This report summarizes the result of a one year seedling project to investigate unusual twinning behavior in shock loaded additive Ti5552. The twinning behavior only occurs when the β phase of Ti5553 is metastable, and it appears to be a type of double twin involving two different twin variants, first a {332}⟨113⟩ twin forms before being consumed by a specific {112}⟨111⟩ twin variant to create a 20o. This behavior has only been detected during shock loading around incipient spall damage. The twinning is investigated by performing postmortem EBSD and PED analysis of gas-gun loaded specimens and preliminary molecular dynamics simulations.
This report presents the current state of knowledge, technology, methodologies, and tools that could be implemented to realize the robust integration of safety, security, and safeguards (3S) for advanced nuclear reactors (ARs) and advanced nuclear fuel cycle facilities. This report was motivated by the global development of ARs which are expected to play a key role in meeting domestic energy and climate objectives. Domestically, with many ARs in the early design phase, the integration of 3S provides an opportunity to achieve risk reduction while using less resources than traditional light water reactors by leveraging interdependencies and synergies between each domain. In addition, domestic policy considerations encourage the convergence of each 3S domain through facility design and operations. Therefore, there is a need to better understand the interdependencies and integration between 3S across ARs and advanced reactor fuel cycle facilities’ lifecycles including design, construction, and operational phases.
Janicki, Tesia D.; Liu, Rui; Im, Soohyun; Wan, Zhongyi; Butun, Serkan; Lu, Shaoning; Basit, Nasir; Voyles, Paul M.; Evans, Paul G.; Schmidt, J.R.
Strontium titanate (SrTiO3, STO) is a complex metal oxide with a cubic perovskite crystal structure. Due to its easily described and understood crystal structure in the cubic phase, STO is an ideal model system for exploring the mechanistic details of solid-phase epitaxy (SPE) in complex oxides. SPE is a crystallization approach that aims to guide crystal growth at low homologous temperatures to achieve targeted microstructures. Beyond planar thin films, SPE can also exploit the addition of a chemically inert, noncrystallizing, amorphous obstacle in the path of crystallization to generate complex three-dimensional structures. The introduction of this mask fundamentally alters the SPE process, inducing a transition from two- to three-dimensional geometries and from vertical to lateral crystal growth under the influence of the crystal/mask/amorphous boundary. Using a combination of molecular dynamics simulations and experiments, we identify several unique phenomena in the nanoscale growth behaviors in both conventional (unmasked) and masked SPE. Examining conventional SPE of STO, we find that crystallization at the interface is strongly correlated to, and potentially driven by, density fluctuations in the region of the amorphous STO near the crystalline/amorphous interface with a strong facet dependence. In the masked case, we find that the crystalline growth front becomes nonplanar near contact with the mask. We also observe a minimum vertical growth requirement prior to lateral crystallization. Both phenomena depend on the relative bulk and interfacial free energies of the three-phase (crystal/mask/amorphous) system.
The motivation for this work came from the simulation of components subjected to impact. In these problems, repeated loading can be generated by vibrational motion between internal parts of the component or by the occurrence of multiple impacts. Graphs of tensile equivalent plastic strain $(\overline{\varepsilon}_T^\rho)$ versus time from such cases had the character shown in Fig. 1. The equivalent plastic strain grew by alternating periods of accumulation and hold. The periods of hold indicate times when $d\overline{\varepsilon}_T^\rho$ did not accumulate. This can be due to the material unloading into the elastic range, or actually plastically reverse loading with hydrostatic stress σh < 0 as was demonstrated for an impact simulation. Similar observations were made from the simulation of a 2-degree-of-freedom mass-elastic-plastic-spring system subjected to impact.
