Reduced order models based on the transport of a lower dimensional manifold representation of the thermochemical state, such as Principal Component (PC) transport and Machine Learning (ML) techniques, have been developed to reduce the computational cost associated with the Direct Numerical Simulations (DNS) of reactive flows. Both PC transport and ML normally require an abundance of data to exhibit sufficient predictive accuracy, which might not be available due to the prohibitive cost of DNS or experimental data acquisition. To alleviate such difficulties, similar data from an existing dataset or domain (source domain) can be used to train ML models, potentially resulting in adequate predictions in the domain of interest (target domain). This study presents a novel probabilistic transfer learning (TL) framework to enhance the trust in ML models in correctly predicting the thermochemical state in a lower dimensional manifold and a sparse data setting. The framework uses Bayesian neural networks, and autoencoders, to reduce the dimensionality of the state space and diffuse the knowledge from the source to the target domain. The new framework is applied to one-dimensional freely-propagating flame solutions under different data sparsity scenarios. The results reveal that there is an optimal amount of knowledge to be transferred, which depends on the amount of data available in the target domain and the similarity between the domains. TL can reduce the reconstruction error by one order of magnitude for cases with large sparsity. The new framework required 10 times less data for the target domain to reproduce the same error as in the abundant data scenario. Furthermore, comparisons with a state-of-the-art deterministic TL strategy show that the probabilistic method can require four times less data to achieve the same reconstruction error.
Fang Liu, Slawomir Skruszewicz, Julian Späthe, Yinyu Zhang, Sebastian Hell, Bo Ying, Gerhard G. Paulus, Bálint Kiss, Krishna Murari, Malin Khalil, Eric Cormier, Li Guang Jiao, Stephan Fritzsche, Matthias Kübel Strong-field ionization can induce electron motion in both the continuum and the valence shell of the parent ion. Here, we explore their interplay by studying laser-induced electron diffraction (LIED) patterns arising from interaction with the potentials of two-hole states of the xenon cation. The quantitative rescattering theory is used to calculate the corresponding photoelectron momentum distributions, providing evidence that the spin-orbit dynamics could be detected by LIED. We identify the contribution of these time-evolving hole states to the angular distribution of the rescattered electrons, particularly noting a distinct change along the backward scattering angles. We benchmark numerical results with experiments using ultrabroad and femtosecond laser pulses centered at \SI3100nm.
The objective of this study is to evaluate whether the number of requisite training samples can be reduced with the use of various transfer learning models for predicting, for example, the chemical source terms of the data-driven reduced-order model that represents the homogeneous ignition process of a hydrogen/air mixture. Principal component analysis is applied to reduce the dimensionality of the hydrogen/air mixture in composition space. Artificial neural networks (ANNs) are used to tabulate the reaction rates of principal components, and subsequently, a system of ordinary differential equations is solved. As the number of training samples decreases at the target task (i.e.,for T0 > 1000 K and various phi), the reduced-order model fails to predict the ignition evolution of a hydrogen/air mixture. Three transfer learning strategies are then applied to the training of the ANN model with a sparse dataset. The performance of the reduced-order model with a sparse dataset is found to be remarkably enhanced if the training of the ANN model is restricted by a regularization term that controls the degree of knowledge transfer from source to target tasks. To this end, a novel transfer learning method is introduced, parameter control via partial initialization and regularization (PaPIR), whereby the amount of knowledge transferred is systemically adjusted for the initialization and regularization of the ANN model in the target task. It is found that an additional performance gain can be achieved by changing the initialization scheme of the ANN model in the target task when the task similarity between source and target tasks is relatively low.
Integration of renewable power sources into grids remains an active research and development area, particularly for less developed renewable energy technologies such as wave energy converters (WECs). WECs are projected to have strong early market penetration for remote communities, which serve as natural microgrids. Hence, accurate wave predictions to manage the interactions of a WEC array with microgrids is especially important. Recently developed, low-cost wave measurement buoys allow for operational assimilation of wave data at remote, site specific locations where real-time data have previously been unavailable. We present the development and assessment of a wave modeling framework with real-time data assimilation capabilities for WEC power prediction. The availability of real-time wave spectra from low-cost wave measurement buoys allows for operational data assimilation with the ensemble Kalman filter technique within a hybrid modeling procedure whereby physics-based numerical wave models are combined with data-driven error models that aim to capture the discrepancy in prescribed boundary conditions. With that aim, measured wave spectra are assimilated for combined state and parameter estimation while taking into account model and observational errors. The analysis allows for more accurate and precise wave characteristic predictions at the locations of interest. Initial deployment data obtained offshore Yakutat, Alaska, indicated that measured wave data from one buoy that were assimilated into the wave modeling framework resulted in improved forecast skill in comparison to traditional numerical forecasts.
In this work we employ an encoder-decoder convolutional neural network to predict the failure locations of porous metal tension specimens based only on their initial porosities. The process we model is complex, with a progression from initial void nucleation, to saturation, and ultimately failure. The objective of predicting failure locations presents an extreme case of class imbalance since most of the material in the specimens do not fail. In response to this challenge, we develop and demonstrate the effectiveness of data- and loss-based regularization methods. Since there is considerable sensitivity of the failure location to the particular configuration of voids, we also use variational inference to provide uncertainties for the neural network predictions. We connect the deterministic and Bayesian convolutional neural networks at a theoretical level to explain how variational inference regularizes the training and predictions. We demonstrate that the resulting predicted variances are effective in ranking the locations that are most likely to fail in any given specimen.
