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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Optical Control of Adaptive Nanoscale Domain Networks

Adaptive networks can sense and adjust to dynamic environments to optimize their performance. Understanding their nanoscale responses to external stimuli is essential for applications in nanodevices and neuromorphic computing. However, it is challenging to image such responses on the nanoscale with crystallographic sensitivity. Here, the evolution of nanodomain networks in (PbTiO 3 ) n /(SrTiO 3 ) n superlattices (SLs) is directly visualized in real space as the system adapts to ultrafast repetitive optical excitations that emulate controlled neural inputs. The adaptive response allows the system to explore a wealth of metastable states that are previously inaccessible. Their reconfiguration and competition are quantitatively measured by scanning x-ray nanodiffraction as a function of the number of applied pulses, in which crystallographic characteristics are quantitatively assessed by assorted diffraction patterns using unsupervised machine-learning methods. The corresponding domain boundaries and their connectivity are drastically altered by light, holding promise for light-programable nanocircuits in analogy to neuroplasticity. Phase-field simulations elucidate that the reconfiguration of the domain networks is a result of the interplay between photocarriers and transient lattice temperature. The demonstrated optical control scheme and the uncovered nanoscopic insights open opportunities for the remote control of adaptive nanoscale domain networks.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Automated Scoring of Morphological Changes in Images of Pentaerythritol Tetranitrate

Recent advances in characterization techniques that generate large datasets of material microstructure images require robust, automated image-processing. We applied an unsupervised anomaly detection method called feature anomaly detection system (FADS) to automatically detect and quantify microstructure changes in images of the explosive pentaerythritol tetranitrate (PETN) aged at various temperatures. We demonstrated the FADS approach on two-dimensional images extracted from computed tomography scans, but the same technique can be readily applied to other imaging modalities. FADS calculates anomaly scores on the basis of differences in filter activations of nominal and test data in pretrained convolutional neural networks. The FADS scores successfully differentiated between pristine PETN and PETN aged at a temperature where material coarsening occurred. Morphological metric analysis of segmented images verified observed trends in FADS scores as a function of aging temperature and aging time, specifically by calculating volume fractions, specific boundary lengths, two-point correlation functions, and local thicknesses. Here, the FADS technique has two important advantages compared to traditional morphological analysis: First, it uses grayscale images as input, rather than images that are segmented to separate the appropriate phases; and second, FADS scores capture any type of changes among image sets, rather than requiring prior knowledge or selection of a relevant set of metrics.

Accelerated aging↗
DOE OSTI2025

Machine Learning‐Guided Discovery of High‐Entropy Perovskite Oxide Electrocatalysts via Oxygen Vacancy Engineering

Abstract High‐entropy perovskite oxides (HEPOs) have recently emerged as multifunctional catalysts. However, the HEPOs’ structural and compositional complexity hinders the easy and accurate extrapolation of activity indicators, which are essential for establishing structure‐property correlations. Here, OxiGraphX, is introduced as a novel graph neural network (GNN) model designed to capture the complex relationships among structure, composition, and atomic chemical environments for accurate prediction of oxygen vacancy formation energies (OVFEs) in HEPOs. By integrating machine learning (ML), density functional theory (DFT), and experimental validation, this work demonstrates an efficient framework for rapidly and accurately screening HEPO electrocatalysts for oxygen evolution reaction (OER). The OxiGraphX predicts OVFEs with a precision exceeding existing data, enabling the identification of compositions of higher oxygen vacancy content (OVC) and, thus, higher catalytic activity. Furthermore, the model explores latent spaces that translate effectively into experimental domains, bridging computational predictions with real‐world applications. This approach accelerates the discovery of high‐performance HEPO catalysts while providing deeper insights into their catalytic mechanisms.

Chemistry↗
DOE OSTI2024

INSPIRED: Inelastic neutron scattering prediction for instantaneous results and experimental design

Inelastic neutron scattering (INS) has unique advantages in probing how atoms vibrate and how the vibrations propagate and interact. Such dynamic information is crucial in understanding various material properties, from heat capacity, thermal conductivity, phase transitions, and chemical reactions to more exotic quantum behavior. The analysis and interpretation of the INS spectra often start from a model structure of the sample, followed by a series of calculations to obtain the simulated spectra to compare with experiments. The conventional way to perform such calculations usually requires significant time, computing resources, and specialized expertise. Here, we present a new program named INSPIRED (Inelastic Neutron Scattering Prediction for Instantaneous Results and Experimental Design), which enables users to perform rapid INS simulations in several different ways on their personal computers in just a few clicks, with the crystal structure as the only input file. Specifically, the users can choose a pre-trained symmetry-aware neural network (coupled with an autoencoder) to predict the phonon density of states (DOS), 1D S(E) and 2D S(|Q|,E) spectra for any given structure. One can also choose an existing density functional theory (DFT) calculation from a database (containing over 12,000 crystals), and quickly obtain the simulated INS spectra for single crystals and powders. It is also possible to use pre-trained universal machine learning force fields to relax a given crystal structure, calculate the phonon dispersion and DOS, and, subsequently, the INS spectra. All these functions are implemented with a PyQt graphic user interface. Finally, we expect these new tools will benefit broad user communities and significantly improve the efficiency of experiment design, execution, and data analysis for INS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Biopolymer-Templated Titania Film Formation for Nanostructured Coatings Revealed by Machine Learning-Supported Time-Resolved Analysis