This study presents the development of a computational framework designed to predict the interaction between permafrost and infrastructure, addressing potential failure modes and mitigation strategies in the context of climate change. The framework, rooted in advanced modeling and simulation (mod/sim) techniques, integrates thermomechanical coupling to account for the complex interplay between heat flow, ice content, and mechanical behavior in permafrost. Existing models fail to fully capture these dynamics, particularly as they relate to the effects of ice saturation on structural integrity. Our innovative Arctic Coastal Erosion (ACE) framework fills this gap by coupling thermal and mechanical models to accurately simulate subsidence and deformation in permafrost environments. We applied the ACE framework to a representative runway, demonstrating its capability to predict settlement due to rising temperatures and subsequent permafrost thaw. This proof-of-concept showcases the potential of the framework to evaluate risks to Arctic infrastructure, which supports over four million people and 70% of existing permafrost-based structures. By simulating various infrastructure types and environmental conditions, our research offers insights into failure mechanisms and evaluates structural solutions to mitigate risk. The anticipated deliverables, including a prototype runway exemplar, position this project as a critical advancement in permafrost infrastructure modeling, with applications in national security and resilience planning.
Many technologies require stable or metastable surface morphology. In this paper we study the factors that control the metastability of a common feature of rough surfaces: "hillocks."We use low energy electron microscopy to follow the evolution of the individual atomic steps in hillocks on Pd(111). We show that the uppermost island in the stack often adopts a static, metastable configuration. Modeling this result shows that the degree of the metastability depends on the configuration of steps dozens of atomic layers lower. Our model allows us to link surface metastability to the atomic processes of surface evolution.
Polymers are an effective test bed for studying topological constraints in condensed matter due to a wide array of synthetically available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time τd,R for rings of length NR blended with linear chains of length Nl to scale as τd,R∼NR2NL3.4.
The Xyce™ Parallel Electronic Simulator has been written to support the simulation needs of Sandia National Laboratories’ electrical designers. Xyce™ is a SPICE-compatible simulator with the ability to solve extremely large circuit problems on large-scale parallel computing platforms, but also includes support for most popular parallel and serial computers. For up-to-date information not available at the time these notes were produced, please visit the Xyce™ web page at http://xyce.sandia.gov.
The transmission interference fringe (TIF) technique was developed to visualize the dynamics of evaporating droplets based on the Reflection Interference Fringe (RIF) technique for micro-sized droplets. The geometric formulation was conducted to determine the contact angle (CA) and height of macro-sized droplets without the need for the prism used in RIF. The TIF characteristics were analyzed through experiments and simulations to demonstrate a wider range of contact angles from 0 to 90°, in contrast to RIF's limited range of 0-30°. TIF was utilized to visualize the dynamic evaporation of droplets in the constant contact radius (CCR) mode, observing the droplet profile change from convex-only to convex-concave at the end of dry-out from the interference fringe formation. The TIF also observed the contact angle increase from the fringe radius increase. This observation is uniquely reported as the interference fringe (IF) technique can detect the formation of interference fringe between the reflection from the center convex profile and the reflection from the edge concave profile on the far-field screen. Unlike general microscopy techniques, TIF can detect far-field interference fringes as it focuses beyond the droplet-substrate interface. The formation of the convex-concave profile during CCR evaporation is believed to be influenced by the non-uniform evaporative flux along the droplet surface.
Caskey, Susan A.; Keating, Charles B.; Katina, Polinpapilinho F.; Bradley, Joseph M.; Hodge, Richard; Martin, James N.
The purpose of this paper is to explore the concept of ‘enterprise’ in the context of Systems Engineering (SE). The term ‘enterprise’ has been used extensively to generally describe large complex entities that have an extensive scope of operations. However, a deeper examination of ‘enterprise’ significance for SE can provide insights as our challenges continue with increasingly complex, uncertain, ambiguous, and integrated entities struggling to thrive in the future. The paper explores three central topics. First, the concept of enterprise is introduced as a central aspect of the future focus for SE, as recognized in the INCOSE SE Vision 2035. Second, a more detailed examination of the enterprise concept is developed in relationship to SE. The thrust of this examination is to understand the nature and role of ‘enterprise’ across a broad spectrum of literature and knowledge, ultimately providing a more informed perspective of enterprise for SE. As part of this exploration, a bibliometric analysis of the term ‘enterprise’ is performed. This exploration extracts key themes (clusters) in the ‘enterprise’ literature. Third, challenges for further development and inculcation of ‘enterprise’ within the SE discipline and support for realization of the SE 2035 Vision are suggested. These challenges point out the need to ‘think differently’ about ‘enterprise’ within the SE context. ‘Enterprise’ is proposed as a central, albeit different, perspective for the SE discipline. Finally, the paper closes with a first–generation perspective for ‘enterprise’ in pursuit of the SE Vision 2035.
