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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Body Mass Variation in an Introduced Wild Pig Population with Changing Ancestry

Total body mass variation was studied in a single wild pig (Sus scrofa) population that originated from three introductions of varying ancestry. Body mass data from 12,257 wild pigs collected over more than five decades were analyzed for differences due to the effects of sex, age class, reproductive status, season, and historic subpopulation groupings. Total body mass data from this population averaged 38 kg and ranged from 0.511 to 189 kg. The overall observed range of body mass data was consistent with previous studies. Very heavy individuals (i.e., >150 kg) made up only a small percentage of the overall population. Males were significantly larger than females, being on average 1.09 times heavier. This significant sexual dimorphic difference was seen in all but the piglet age class. This percent dimorphic difference increased with age. Body mass variation and overlap between the age classes also increased with age. Males were more variable than females within the same age class. The study area’s wild pigs were on average born at slightly less than one percent of their adult body mass. Percent weight gain toward the adult body mass increased with age and was slightly greater in females than in males. In contrast, absolute weight gain between age classes was greater in males. Pregnant sows were significantly heavier than non-pregnant females in all age class comparisons; however, this difference decreased with age. There was a seasonal shift in body mass with age, with younger age classes being heaviest in the fall-winter period and the older age classes being heaviest in spring-summer. Having originated from different ancestral stocks, two major subpopulations of wild pigs on the study area differed significantly in body mass in all sex and age class comparisons. The SRS wild pig population showed a decrease in body mass during the 1990s that was significant. This change may have been the result of both ancestral and population density variation, as well as unspecified environmental factors

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Description of the Three-Dimensional Large-Scale Forcing Data from the 3D Constrained Variational Analysis (VARANAL3D)

This technical report introduces a Three-Dimensional Constrained Variational Analysis (3DCVA) (Tang and Zhang 2015) and its product of three-dimensional large-scale forcing data to drive single-column models (SCM), cloud-resolving models (CRM), and large-eddy simulation (LES) models, and to evaluate model results. The 3DCVA algorithm is an extension of the original 1D constrained variational analysis (1DCVA) (Zhang and Lin 1997, Zhang et al. 2001). The three-dimensional structure of the forcing data allows studies of spatial variation of the large-scale forcing fields and tests of physical parameterizations across scales. In the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility, the 3D forcing data are assigned the datastream name varanal3d. In this technical report, 3DCVA will be used to refer to the algorithm, while VARANAL3D will be used to refer to the data product.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Fifty ways to build a deuteron: a variational calculation of two-nucleon systems

A variational study of two-nucleon systems with lattice quantum chromodynamics is performed using a wide range of interpolating operators: dibaryon operators built from products of momentum-projected nucleons, hexaquark operators built from six spatially localized quarks, and quasi-local operators inspired by two-nucleon bound-state wavefunctions in nuclear effective field theories. Correlation-function matrices involving products of these operators are constructed by computing timeslice-to-all quark propagators with sparsening techniques. Comparisons between results obtained using the same gauge-field ensemble but different interpolating-operator sets demonstrate that interpolating-operator dependence can lead to significant effects on the two-nucleon energy spectra obtained using both variational and non-variational methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers

Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ansätze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number n of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size 2 n − 2 can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such "complete" pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings.

Shkolnikov, V. O.↗
DOE OSTI2023

Leveraging microfluidic dielectrophoresis to distinguish compositional variations of lipopolysaccharide in E. coli

Lipopolysaccharide (LPS) is the unique feature that composes the outer leaflet of the Gram-negative bacterial cell envelope. Variations in LPS structures affect a number of physiological processes, including outer membrane permeability, antimicrobial resistance, recognition by the host immune system, biofilm formation, and interbacterial competition. Rapid characterization of LPS properties is crucial for studying the relationship between these LPS structural changes and bacterial physiology. However, current assessments of LPS structures require LPS extraction and purification followed by cumbersome proteomic analysis. This paper demonstrates one of the first high-throughput and non-invasive strategies to directly distinguish Escherichia coli with different LPS structures. Using a combination of three-dimensional insulator-based dielectrophoresis (3DiDEP) and cell tracking in a linear electrokinetics assay, we elucidate the effect of structural changes in E. coli LPS oligosaccharides on electrokinetic mobility and polarizability. We show that our platform is sufficiently sensitive to detect LPS structural variations at the molecular level. To correlate electrokinetic properties of LPS with the outer membrane permeability, we further examined effects of LPS structural variations on bacterial susceptibility to colistin, an antibiotic known to disrupt the outer membrane by targeting LPS. Our results suggest that microfluidic electrokinetic platforms employing 3DiDEP can be a useful tool for isolating and selecting bacteria based on their LPS glycoforms. Future iterations of these platforms could be leveraged for rapid profiling of pathogens based on their surface LPS structural identity.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Whole-Genome Resequencing to Evaluate Life History Variation in Anadromous Migration of Oncorhynchus mykiss

