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DOE OSTI2024

A brief review on strain engineering of ferroelectric K x Na 1- x NbO 3 epitaxial thin films: Insights from phase-field simulations

Strains play a pivotal role in determining the phase equilibrium, domain configuration, and functional properties of the low-dimensional ferroelectrics. There is growing interest in the strain engineering of ferroelectric K x Na 1- x NbO 3 (KNN) epitaxial thin films, which exhibit excellent physical properties and promise as eco-friendly alternatives to lead-based ferroelectrics for microdevice applications. Further, advances have been made in understanding the phase equilibria and transitions, domains and domain walls, and their relations to the physical properties of KNN epitaxial thin films using a combination of experiments and theoretical modeling, particularly phase-field simulations. Here, we review recent progress in these aspects and showcase the phase-field method for establishing strain phase diagrams, elucidating the domain and domain wall structures at equilibrium, and predicting the structure–property relationships in ferroelectric KNN thin films. We also discuss challenges and opportunities to further advance our understanding of KNN thin films and potentially unlock new functionalities by leveraging phase-field simulations.

36 MATERIALS SCIENCE↗

NASA NTRS1991

Lyapunov exponent of magnetospheric activity from AL time series

A correlation dimension analysis of the AE index indicates that the magnetosphere behaves as a low-dimensional chaotic system with a dimension close to 4. Similar techniques are used to determine if the system's behavior is due to an intrinsic sensitivity to initial conditions and thus is truly chaotic. The quantity used to measure the sensitivity to initial conditions is the Liapunov exponent. Its calculation for AL shows that it is nonzero (0.11 + or - 0.05/min). This gives the exponential rate at which initially similar configurations of the magnetosphere evolve into completely different states. Also, predictions of deterministic nonlinear models are expected to deviate from the observed behavior at the same rate.

Vassiliadis, D.↗

DOE OSTI2024

CO 2 storage site characterization using ensemble-based approaches with deep generative models

Estimating spatially distributed properties such as permeability from available sparse measurements is a great challenge in efficient subsurface CO 2 storage operations. In this paper, a deep generative model that can accurately capture complex subsurface structure is tested with an ensemble-based inversion method for accurate and accelerated characterization of CO 2 storage sites. We chose Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) for its realistic reservoir property representation and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) for its robust data fitting and uncertainty quantification capability. WGAN-GP are trained to generate high-dimensional permeability fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface site characterization examples including Gaussian, channelized, and fractured reservoirs are used to evaluate the accuracy and computational efficiency of the proposed method and the main features of the unknown permeability fields are characterized accurately with reliable uncertainty quantification. Furthermore, the estimation performance is compared with a widely-used variational, i.e., optimization-based, inversion approach, and the proposed approach outperforms the variational inversion method in several benchmark cases. We explain such superior performance by visualizing the objective function in the latent space: because of nonlinear and aggressive dimension reduction via generative modeling, the objective function surface becomes extremely complex while the ensemble approximation can smooth out the multi-modal surface during the minimization. This suggests that the ensemble-based approach works well over the variational approach when combined with deep generative models at the cost of forward model runs unless convergence-ensuring modifications are implemented in the variational inversion.

42 ENGINEERING↗

NASA NTRS1990

Modeling and stability of segmented reflector telescopes - A decentralized approach

The decentralization of a segmented reflector telescope based on a finite-element model of its structure is considered. The decentralization of the system at the panel level is considered. Each panel is originally treated as an isolated subsystem so that the controller design is performed independently at the local level, and then applied to the composite system for stability analysis. The panel-level control laws were designed by means of pole placement using local output feedback. Simulation results show a better 1000:1 vibration attenuation in panel position when compared to the open-loop system. It is shown that the overall closed-loop system is exponentially stable provided that certain conditions are met. The advantage to the decentralized approach is that the design is performed in terms of the low-dimensionality subsystems, thus drastically reducing the design computational complexities.

