explored neural-network-based variational methods for scalar field theory in position space, a systematic benchmark of the analytically solvable Klein-Gordon ground state—particularly in the momentum-space field basis—has been lacking. In this work, we represent the ground-state wavefunctional as a neural network defined on a discretized set of field configurations and train it by minimizing the Hamiltonian expectation value. This framework enables direct comparison to exact analytic results for a range of key observables, including the ground-state energy, two-point correlators, expectation value of the field, and the structure of the learned wavefunctional itself. Our results provide quantitative diagnostics of accuracy and establish a validated foundation for extending neural-network wavefunctional methods to interacting field theories and position-space formulations.
Klein-Gordon model↗
Quantum Chemical Density Matrix Renormalization Group Method Boosted by Machine Learning
The use of machine learning (ML) to refine low-level theoretical calculations to achieve higher accuracy is a promising and actively evolving approach known as Δ-ML. The density matrix renormalization group (DMRG) is a powerful variational approach widely used for studying strongly correlated quantum systems. High computational efficiency can be achieved without compromising accuracy. Here, we demonstrate the potential of a simple ML model to significantly enhance the performance of the quantum chemical DMRG method.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Constructing nested coordinates inside strongly shaped toroids using an action principle
A new approach for constructing polar-like boundary-conforming coordinates inside a toroid with strongly shaped cross-sections is presented. A coordinate mapping is obtained through a variational approach, which involves identifying extremal points of a proposed action in the mapping space from [0,2π] 2 ×[0,1] to a toroidal domain in $\mathbb{R}$ 3 . This approach employs an action built on the squared Jacobian and radial length. Extensive testing is conducted on general toroidal boundaries using a global Fourier–Zernike basis via action minimisation. The results demonstrate successful coordinate construction capable of accurately describing strongly shaped toroidal domains. The coordinate construction is successfully applied to the computation of three-dimensional magnetohydrodynamic equilibria in the GVEC code where the use of traditional coordinate construction by interpolation from the boundary failed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Nonlinear saturation of ballooning modes in stellarators
Ballooning mode saturation is investigated in realistic stellarator configurations using the flux tube approach of Ham et al (2018 Plasma Phys. Control. Fusion 60 075017), Ham et al (2016 Phys. Rev. Lett. 116 235001). The method is adapted to account for the lack of exact force balance in stellarator equilibrium solvers that assume existence of nested flux surfaces. A variational approach for calculating flux tube energy is developed to overcome this force error problem in stellarator numerical equilibria. Saturated (equilibrium) flux tube states that cross 10%–20% of the plasma minor radius are shown to exist for linearly ballooning unstable profiles. It is shown that several features of the displaced flux tube structure in a full nonlinear MHD simulation of Wendelstein 7X are reproduced by our model. Saturated states are found in a compact stellarator equilibrium close but below the marginal ballooning linear instability, i.e. the unperturbed equilibrium is metastable. This suggests that edge-localized-mode-like explosive MHD behavior may be possible in stellarators.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Classical and quantum simulations of 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory at finite temperature and density
Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics with fundamental implications for condensed matter physics. Here, we simulate such systems using minimally entangled typical thermal state (METTS) approaches, which combine classical random sampling with imaginary-time evolution, implementable on either classical or quantum computers, to estimate thermal averages of observables. We study 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory coupled to spinless fermionic matter, which maps onto a local quantum spin chain. We benchmark both a classical matrix-product-state implementation of METTS and a recently proposed adaptive variational approach for near-term quantum devices, focusing on the equation of state and measures of fermion confinement. Of particular importance is the choice of basis for METTS sampling, which impacts both the sampling overhead and quantum circuit complexity. Our work sets the stage for future studies of strongly coupled gauge theories using classical and quantum hardware.
Chen, I-Chi [Iowa State Univ., Ames, IA (United St↗
Larger than uncorrelated vacancy diffusion contributions in chemically disordered crystalline materials
Arising from a variational approach to compute diffusion coefficients, we introduce “superkinetic kinosons”, which are contributions to the diffusion flux of mobile defects and atomic species by single jump mechanisms that can exceed their uncorrelated values. In vacancy-mediated diffusion in crystalline random and high entropy materials, these contributions primarily arise from intermittent jumps of slow moving atoms that remove the vacancy out of correlation traps and enable a quantification of such effects on the diffusion coefficients. They can be significant contributors to diffusion, even when faster moving atoms have infinite percolation networks. Furthermore, their existence and importance provide fundamental insights about underlying aspects of vacancy diffusion such as formation of localized correlation traps and deviation of vacancy diffusion from percolation behavior.