Anadromous fish experience physiological modifications necessary to migrate between vastly different freshwater and marine environments, but some species such as Oncorhynchus mykiss demonstrate variation in life history strategies with some individuals remaining exclusively resident in freshwater, whereas others undergo anadromous migration. Because there is limited understanding of genes involved in this life history variation across populations of this species, we evaluated the genomic difference between known anadromous ( n = 39) and resident ( n = 78) Oncorhynchus mykiss collected from the Klickitat River, WA, USA, with whole-genome resequencing methods. Sequencing of these collections yielded 5.64 million single-nucleotide polymorphisms that were tested for significant differences between resident and anadromous groups along with previously identified candidate gene regions. Although a few regions of the genome were marginally significant, there was one region on chromosome Omy12 that provided the most consistent signal of association with anadromy near two annotated genes in the reference assembly: COP9 signalosome complex subunit 6 (CSN6) and NACHT, LRR, and PYD domain–containing protein 3 (NLRP3). Previously identified candidate genes for anadromy within the inversion region of chromosome Omy05 in coastal steelhead and rainbow trout were not informative for this population as shown in previous studies. Results indicate that the significant region on chromosome Omy12 may represent a minor effect gene for male anadromy and suggests that this life history variation in Oncorhynchus mykiss is more strongly driven by other mechanisms related to environmental rearing such as epigenetic modification, gene expression, and phenotypic plasticity. Further studies into regulatory mechanisms of this trait are needed to understand drivers of anadromy in populations of this protected species.

Collins, Erin E.↗
DOE OSTI2025

Modeling and Analysis of Wind Turbine Wake Vortex Evolution Due to Time-Constant Spatial Variations in Atmospheric Flow

Modern utility-scale wind turbines are evolving toward larger, lighter, and more flexible designs to meet the growing demand for renewable energy while minimizing logistical costs. However, these advancements in lightweight design result in heightened aeroelastic sensitivity, leading to complex interactions which affect the rotor’s capacity to withstand aerodynamic loading and the cascading effects that manifest in the wake’s vortex-structure evolution under variable atmospheric conditions. In this paper, we analyze the influence of stream-wise fluctuating atmospheric flow conditions on wind turbines with large, flexible rotors through simulations of the National Rotor Testbed (NRT) turbine, located at Sandia National Labs’ Scaled Wind Farm Technology (SWiFT) facility in Lubbock, Texas. The Common Ordinary Differential Equation Framework (CODEF) modeling suite is used to simulate wind turbine aeroelastic oscillatory behavior and wind farm vortex–wake interactions for a range of conditions with spatially variant atmospheric flow. CODEF solutions for turbine operation in wind conditions featuring only one parameter fluctuation are compared to wind conditions with several wind parameter variations in combination. By isolating individual inflow variations and comparing them to multi-parameter scenarios, we determine the contributions of each atmospheric factor to rotor dynamics, wake evolution, and downstream wind farm interactions. The purpose of this paper is to analyze the effects of spatial variations in atmospheric flow on the topological evolution of wind turbine vortex wakes, which constitutes a gap in the current understanding of wind turbine wake dynamics. The insights gained from this study are particularly valuable for the development of wind farm control strategies aimed at mitigating the adverse effects of wake interactions, enhancing energy capture, and improving the overall stability of wind farm operations. With these insights, we aim to contribute to the development of modeling and simulation tools to optimize utility-scale wind power plants operating in diverse atmospheric environments.