Ryaciotaki-Boussalis, Helen A.↗

DOE OSTI2025

Statistical Analysis of Intertube Tunneling Contacts in the Macroscopic Electrical Conductivity of Carbon Nanotube Fibers

Here, this study investigates the influence of tunneling contact resistances between carbon nanotubes (CNTs) on electron transport and electrical conductivity of macroscopic carbon nanofibers (CNFs), which profoundly impacts the performance of CNT thin film electronics, CNF electron emitters and cathodes, and energy conversion and storage devices. Utilizing a self-consistent electrical contact model coupling a transmission line model with tunneling current, we calculate the contact resistances of a plethora of CNT-CNT contacts within a CNF fiber, which consists of aligned, densely packed CNTs. A statistical analysis is conducted, using Gaussian distributions to account for variations in contact lengths, tunneling gap distances, and single CNT aspect ratios, to calculate the CNT-CNT contact resistance and the overall resistance of CNT fiber. By scaling our model to a macroscopic level, our results are in good agreement with experimental measurements. Our calculation suggests that while increasing the contact overlap length diminishes individual CNT-CNT contact resistance, it could paradoxically increase macroscopic CNT fiber resistance for a given constant CNF mass density, which is due to that fact that a larger overlap length allows more CNTs to pack along an electrical conduction path per unit length, leading to more tunneling contact junctions connected in series and thus less number of parallel conduction paths within the fiber cross section. Increasing tunneling gap distance increases both individual contact and overall fiber resistance. This research provides a simple design tool for tailoring CNT fiber electrical properties to promote real-world applications using CNTs or similar low-dimensional materials.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Tensor network simulations of quasi-GPDs in the massive Schwinger model

Generalized parton distribution functions (GPDs) are off-diagonal light-cone matrix elements that encode the internal structure of hadrons in terms of quark and gluon degrees of freedom. In this work, we present the first nonperturbative study of quasi-GPDs in the massive Schwinger model, quantum electrodynamics in 1+1 dimensions (QED 2 ), within the Hamiltonian formulation of lattice field theory. Quasidistributions are spatial correlation functions of boosted states, which approach the relevant light-cone distributions in the luminal limit. Using tensor networks, we prepare the first excited state in the strongly coupled regime and boost it to close to the light-cone on lattices of up to 400 lattice sites. We compute both quasiparton distribution functions and, for the first time, quasi-GPDs, and study their convergence for increasingly boosted states. In addition, we perform analytic calculations of GPDs in the two-particle Fock-space approximation and in the Reggeized limit, providing qualitative benchmarks for the tensor network results. Our analysis establishes computational benchmarks for accessing partonic observables in low-dimensional gauge theories, offering a starting point for future extensions to higher dimensions, non-Abelian theories, and quantum simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

The influence of cooling rates on strain phase diagrams and domain structures of ferroelectric thin films: A case study of PbTiO 3

Strain engineering has been established as an effective approach to control phase equilibria, domain configurations, and functional properties of ferroelectric thin films. Temperature-strain phase diagrams have been used as powerful tools for providing insights into strain engineering. However, almost all existing phase diagrams established using the phase-field approach assume quenching conditions without considering actual cooling rates during the post-deposition annealing process of ferroelectric thin films. Within this work, we systematically investigate the influence of cooling rates on domain structures and the strain-phase diagram of ferroelectric thin films using phase-field simulations, taking PbTiO 3 thin films as a model system. We found that both the position of phase boundaries in the strain phase diagrams and the domain morphology are significantly influenced by the cooling rates. It is revealed that while the paraelectric-ferroelectric phase boundary remains invariant, the phase boundaries between single-phase and multi-phase regions tend to shift toward the corresponding multi-phase region as the cool rate reduces. Slow cooling generally leads to more ordered domain structures with increased domain size. Using the obtained equilibrium domain structures, we calculated effective thermal conductivities and found significant variations that can be tuned by the cooling rates. In conclusion, this work reveals an underexplored yet critical impact of cooling rates on phase equilibria and domain structures in ferroelectric thin films, which may inspire further fine-tuning of domains and domain walls in low-dimensional ferroelectrics for multifunctional applications.

Domain structures↗

DOE OSTI2025

Renormalization of states and quasiparticles in many-body downfolding

We explore the principles of many-body Hamiltonian complexity reduction via downfolding on an effective low-dimensional representation. We show that the renormalization factor provides a unique measure of the quality of the compression as it directly represents the projection between the approximate stationary state of the many-body Hamiltonian and the full many-body wavefunction. Hence, the renormalization factor is a measure of fidelity between the effective (reduced-rank) description and the full many-body treatment for arbitrary (i.e., ground and excited) states. When the entire problem is mapped on a system of interacting quasiparticles [Romanova et al., npj Comput. Mater. 9, 126 (2023)], the effective Hamiltonians can faithfully reproduce the physics only when a clear energy scale separation exists between the subsystems and their environment. We also demonstrate that it is necessary to include quasiparticle renormalization at distinct energy scales, capturing the distinct interaction between subsystems and their surrounding environments. Numerical results from simple, exactly solvable models highlight the limitations and strengths of this approach, particularly for ground and low-lying excited states. This work lays the groundwork for applying dynamical downfolding techniques to problems concerned with (quantum) interfaces.