Organizations play a key role in supporting various societal functions, ranging from environmental governance to the manufacturing of goods. Here, the behaviors of organization are impacted by various influences, including information, technology, authority, economic leverage, historical experiences, and external factors, such as regulations. This paper introduces a generalized framework, focused on the relative structure of an organization (tight vs. loose), that can be used to understand how different influence pathways can impact decision-making within differently structured organizations. This generalized framework is then translated into a modeling and simulation platform to support and assess implications of these structural differences in resilience to disinformation (measured by organizational behaviors of timeliness and inclusion of quality information) using a systems dynamics approach Preliminary results indicate that a tightly structured organization may be less timely at processing information but could be more resilient against using poor quality information in organizational decisions compared to a loosely structured organization. Ongoing work is underway to understand the robustness of these findings and to validate current model design activities with empirical insights.
Estimating spatially distributed properties such as permeability from available sparse measurements is a great challenge in efficient subsurface CO2 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 CO2 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.
The Disposal Research and Development (R&D) Program of the US Department of Energy (DOE) office of Nuclear Energy (NE-8) Spent Fuel and Waste Science and Technology (SFWST) Campaign is to conduct R&D on disposal of spent nuclear fuel (SNF) and high-level waste (HLW). The goal of the Geologic Disposal Safety Assessment (GDSA) within this project is to develop a disposal system modeling and analysis capability that supports the integrated modeling of coupled processes controlling disposal system performance of deep geologic repositories, including uncertainty. This report describes specific activities in the Fiscal Year (FY) 2024 associated with the GDSA Repository Systems Analysis (RSA) work package. The overall objective of the GDSA RSA work package is to develop generic deep geologic repository concepts and repository system performance models in crystalline, argillite, salt, and unsaturated alluvium potential host-rock environments, and to simulate and analyze these generic repository concepts and models using GDSA Framework toolkit, and other tools as needed.
This report summarizes the work performed under the author's two-year John von Neumann LDRD project, which involves the non-intrusive surrogate modeling of dynamical systems with remarkable structural properties. After a brief introduction to the topic, technical accomplishments and project metrics are reviewed including peer-reviewed publications, software releases, external presentations and colloquia, as well as organized conference sessions and minisymposia. The report concludes with a summary of ongoing projects and collaborations which utilize the results of this work.
BeyondFingerprinting was a 2021-2024 Sandia Grand Challenge LDRD exploring the potential to develop new resilient materials and manufacturing processes by taking an artificial-intelligence (AI)-guided approach that integrates human-subject-matter expertise with algorithms enriched with physics-based constraints to unearth process-structure-property correlations. Such algorithms, trained on high-throughput experiments and simulations, are shown to serve as surrogate models that efficiently detect key “fingerprints” in materials data, prognose material performance, and guide effective process improvements. To accelerate broader adoption across mission areas, this AI-guided approach was demonstrated with three complex process-centric exemplars: electroplating, physical vapor deposition, and laser powder bed fusion. Together, these exemplars impact nearly every hardware component relevant to DOE and NNSA national security missions.