Farrell, Alayna (ORCID:000000023555720X)↗
DOE OSTI2025

The DESI Y1 RR Lyrae catalog I: Empirical modeling of the cyclic variation of spectroscopic properties and a chemodynamical analysis of the outer halo

We present the catalog of RR Lyrae stars observed in the first year of operations of the Dark Energy Spectroscopic Instrument (DESI) survey. This catalog contains 6,240 RR Lyrae stars out to $\sim100$ kpc from the Galactic center and over 12,000 individual epochs with homogeneously-derived stellar atmospheric parameters. We introduce a novel methodology to model the cyclical variation of the spectroscopic properties of RR Lyrae from single-epoch measurements. We employ this method to infer the radial velocity and effective temperature variation of fundamental mode and first-overtone RR Lyrae stars and to determine their systemic velocities and mean temperatures. For fundamental mode pulsators, we obtain radial velocity curves with amplitudes of $\sim$30--50 km s$^{-1}$ and effective temperature curves with 300--1,000 K variations, whereas for first-overtone pulsators these amplitudes are $\sim20$ km s$^{-1}$ and $\sim 600$ K, respectively. We use our sample to study the metallicity distribution of the halo and its dependence on Galactocentric distance ($R_{\rm GC}$). Using a radius-dependent mixture model, we split the data into chemodynamically distinct components and find that our inner halo sample ($R_{\rm GC}\lesssim50$ kpc) is predominantly composed of stars with [Fe/H] $\sim-1.5$ dex and largely radial orbits (with an anisotropy parameter $\beta\sim0.94$), that we associate with the Gaia-Sausage-Enceladus merger event. Stars in the outer halo field exhibit a broader and more metal-poor [Fe/H] distribution with more circular orbits ($\beta\sim0.39$). The metallicity gradient of the metal-rich and the metal-poor components is found to be $0.005$ and $0.010$ dex kpc$^{-1}$, respectively. Our catalog highlights DESI's tantalizing potential for studying the Milky Way and the pulsation properties of RR Lyrae stars in the era of large spectroscopic surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Therapeutic genetic variation revealed in diverse Hsp104 homologs

The AAA+ protein disaggregase, Hsp104, increases fitness under stress by reversing stress-induced protein aggregation. Natural Hsp104 variants might exist with enhanced, selective activity against neurodegenerative disease substrates. However, natural Hsp104 variation remains largely unexplored. Here, we screened a cross-kingdom collection of Hsp104 homologs in yeast proteotoxicity models. Prokaryotic ClpG reduced TDP-43, FUS, and α-synuclein toxicity, whereas prokaryotic ClpB and hyperactive variants were ineffective. Furthermore, we uncovered therapeutic genetic variation among eukaryotic Hsp104 homologs that specifically antagonized TDP-43 condensation and toxicity in yeast and TDP-43 aggregation in human cells. We also uncovered distinct eukaryotic Hsp104 homologs that selectively antagonized α-synuclein condensation and toxicity in yeast and dopaminergic neurodegeneration in C. elegans . Surprisingly, this therapeutic variation did not manifest as enhanced disaggregase activity, but rather as increased passive inhibition of aggregation of specific substrates. By exploring natural tuning of this passive Hsp104 activity, we elucidated enhanced, substrate-specific agents that counter proteotoxicity underlying neurodegeneration.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Crossing The Gap Using Variational Quantum Eigensolver: A Comparative Study

Within the evolving domain of quantum computational chemistry, the Variational Quantum Eigensolver (VQE) has been developed to explore not only the ground state but also the excited states of molecules. In this study, we compare the performance of Variational Quantum Deflation (VQD) and Subspace-Search Variational Quantum Eigensolver (SSVQE) methods in determining the low-lying excited states of $LiH$. Our investigation reveals that while VQD exhibits a slight advantage in accuracy, SSVQE stands out for its efficiency, allowing the determination of all low-lying excited states through a single parameter optimization procedure. We further evaluate the effectiveness of optimizers, including Gradient Descent (GD), Quantum Natural Gradient (QNG), and Adam optimizer, in obtaining $LiH$'s first excited state, with the Adam optimizer demonstrating superior efficiency in requiring the fewest iterations. Moreover, we propose a novel approach combining Folded Spectrum VQE (FS-VQE) with either VQD or SSVQE, enabling the exploration of highly excited states. We test the new approaches for finding all three $H_4$'s excited states. Folded Spectrum SSVQE (FS-SSVQE) can find all three highly excited states near $-1.0$ Ha with only one optimizing procedure, but the procedure converges slowly. In contrast, although Folded spectrum VQD (FS-VQD) gets highly excited states with individual optimizing procedures, the optimizing procedure converges faster.