Green-functions technique↗

DOE OSTI2025

Ultrafast-induced coherent acoustic phonons in the two-dimensional magnet CrSBr

Magnetism in two-dimensional (2D) van der Waals (vdW) crystals offers promising new directions for low-dimensional physics and devices. In this work, mega-electron volt (MeV) ultrafast electron diffraction was employed to investigate the ultrafast atomic dynamics of a novel, 2D vdW magnetic single-crystal CrSBr. Femtosecond (fs) optical pump pulses excited non-equilibrium atomic displacements shown to be coherent acoustic phonons (CAPs). Phonon frequencies were extracted by analyzing oscillations of different Bragg peak (BP) intensities and were determined to be GHz acoustic disturbances that propagated as strain waves. Phonon modes exhibit anisotropy with respect to the a and b crystal axes. Subharmonic phonon frequencies were also observed, and this provided a signature of nonlinear oscillatory coupling between the laser-induced pumping phonon frequency and secondary phonon frequencies. Thus, CrSBr was found to serve as a nonlinear phononic frequency converter. The ultrafast time dependence of the Bragg intensity was simulated by incorporating an oscillating deviation parameter ansatz into expressions for the dynamical scattering intensity yielded excellent modeling of the ultrafast structural dynamics of the photo-excited 2D crystal. Our work provides a foundation for exploring how fs light pulses can influence phonon dynamics in materials with strong spin-lattice coupling. These results suggest that CAPs can match the magnon frequencies and show the promise of CrSBr for use in optical-to-microwave transducers and phononic devices.

43 PARTICLE ACCELERATORS↗

NASA NTRS2000

Low-dimensional Representation of Error Covariance

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

Tippett, Michael K.↗

DOE OSTI2025

Epitaxy of Emerging Materials and Advanced Heterostructures for Microelectronics and Quantum Sciences

Abstract Epitaxy, a process to prepare crystalline materials in nanostructures and thin films, is the core technology for preparing high‐quality materials as a key enabler of next‐generation microelectronics and quantum information system. Progress in epitaxy has been expanding the choice of materials and their heterostructures beyond the combinations limited by materials compatibility. However, the improvement of material quality, physical implementation of materials with unique properties, and integration of incommensurate materials in an architecture have been the challenging issues. Emerging materials, including 2D materials and quantum materials, have opened opportunities to study epitaxy mechanisms and realize various functional devices. Acceleration of discovery and progress in epitaxy research should be accomplished by “understanding of epitaxy under various circumstances at multiple length scales” and “integration of experiments and models.” In the perspective, a basic summary of the status of epitaxially grown materials, the challenges in epitaxy research, and integration of modeling epitaxy and ultimate control of the epitaxy process with advanced characterization techniques are discussed.

Materials Science↗

DOE OSTI2025

Enhancing Interpretability in Generative Modeling: Statistically Disentangled Latent Spaces Guided by Generative Factors in Scientific Datasets

This study addresses the challenge of statistically extracting generative factors from complex, high-dimensional datasets in unsupervised or semi-supervised settings. We investigate encoder-decoder-based generative models for nonlinear dimensionality reduction, focusing on disentangling low-dimensional latent variables corresponding to independent physical factors. Introducing Aux-VAE, a novel architecture within the classical Variational Autoencoder framework, we achieve disentanglement with minimal modifications to the standard VAE loss function by leveraging prior statistical knowledge through auxiliary variables. These variables guide the shaping of the latent space by aligning latent factors with learned auxiliary variables. We validate the efficacy of Aux-VAE through comparative assessments on multiple datasets, including astronomical simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a set of low-dimensional (latent) descriptors that efficiently parameterize the response of the high-dimensional computational model. To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data. Since operations on the Grassmann require the data to be concentrated, we propose an adaptive algorithm based on Riemannian K-means and the minimization of the sample Fréchet variance on the Grassmann manifold to identify “local” principal geodesic submanifolds that represent different system behavior across the parameter space. Polynomial chaos expansion is then used to construct a mapping between the random input parameters and the projection of the response on these local principal geodesic submanifolds. Here, the method is demonstrated on four test cases, a toy-example that involves points on a hypersphere, a Lotka-Volterra dynamical system, a continuous-flow stirred-tank chemical reactor system, and a two-dimensional Rayleigh-Bénard convection problem.