For multi-scale multi-physics applications e.g., the turbulent combustion code Pele, robust and accurate dimensionality reduction is crucial to solving problems at exascale and beyond. A recently developed technique, Co-Kurtosis based Principal Component Analysis (CoK-PCA) which leverages principal vectors of co-kurtosis, is a promising alternative to traditional PCA for complex chemical systems. To improve the effectiveness of this approach, we employ Artificial Neural Networks for reconstructing thermo-chemical scalars, species production rates, and overall heat release rates corresponding to the full state space. Our focus is on bolstering confidence in this deep learning based non-linear reconstruction through Uncertainty Quantification (UQ) and Sensitivity Analysis (SA). UQ involves quantifying uncertainties in inputs and outputs, while SA identifies influential inputs. One of the noteworthy challenges is the computational expense inherent in both endeavors. To address this, we employ the Monte Carlo methods to effectively quantify and propagate uncertainties in our reduced spaces while managing computational demands. Our research carries profound implications not only for the realm of combustion modeling but also for a broader audience in UQ. By showcasing the reliability and robustness of CoK-PCA in dimensionality reduction and deep learning predictions, we empower researchers and decision-makers to navigate complex combustion systems with greater confidence.
The effects of raw water leaching at the U.S. SPR were modeled using SANSMIC. In addition to 18 caverns identified in previous leaching reports, six caverns have been identified for further monitoring based on the results of this report. SANSMIC continues to serve as a useful tool for monitoring changes in cavern shape. However, some caverns where string cuts were made in the middle of drawdowns are showing overprediction in the SANSMIC model when compared with recent sonars.
Bugs in digital logic have led to some significant security vulnerabilities. Hardware bugs are particularly troublesome since they cannot be easily patched. Additionally, if the bug is in the root of trust, all trust built upon it can be vulnerable. Traditional testing either require a deep knowledge of the system, creative attack vectors and lots of human interaction. This is not scalable as there are very few engineers that can wear the hat of a designer, a verification engineer, and a cybersecurity expert. Hardware fuzzing is a relatively new research area in dynamic hardware testing. It has proven to be an effective method for discovering bugs, unexpected behaviors, and security vulnerabilities in software. While hardware fuzzing is new to the hardware domain, it has a strong track record in software testing. Fuzzing is a testing technique that randomly mutates the input data to uncover bugs or vulnerabilities in the design. It is especially good at finding corner cases that test engineers can not envision. Another advantage over other dynamic testing techniques is that, if done well, deep knowledge of the design is not required. Additionally, fuzzing scales well. If the system is set up correctly, it can run unsupervised for weeks if necessary. In this work, we propose using hardware fuzzing to improve the input vector generation for an information flow tracking tool. To get reasonable throughput of test vectors, an emulator is targeted as the execution platform. Efficient emulator execution has some specific requirements.
In this project we uncovered structure-function relationships of donor-acceptor co-crystals used to develop next-generation optoelectronic devices. Unraveling the photodynamics of molecular crystalline materials poses many challenges for spectroscopy due to broad, overlapping features representing numerous underlying dynamical processes. This leads researchers to make many assumptions about the dynamics of a system in choosing an appropriate kinetic fitting model. Computationally, electronic structure methods are either prohibitively expensive or underdeveloped for computing the excited state structure of molecular materials, especially states that exhibit charge transfer. Researchers must therefore perform calculations of excited electronic states using truncated models of molecular materials. Here we present a joint experimental-theoretical approach to bridging the gap between the photodynamics of a molecular material and its constituent molecules. We focus our efforts on quantifying the timescales and mechanisms of photoexcitation in donor-acceptor co-crystals and donor-acceptor dimers where the lowest-lying excited state is characterized by charge transfer from the donor to the acceptor. We employ ultrafast UV pump, UV-Vis probe transient absorption spectroscopy to unravel the time-resolved spectroscopic signatures of the photodynamics in both the crystalline material and donor-acceptor dimers in solution. We perform electronic structure and excited state dynamics calculations of the dimers to inform kinetic fitting models and assign the spectral features. The photodynamics of the crystal vs. dimer systems have many similarities, enabling unprecedented insights into the formation and evolution of charge transfer excitons in the crystalline systems.