36 MATERIALS SCIENCE↗
Scaling and merging time-resolved pink-beam diffraction with variational inference
Time-resolved x-ray crystallography (TR-X) at synchrotrons and free electron lasers is a promising technique for recording dynamics of molecules at atomic resolution. While experimental methods for TR-X have proliferated and matured, data analysis is often difficult. Extracting small, time-dependent changes in signal is frequently a bottleneck for practitioners. Recent work demonstrated this challenge can be addressed when merging redundant observations by a statistical technique known as variational inference (VI). However, the variational approach to time-resolved data analysis requires identification of successful hyperparameters in order to optimally extract signal. In this case study, we present a successful application of VI to time-resolved changes in an enzyme, DJ-1, upon mixing with a substrate molecule, methylglyoxal. We present a strategy to extract high signal-to-noise changes in electron density from these data. Furthermore, we conduct an ablation study, in which we systematically remove one hyperparameter at a time to demonstrate the impact of each hyperparameter choice on the success of our model. We expect this case study will serve as a practical example for how others may deploy VI in order to analyze their time-resolved diffraction data.
47 OTHER INSTRUMENTATION↗
Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements
The adaptive variational quantum dynamics simulation (AVQDS) method performs real-time evolution of quantum states using automatically generated parametrized quantum circuits that often contain substantially fewer gates than Trotter circuits. Here we report an improved version of the method, which we call AVQDS(T), by porting the tiling efficient trial circuits with rotations implemented simultaneously technique. The algorithm adaptively adds layers of disjoint unitary gates to the ansatz circuit so as to keep the McLachlan distance, a measure of the accuracy of the variational dynamics, below a fixed threshold. Here we perform benchmark noiseless AVQDS(T) simulations of quench dynamics in local spin models and compare with an alternative adaptive variational approach on quantum resource requirement. Quantum dynamical simulations implementing realistic noise channels are also reported. Finally, we propose a way to substantially alleviate the measurement overhead of AVQDS(T) while maintaining high accuracy by synergistically integrating quantum circuit calculations on quantum processing units with classical calculations using, e.g., tensor networks to evaluate the quantum geometric tensor. We showcase that this approach enables AVQDS(T) to deliver more accurate results than simulations using a fixed ansatz of comparable final depth for a significant time duration with fewer quantum resources.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Advancing the Frontiers of Deep Learning for Low-Dose 3D Cone-Beam CT Reconstruction
X-ray computed tomography (CT) is an important noninvasive medical imaging modality for studying the structural details of internal organs. Image reconstruction in CT is an inverse problem of recovering an object's internal structure from the absorption profile of X-ray beams (sinogram) measured using a detector. The classical variational approach for CT reconstruction minimizes an energy functional using an appropriate iterative algorithm. Motivated by the success of deep learning (DL), researchers have begun to leverage training data and enhanced computing capabilities in recent years to produce high-fidelity reconstructed images. Nonetheless, much of the academic research in DL algorithms for CT has focused primarily on the two-dimensional setting (with simplified forward operators and noise model) for proofs-of-concept, and a comprehensive benchmarking of various classical and data-driven CT reconstruction approaches has not beenundertaken. The key objective of our CT reconstruction grand challenge was to promote methodological advancements for both classical and DL-based approaches for clinical CT with a reasonably accurately simulated 3D CT forward operator and noise model. We have utilized the publicly available LIDC-IDRI dataset and simulated sinograms and FDK images corresponding to two dose levels (clinical- and low-dose, constituting two tracks of the challenge) starting from the normal-dose images as the ground truth. In this paper, we summarize the motivation, context, and results of our challenge, and highlight the future research directions in DL for clinical CT.
X-ray tomography↗
DNN-based Signal Processing for Liquid Argon Time Projection Chambers
We investigate a deep learning-based signal processing for liquid argon time projection chambers (LArTPCs), a leading detector technology in neutrino physics. Identifying regions of interest (ROIs) in LArTPCs is challenging due to signal cancellation from bipolar responses and various detector effects observed in real data. We approach ROI identification as an image segmentation task, and employ a U-ResNet architecture. The network is trained on samples that incorporate detector geometry information and include a range of detector variations. Our approach significantly outperforms traditional methods while maintaining robustness across diverse detector conditions. This method has been adopted for signal processing in the Short-Baseline Neutrino program and provides a valuable foundation for future experiments such as the Deep Underground Neutrino Experiment.