Chen, I-Chi↗
DOE OSTI2023

A dynamic variational multiscale method on unstructured meshes for stationary transport problems

Here, this paper presents a variational multiscale (VMS) based finite element method where the stabilization parameter is computed dynamically. The current dynamic procedure takes in a general structure/form of the stabilization parameter with unknown coefficients and computes them dynamically in a local fashion resulting in a dynamic VMS-based finite element method. Thus, a static stabilization parameter with pre-defined coefficients is not needed. A variational Germano identity (VGI) based local procedure suitable for unstructured meshes is developed to perform the dynamic computation in a local fashion. The local VGI based procedure is applied for each interior vertex in the mesh and unknown coefficients are first determined locally at each vertex, and subsequently, for each element a maximum value is taken over the vertices of the element. To make the current procedure practical, a coarser secondary solution is constructed from the primary coarse-scale solution, which is done locally over a patch of elements around each interior vertex. Further, averaging steps are employed to make the local dynamic procedure robust. Currently, the new dynamic VMS formulation is applied to steady problems governed by the advection-diffusion and incompressible Navier-Stokes equations in both 1D and 2D to demonstrate its efficacy and effectiveness.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

CAFQA: A Classical Simulation Bootstrap for Variational Quantum Algorithms

Classical computing plays a critical role in the advancement of quantum frontiers in the NISQ era. In this spirit, this work uses classical simulation to bootstrap Variational Quantum Algorithms (VQAs). VQAs rely upon the iterative optimization of a parameterized unitary circuit (ansatz) with respect to an objective function. Since quantum machines are noisy and expensive resources, it is imperative to classically choose the VQA ansatz initial parameters to be as close to optimal as possible to improve VQA accuracy and accelerate their convergence on today’s devices. This work tackles the problem of finding a good ansatz initialization, by proposing CAFQA, a Clifford Ansatz For Quantum Accuracy. The CAFQA ansatz is a hardware-efficient circuit built with only Clifford gates. In this ansatz, the parameters for the tunable gates are chosen by searching efficiently through the Clifford parameter space via classical simulation. The resulting initial states always equal or outperform traditional classical initialization (e.g., Hartree-Fock), and enable high-accuracy VQA estimations. CAFQA is well-suited to classical computation because: a) Clifford-only quantum circuits can be exactly simulated classically in polynomial time, and b) the discrete Clifford space is searched efficiently via Bayesian Optimization. For the Variational Quantum Eigensolver (VQE) task of molecular ground state energy estimation (up to 18 qubits), CAFQA’s Clifford Ansatz achieves a mean accuracy of nearly 99% and recovers as much as 99.99% of the molecular correlation energy that is lost in Hartree-Fock initialization. CAFQA achieves mean accuracy improvements of 6.4x and 56.8x, over the state-of-the-art, on different metrics. Here, the scalability of the approach allows for preliminary ground state energy estimation of the challenging chromium dimer (Cr2) molecule. With CAFQA’s high-accuracy initialization, the convergence of VQAs is shown to accelerate by 2.5x, even for small molecules. Furthermore, preliminary exploration of allowing a limited number of non-Clifford (T) gates in the CAFQA framework, shows that as much as 99.9% of the correlation energy can be recovered at bond lengths for which Clifford-only CAFQA accuracy is relatively limited, while remaining classically simulable.

bayesian optimization↗
DOE OSTI2020

Variations in northeast Asian summer precipitation driven by the Atlantic multidecadal oscillation

By analysing a 113–year (1900–2012) observational dataset, it is shown in this work that the interdecadal fluctuation of the summer precipitation over Northeast Asia differs from that in central East Asia during the 20th century, and has experienced three interdecadal shifts in the 1920s, mid-1960s and late 1990s. That fluctuation coincides well with the multidecadal fluctuation of the sea surface temperature in the North Atlantic, known as the Atlantic Multidecadal Oscillation (AMO). The AMO affects Northeast Asia via a circumglobal teleconnection pattern extending from the North Atlantic to North America. Corresponding with the positive phase of this teleconnection pattern, a tripolar pattern emerges in the Asian–North Pacific sector, with anomalous low pressure over Northeast Asia and high pressure over Lake Baikal and the mid-latitude western North Pacific. These results suggest that the positive phase of the AMO favours the occurrence of cold vortex over Northeast Asia and anomalous highs over Lake Baikal and the mid-latitude western North Pacific in summer, which enhances the East Asian summer monsoon and southward intrusion of high-latitude cold air, and eventually increases the summer precipitation in Northeast Asia. Furthermore, initialized decadal prediction simulations using the CCSM4 model reproduce well the observed variations of the AMO and its associated atmospheric teleconnection but with slightly shifted geographic locations. The simulated anomalous Northeast Asia cold vortex and strong East Asian summer monsoon, lead to above-normal summer precipitation over Northeast Asia. The modelling results confirm that the multidecadal variability in the North Atlantic can cause the observed interdecadal variations of Northeast Asia summer precipitation. Our results suggest that to understand and predict interdecadal climate change over Northeast Asia, it is important to consider the key role of the AMO.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A semi-agnostic ansatz with variable structure for variational quantum algorithms