The motivation behind this research is the growing challenge of handling the massive amounts of data generated by modern imaging systems. Conventional digital image processing techniques are struggling to keep pace with the demands of high-resolution and high-speed imaging systems for remote sensing due to their high-power consumption and data storage requirements. We present a novel approach based on analog photonics to address this challenge. The proposed system utilizes a silicon-photonics-based image encoder positioned after image formation and initial optical-to-electrical conversion. The photonic encoder compresses image data using a passive disordered photonic structure to perform kernel-type random projections of the raw data. The compressed data is then processed by a back-end neural network, which reconstructs the original image with high fidelity (structural similarity exceeding 90%). Our proposed approach has the potential to compress images with ~ 1000X lower power consumption compared to digital approaches with data rates exceeding 1 terapixel/second.
The Department of Energy Hydrogen Fuel Cell Technology Office and Wind Energy Technologies Office’s Wind-H2-Green Steel/Ammonia project is an initiative to demonstrate the feasibility and efficacy of GW-scale integrated energy systems. The team designed reference facilities that utilize wind- and solar-produced hydrogen for industrial steel and ammonia production. This novel concept warranted review of safety codes and standards as they apply to the designs and the identification of codes and standards as they apply to the designs and the identification of codes and standards gaps. This report reviews hydrogen production and storage codes and standards using reference design specifications from a Minnesota steel plant. Requirements, recommendations, and exclusions for the system were identified. Observed gaps included non-specific salt cavern storage requirements, electrolyzer capacity beyond regulated ranges, and lack of requirements for iron reduction via hydrogen. This report will aide future project design efforts and may provide a basis for safety reviews in new designs for industrial facilities with hydrogen production integration.
Nitrogen-containing organic molecules play essential roles in nearly every aspect of chemistry. The importance of these species within gas-phase chemistry has increased in recent years, due to their emissions from wildfires, crude biofuels, ammonia combustion, and CO2 capture facilities. However, there is a lack of detailed relevant mechanistic and kinetic studies of N-compounds, resulting in poor representation of these pathways within chemical models. In this report, we detail our exploration of the gas-phase oxidation mechanisms of pyrrole, imidazole, pyrrolidine, methylamine, and dimethylamine, done by employing multiplexed VUV photoionization mass spectrometry coupled with KinBot, a computational tool that automatically explores multi-well potential energy surfaces. Overall, we vastly expanded the known gas-phase oxidation mechanisms and chemical kinetics of these species. This work will improve the accuracy and completeness of atmospheric and combustion chemistry models, ultimately leading to better-informed decision-makers in the energy and environmental sectors.
Sandia National Laboratories has fabricated a Seismic Sensor Temperature Testbed (SSTT) suitable for exposing sensors under test to a range of reasonably stable temperatures while a co-located reference sensor is maintained at room temperature. The testbed has proven sufficiently quiet to allow recording of high-coherence signals from regional earthquakes in the passband of the seismometers, allowing a direct comparison of signals between the sensors under test and the reference sensor.
The Sea Change Project, managed and financed by SWITCH Maritime, produced the first zero-emission 100% hydrogen fuel-cell powered commercial ferry in the world. The MV Sea Change is a 70-foot catamaran equipped with a 360-kW fuel cell powertrain and a 250-bar 246 kg capacity hydrogen storage system. The 75-passenger vessel began public passenger service in July 2024 as part of the San Francisco Bay Ferry system. Summarized here are aspects of the design of the vessel, its construction, and vessel bunkering with high-pressure hydrogen. Results from a fuel cell performance analysis are also presented, along with estimates of the greenhouse gas (GHG) and criterial pollutant emissions assuming different sourcings of hydrogen. Lessons learned from the project will be briefly reviewed.
While quantum computing offers the promise of exponential advantages, limited quantum speedups are known, especially for practical applications. To open new avenues for quantum advantages, we propose Unconventional Quantum Advantages for Computation (U-QuACs), with respect to unconventional resources such as space (number of bits or quantum bits of memory required to solve a problem), accuracy of solution, communication, or energy consumption. We focus on space-efficient quantum algorithms, where we seek to design algorithms that solve a problem using much less space than the total size of the input. A natural setting in which space is critical is the streaming model of computation, where the input data arrives sequentially in pieces that must each be processed individually. Streaming is motivated by a variety of problems including analysis of internet traffic or social networks. We design the first exponential quantum space advantage for a natural streaming problem, which also constitutes the first quantum advantage for approximating a discrete optimization problem, albeit with respect to space.