Bhat, Avinay [Chicago U.]↗
Role of momentum in the generator-coordinate method applied to barrier penetration
Nuclear fission at barrier-top energies is conventionally modeled by a one-dimensional Schrödinger equation applied to internal fission channels, but that treatment is hard to justify in the configuration-interaction approach to nuclear Hamiltonians. Here we show that inclusion of states of finite momentum by the generator coordinate method (GCM) considerably extends the range of energies at which GCM-based Hamiltonians could reproduce the Schrödinger treatment. Furthermore, the transmission probabilities for crossing the barrier are calculated by a discrete version of Kohn's variational method, which may also be useful for other systems of interacting fermions.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Counterdiabatic Driving with Performance Guarantees
Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations that do not have performance guarantees. We propose and analyze a nonvariational, system-agnostic CD expansion method and analytically show that it converges exponentially quickly in the expansion order. In finite systems, the required resources scale inversely with the spectral gap, which we argue is asymptotically optimal. To extend our method to the thermodynamic limit and suppress errors stemming from high-frequency transitions, we leverage finite-time adiabatic protocols. In particular, we show that a time determined by the quantum speed limit is sufficient to prepare the desired ground state, without the need to optimize the adiabatic trajectory. Numerical tests of our method on the quantum Ising chain show that our method can outperform state-of-the-art variational CD approaches.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Evaluating switch lifetime in soft-switched single-stage differential-mode SST
The reliability of semiconductor switches in single-stage differential-mode solid-state transformers (DM-SSTs) has not been systematically evaluated under soft-switching operation and realistic grid conditions. This paper presents a switch-level reliability analysis for soft-switched and hard-switched DM-SST configurations by integrating converter-specific power loss modeling with empirical lifetime prediction. Analytical derivation of device current profiles specific to the DM-SST is used to characterize electrothermal stress, which is then mapped to lifetime using degradation models obtained from power cycling tests (PCTs). Applied to realistic SST load profiles and grid voltage variations, this approach provides a probabilistic prediction of switch lifetime for the DM-SST. Lifetime estimates for both SiC MOSFETs and Si IGBTs are presented, offering insight into device degradation under converter operating conditions. The results quantify the reliability benefits of soft switching in single-stage SSTs, highlighting how switching dynamics influence long-term switch degradation.
14 SOLAR ENERGY↗
Sensitivity of the Shallow‐To‐Deep Convective Transition to Moisture and Wind Shear in the Amazon
Deep convection is the primary influence on weather and climate in tropical regions. However, understanding and simulating the shallow‐to‐deep (STD) convective transition has long been challenging. Here, we conduct high‐resolution numerical simulations to assess the environmental controls on the evolution of isolated convection in the Amazon during the wet season. The large‐scale forcing derived through a constrained variational analysis approach for the GoAmazon2014/5 Experiment is used in the simulations. Through sensitivity experiments, we examine the relative importance of moisture and wind shear in controlling the shallow‐to‐deep convective transition for isolated convective events. Convection exhibits the greatest sensitivity to humidity within the lowest 1.5 km, where a 4 mm reduction in column water vapor nearly suppresses ice water formation on deep convective days. In contrast, a reduction in column water vapor in the free troposphere by a factor of two or more is necessary to produce a comparable impact on convection. Increasing low‐level wind speed from 6 to 9 m s -1 enhances afternoon deep convection, raising the cloud ice mixing ratio by approximately 25%. Conversely, upper‐level wind shear reveals the weakest correlation with daytime convection in our simulations. Our results help characterize the role of moisture and wind shear on the STD transition and our understanding of the underlying mechanisms.
environmental controls↗
State preparation of lattice field theories using quantum optimal control
Here, we explore the application of quantum optimal control (QOC) techniques to state preparation of lattice field theories on quantum computers. As a first example, we focus on the Schwinger model, quantum electrodynamics in 1+1 dimensions. We demonstrate that QOC can significantly speed up the ground state preparation compared to gate-based methods, even for models with long-range interactions. Using classical simulations, we explore the dependence on the interqubit coupling strength and the device connectivity, and we study the optimization in the presence of noise. While our simulations indicate potential speedups, the results strongly depend on the device specifications. In addition, we perform exploratory studies on the preparation of thermal states. Our results motivate further studies of QOC techniques in the context of quantum simulations for fundamental physics.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Neuralized fermionic tensor networks for quantum many-body systems
In this work, we describe a class of neuralized fermionic tensor network states (NN-fTNSs) that introduce nonlinearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction uses the fTNS algebra to implement a natural fermionic sign structure and is compatible with standard tensor network algorithms but gains enhanced expressivity through the neural network parametrization. Using the 1D and 2D Fermi-Hubbard models as benchmarks, we demonstrate that NN-fTNSs achieve order of magnitude improvements in the ground-state energy compared to pure fTNSs with the same bond dimension and can be systematically improved through both the tensor network bond dimension and the neural network parametrization. Compared to existing fermionic neural quantum states based on Slater determinants and Pfaffians, NN-fTNSs offer a physically motivated alternative fermionic structure. Furthermore, compared to such states, NN-fTNSs naturally exhibit improved computational scaling and we demonstrate a construction that achieves linear scaling with the lattice size.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