42 ENGINEERING↗

DOE OSTI2024

Unsupervised multimodal fusion of in-process sensor data for advanced manufacturing process monitoring

Effective monitoring of manufacturing processes is crucial for maintaining product quality and operational efficiency. Modern manufacturing environments often generate vast amounts of complementary multimodal data, including visual imagery from various perspectives and resolutions, hyperspectral data, and machine health monitoring information such as actuator positions, accelerometer readings, and temperature measurements. However, fusing and interpreting this complex, high-dimensional data presents significant challenges, particularly when labeled datasets are unavailable or impractical to obtain. This paper presents a novel approach to multimodal sensor data fusion in manufacturing processes, inspired by the Contrastive Language-Image Pre-training (CLIP) model. We leverage contrastive learning techniques to correlate different data modalities without the need for labeled data, overcoming limitations of traditional supervised machine learning methods in manufacturing contexts. Our proposed method demonstrates the ability to handle and learn encoders for five distinct modalities: visual imagery, audio signals, laser position (x and y coordinates), and laser power measurements. By compressing these high-dimensional datasets into low-dimensional representational spaces, our approach facilitates downstream tasks such as process control, anomaly detection, and quality assurance. The unsupervised nature of our method makes it broadly applicable across various manufacturing domains, where large volumes of unlabeled sensor data are common. We evaluate the effectiveness of our approach through a series of experiments, demonstrating its potential to enhance process monitoring capabilities in advanced manufacturing systems. This research contributes to the field of smart manufacturing by providing a flexible, scalable framework for multimodal data fusion that can adapt to diverse manufacturing environments and sensor configurations. The proposed method paves the way for more robust, data-driven decision-making in complex manufacturing processes.

Contrastive Learning↗

DOE OSTI2025

Discriminative versus generative approaches to simulation-based inference

Most of the fundamental, emergent, and phenomenological parameters of particle and nuclear physics are determined through parametric template fits. Simulations are used to populate histograms which are then matched to data. This approach is inherently lossy, since histograms are binned and low-dimensional. Deep learning has enabled unbinned and high-dimensional parameter estimation through neural likelihood(-ratio) estimation. We compare two approaches for neural simulation-based inference (NSBI): one based on discriminative learning (classification) and one based on generative modeling. These two approaches are directly evaluated on the same datasets, with a similar level of hyperparameter optimization in both cases. In addition to a Gaussian dataset, we study NSBI using a Higgs boson dataset from the FAIR Universe Challenge. We find that both the direct likelihood and likelihood ratio estimation are able to effectively extract parameters with reasonable uncertainties. For the numerical examples and within the set of hyperparameters studied, we found that the likelihood ratio method is more accurate and/or precise. Both methods have a significant spread from the network training and would require ensembling or other mitigation strategies in practice.

high energy physics↗

DOE OSTI2026

Quasi-One-Dimensional Spin Excitations in the Iron Pnictide NaFe 0.53 ⁢Cu 0.47 ⁢As

Spectroscopic measurements in model 1D correlated systems offer insights for understanding their two-dimensional counterparts, which include the cuprate and iron pnictide/chalcogenide superconductors. A major challenge is the identification of such correlated systems with dominantly 1D physics. Here, in this Letter, inelastic neutron scattering measurements on NaFe 0.53⁢ Cu 0.47 ⁢As single crystal directly reveal quasi-1D spin excitations, resulting from atomic order that leads to magnetic Fe and nonmagnetic Cu chains. The dominant exchange interaction is antiferromagnetic along the chain [𝑆⁢𝐽 ∥ ≈ 90.1⁢(3) meV], whereas the inter-chain couplings are much weaker [𝑆⁢𝐽 ⊥ ≈ −2.4⁢(1) meV and 𝑆⁢𝐽 c ≈ 0.15⁢(5) meV]. The quasi-1D spin excitations in NaFe 0.53 ⁢Cu 0.47⁢ As stem from both the Néel and stripe vectors, with Néel excitations sensitive to Fe impurities on the Cu site. The spin excitations in quasi-1D NaFe 0.53 ⁢Cu 0.47⁢ As and quasi-2D FeSe exhibit a striking resemblance, suggesting a common origin for their coexistent stripe and Néel excitations. Our findings demonstrate magnetic dilution in NaFeAs leads to dimension reduction of its magnetic degree of freedom, presenting a strategy for discovering low-dimensional quantum materials.

Wang, Yifan [Zhejiang Univ., Hangzhou (China)]↗

DOE OSTI2025

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks

Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. In addition, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.

97 MATHEMATICS AND COMPUTING↗