In computer science, Document Summarization is the task of condensing some quantity of text and related content through automated means. In this document, we review recent literature in text summarization. “Hybrid” extractive-abstractive approaches continue to be explored. Some of the latest efforts have also sought to enable users to adjust summaries with queries or other structure and begun to test reinforcement-learning style agentic LLM-based solutions.
MACCS is used by the Nuclear Regulatory Commission (NRC) and various national and international organizations for probabilistic consequence analysis of nuclear power accidents. This user guide is intended to assist analysts in understanding the MACCS/MACCS-UI User Interface (UI) model and to provide information regarding the code. This user guide version describes MACCS Version 5.0, model history, explains how to set up and execute a problem, and informs the user of the definition of various input parameters and any constraints placed on those parameters. This report is part of a series of reports documenting MACCS. Other reports include the MACCS Theory Manual, MACCS Verification Report, Technical Bases for Consequence Analyses Using MACCS, as well as documentation for preprocessor codes including SecPop, MelMACCS, and COMIDA2.
Modern computing systems are capable of exascale calculations, which are revolutionizing the development and application of high-fidelity numerical models in computational science and engineering. While these systems continue to grow in processing power, the available system memory has not increased commensurately, and electrical power consumption continues to grow. A predominant approach to limit the memory usage in large-scale applications is to exploit the abundant processing power and continually recompute many low-level simulation quantities, rather than storing them. However, this approach can adversely impact the throughput of the simulation and diminish the benefits of modern computing architectures. We present three novel contributions to reduce the memory burden while maintaining, and sometimes improving, performance in simulations based on finite element discretizations. The first contribution develops dictionary-based data compression schemes that detect and exploit the structure of the discretization, due to redundancies across the finite element mesh. While these schemes are shown to reduce memory requirements by more than 99% on meshes with large numbers of identical mesh cells, there are applications where this structure does not exist. The second contribution leverages a recently developed augmented Lagrangian optimization algorithm to enable r-adaptivity for meshes with the goal of enhancing the redundancies in the mesh. The third contribution extends these methods to patch-based linear solvers and preconditioners by compressing local matrices. Numerical results demonstrate the effectiveness of the proposed methods to detect, enhance and exploit mesh structure on a suite of examples inspired by large-scale applications.
The Gamma Detector Response and Analysis Software (GADRAS) package includes an inverse modeling tool that is helpful in identifying characteristics of unknown radioactive materials. Traditionally, uncertainties in this analysis were derived solely from measurement data quality and the fit of synthetic spectra. This paper aims to rigorously quantify additional sources of uncertainty, focusing on uncertainties arising from measurements being analyzed, Detector Response Function (DRF) characterization, and DRF extrapolation. Applying these findings to the BeRPBall benchmark data set, we demonstrated the impact of these uncertainties on plutonium and polyethylene estimates. The results underscore the importance of incorporating diverse uncertainty sources to enhance the accuracy and reliability of GADRAS’s inverse modeling capabilities.
This report summarizes the findings of a four months FY24 Advanced Science & Technology (AS&T) LDRD Quick Targeted Investigation (QTI) project focused on the exploration of supervised dimension reduction approaches based on autoencoders. Autoencoders have been extensively employed in literature for unsupervised learning tasks, however, their use for supervised regression tasks, which are common within scientific applications, has been limited. Motivated by linear dimension reduction strategies like Active Subspaces and Adaptive Basis, we explored the possibility of employing autoencoders to discover a non-linear manifold able to represent the original function in fewer dimensions. In this report, we discuss a neural network architecture and we perform a numerical campaign on several problems ranging from simple two-dimensional functions to a model problem for magnetohydrodynamics in five dimensions. In our preliminary results, we show that the proposed approach is found to be superior to linear dimension reduction strategies in representing the target function even with a single latent variable.