Quantum machine learning—and specifically Variational Quantum Algorithms (VQAs)—offers a powerful, flexible paradigm for programming near-term quantum computers, with applications in chemistry, metrology, materials science, data science, and mathematics. Here, one trains an ansatz, in the form of a parameterized quantum circuit, to accomplish a task of interest. However, challenges have recently emerged suggesting that deep ansatzes are difficult to train, due to flat training landscapes caused by randomness or by hardware noise. This motivates our work, where we present a variable structure approach to build ansatzes for VQAs. Our approach, called VAns (Variable Ansatz), applies a set of rules to both grow and (crucially) remove quantum gates in an informed manner during the optimization. Consequently, VAns is ideally suited to mitigate trainability and noise-related issues by keeping the ansatz shallow. We employ VAns in the variational quantum eigensolver for condensed matter and quantum chemistry applications, in the quantum autoencoder for data compression and in unitary compilation problems showing successful results in all cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Bi-fidelity variational auto-encoder for uncertainty quantification

Quantifying the uncertainty of quantities of interest (QoIs) from physical systems is a primary objective in model validation. However, achieving this goal entails balancing the need for computational efficiency with the requirement for numerical accuracy. To address this trade-off, we propose a novel bi-fidelity formulation of variational auto-encoders (BF-VAE) designed to estimate the uncertainty associated with a QoI from low-fidelity (LF) and high-fidelity (HF) samples of the QoI. Here, this model allows for the approximation of the statistics of the HF QoI by leveraging information derived from its LF counterpart. Specifically, we design a bi-fidelity auto-regressive model in the latent space which is integrated within the VAE’s probabilistic encoder–decoder structure. An effective algorithm is proposed to maximize the variational lower bound of the HF log-likelihood in the presence of limited HF data, resulting in the synthesis of HF realizations with a reduced computational cost. Additionally, we introduce the concept of the bi-fidelity information bottleneck (BF-IB) to provide an information-theoretic interpretation of the proposed BF-VAE model. Our numerical results demonstrate that the BF-VAE leads to considerably improved accuracy, as compared to a VAE trained using only HF data, when limited HF data is available.

42 ENGINEERING↗
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

Probing the role of local tunnel variations in early-stage lithiation of α-MnO₂ nanowires via in situ TEM

Understanding lithium-ion transport in tunnel-structured manganese oxides is essential for designing high-performance lithium-ion battery electrode materials. Here, we elucidate the early-stage lithiation mechanism of potassium-stabilized α-MnO 2 nanowires using in situ transmission electron microscopy (TEM) coupled with electron energy-loss spectroscopy (EELS), high-resolution TEM (HRTEM), and geometric phase analysis (GPA). Real-time TEM imaging reveals clear volume expansion at the reaction front, while EELS analysis uncovers lithium-ion diffusion far beyond this region, where no visible expansion is observed, indicating fast, defect-assisted transport. GPA and HRTEM analyses show that localized tensile and compressive strain fields, originating from pre-existing local tunnel structural variations, persist after lithiation. The tensile-strained regions enable lithium-ion insertion with minimal lattice distortion, offering additional free volume that facilitates rapid lithium-ion accommodation ahead of the structural transformation. Our results demonstrate a local tunnel variation-mediated fast diffusion pathway that precedes bulk reaction, underscoring the critical role of local strain in enabling early-stage lithium transport. Given the structural versatility of MnO 2 and its ability to accommodate diverse atomic arrangements beyond the well-known tunnel phases (β-, γ-, δ-, λ-, R-phases), our findings highlight the importance of understanding and engineering local structural environments. This work provides fundamental insights into the interplay between defects, strain, and ion dynamics, and presents defect engineering as a promising approach to enhance both rate performance and structural stability in manganese-based cathodes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

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↗