Material produced by current metal additive manufacturing processes is susceptible to variable performance due to imprecise control of internal porosity, surface roughness, and conformity to designed geometry. Using a double U-notched specimen, we investigate the interplay of nominal geometry and porosity in determining ductile failure characteristics during monotonic tensile loading. We simulate the effects of distributed porosity on plasticity and damage using a statistical model based on populations of pores visible in computed tomography scans and additional sub-threshold voids required to match experimental observations of deformation and failure. We interpret the simulation results from a physical viewpoint and provide statistical models of the probability of failure near stress concentrations. We provide guidance for designs where material defects could cause unexpected failures depending on the relative importance of these defects with respect to features of the nominal geometry.
We present a time-dependent density functional theory (TDDFT) based approach to compute the light-matter couplings between two different manifolds of excited states relative to a common ground state. These quantities are the necessary ingredients to solve the Kramers--Heisenberg equation for resonant inelastic X-ray scattering (RIXS) and several other types of two-photon spectroscopies. The procedure is based on the pseudo-wavefunction approach, where TDDFT eigenstates are treated as a configuration interaction wavefunction with single excitations, and on the restricted energy window approach, where a manifold of excited states can be rigorously defined based on the energies of the occupied molecular orbitals involved in the excitation process. We illustrate the applicability of the method by calculating the 2p4d RIXS maps of three representative Ruthenium complexes and comparing them to experimental results. The method is able to accurately capture all the experimental features in all three complexes, with relative energies correct to within 0.6 eV at the cost of two independent TDDFT calculations.
With the help of newly developed X-ray free-electron laser (XFEL) sources, creating double core holes simultaneously at the same or different atomic sites in a molecule has now become possible. Double core hole (DCH) X-ray emission is a new form of X-ray nonlinear spectroscopy that can be studied with a XFEL. Here we computationally explore the metal K-edge valence-to-core (VtC) X-ray emission spectroscopy (XES) of metal/metal and metal/ligand double core hole states in a series of transition metal complexes with time-dependent density functional theory. The simulated DCH VtC-XES signals are compared with conventional single core hole (SCH) XES signals. The energy shifts and intensity changes of the DCH emission lines with respect to the corresponding SCH-XES features are fingerprints of the coupling between the second core hole and the occupied orbitals around the DCHs that contain important chemical bonding information of the complex. The core hole localization effect on DCH VtC-XES is also briefly discussed. We theoretically demonstrate that DCH XES provides subtle information on the local electronic structure around metal centers in transition metal complexes beyond conventional linear XES. Our predicted changes from calculations between SCH-XES and DCH-XES features should be detectable with modern XFEL sources.
The advent of fabrication techniques such as additive manufacturing has focused attention on the considerable variability of material response due to defects and other microstructural aspects. This variability motivates the development of an enhanced design methodology that incorporates inherent material variability to provide robust predictions of performance. In this work, we develop plasticity models capable of representing the distribution of mechanical responses observed in experiments using traditional plasticity models of the mean response and recently developed uncertainty quantification (UQ) techniques. We demonstrate that the new method provides predictive realizations that are superior to more traditional ones, and how these UQ techniques can be used in model selection and assessing the quality of calibrated physical parameters.
Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra and show that this leads to corrections to all quantum mechanical systems. We also demonstrate that such a deformation implies a discrete spectrum for time. In other words, time behaves like a crystal. As an application of our formalism, we analyze the effect of such a deformation on the rate of spontaneous emission in a hydrogen atom.
In this paper, we propose a novel hybrid plasmonic waveguide fed broadband optical patch nano-antenna for nanophotonic applications. Through full wave electromagnetic simulation, we demonstrated our proposed antenna to radiate and receive signal at all optical communication windows (e.g. $\lambda$ = 850nm, 1310nm & 1550nm) with around 86% bandwidth within the operational domain. Moreover numerical results demonstrate that the proposed nano-antenna has directional radiation pattern with satisfactory gain over all three communication bands. Additionally, we evaluated the antenna performances with two different array arrangements (e.g. one dimensional and square array). The proposed broadband antenna can be used for prominent nanophotonic applications such as optical wireless communication in inter and intra-chip devices, optical sensing and optical energy harvesting etc.
Metallic nano-structured lens has the potential applications of transporting subwavelength imaging information and it is achieved by manipulating the length of the nanorod and the periodicity of the rod array. In this paper, we demonstrate the impact of filling ratio on the subwavelength imaging capabilities of such a lens. Through full-wave electromagnetic simulation, we have demonstrated that the imaging performance of silver (Ag) nanorod array does not only depend on the length and periodicity but also on the filling ratios or the radius of the wire medium. We have investigated two different geometries for nanorod e.g., cylindrical and triangular rod and examined their performance for different filling ratios.
Femtosecond high-order harmonic transient absorption spectroscopy is used to resolve the complete |j,m> quantum state distribution of Xe+ produced by optical strong-field ionization of Xe atoms at 800nm. Probing at the Xe N_4/5 edge yields a population distribution rho_j,|m| of rho_3/2,1/2 : rho_1/2,1/2 : rho_3/2,3/2 = 75 +- 6 : 12 +- 3 : 13 +- 6 %. The result is compared to a tunnel ionization calculation with the inclusion of spin-orbit coupling, revealing nonadiabatic ionization behavior. The sub-50-fs time resolution paves the way for table-top extreme ultraviolet absorption probing of ultrafast dynamics.
Braneshop, and
the US National Science Foundation.
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