This study presents a machine learning approach to derive the film formation of biopolymer-templated titania nanostructures during spray deposition, in combination with in situ grazing-incidence small-angle X-ray scattering (GISAXS). A neural network trained on synthetic GISAXS data directly predicts domain-size distributions from experimental two-dimensional scattering patterns, capturing the full kinetics of nanostructure evolution with high temporal resolution. The predictions reveal hierarchical size distributions and periodic growth features, consistent with layer-by-layer spray deposition and validated by complementary scanning electron microscopy (SEM) imaging. Quantitative comparison with conventional parametric GISAXS fits shows good qualitative agreement, with systematic differences explained by domain-shape assumptions and resolved by applying a geometric scaling factor. Simulated SEM-like surfaces derived from neural network outputs reproduce the porous, foam-like nanoscale morphology observed experimentally, reinforcing the method’s credibility. This integrated approach enables real-time, nondestructive, statistically averaged monitoring of bulk nanostructure development in functional coatings, offering a scalable methodology to accelerate the characterization and process control of sustainably manufactured nanostructured titania films for energy-related applications such as photocatalysis and photovoltaics.

Heger, JulianEliah↗
DOE OSTI2025

Microscopic insights into the solvation of polyethylene glycol chains in water: A machine learning potential approach

Polyethylene glycol (PEG) is a structurally simple, nontoxic, and water-soluble polymer widely utilized in medical and pharmaceutical applications. Notably, when a PEG chain is immersed in water, the surrounding water molecules play a key role in driving conformational changes of this macromolecule. In this study, we explore the solvation behavior of PEG under mechanical strain using molecular dynamics simulations, with an interatomic potential obtained from machine learning. Our focus is on the transition from the favored coil-like conformation to an extended one under external force. Through analyses of radial distribution functions, hydrogen bonding, and solvation dynamics, we uncover how mechanical stretching influences the local hydration environment. Furthermore, we disentangle the enthalpic and entropic contributions to the conformational stability of PEG in water. Surprisingly, our neural network potential model identifies dewetting of PEG C-atoms, and not water H-bonding with PEG O-atoms, as the main enthalpic driving force for the coiling of PEG in water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1989

SSME fault monitoring and diagnosis expert system

An expert system, called LEADER, has been designed and implemented for automatic learning, detection, identification, verification, and correction of anomalous propulsion system operations in real time. LEADER employs a set of sensors to monitor engine component performance and to detect, identify, and validate abnormalities with respect to varying engine dynamics and behavior. Two diagnostic approaches are adopted in the architecture of LEADER. In the first approach fault diagnosis is performed through learning and identifying engine behavior patterns. LEADER, utilizing this approach, generates few hypotheses about the possible abnormalities. These hypotheses are then validated based on the SSME design and functional knowledge. The second approach directs the processing of engine sensory data and performs reasoning based on the SSME design, functional knowledge, and the deep-level knowledge, i.e., the first principles (physics and mechanics) of SSME subsystems and components. This paper describes LEADER's architecture which integrates a design based reasoning approach with neural network-based fault pattern matching techniques. The fault diagnosis results obtained through the analyses of SSME ground test data are presented and discussed.

Ali, Moonis↗
DOE OSTI2024

Active and Transfer Learning of High-Dimensional Neural Network Potentials for Transition Metals

Classical molecular dynamics (MD) simulations represent a very popular and powerful tool for materials modeling and design. The predictive power of MD hinges on the ability of the interatomic potential to capture the underlying physics and chemistry. There have been decades of seminal work on developing interatomic potentials, albeit with a focus predominantly on capturing the properties of bulk materials. Such physics-based models, while extensively deployed for predicting the dynamics and properties of nanoscale systems over the past two decades, tend to perform poorly in predicting nanoscale potential energy surfaces (PESs) when compared to high-fidelity first-principles calculations. These limitations stem from the lack of flexibility in such models, which rely on a predefined functional form. Machine learning (ML) models and approaches have emerged as a viable alternative to capture the diverse size-dependent cluster geometries, nanoscale dynamics, and the complex nanoscale PESs, without sacrificing the bulk properties. Here, in this study, we introduce an ML workflow that combines transfer and active learning strategies to develop high-dimensional neural networks (NNs) for capturing the cluster and bulk properties for several different transition metals with applications in catalysis, microelectronics, and energy storage, to name a few. Our NN first learns the bulk PES from the high-quality physics-based models in literature and subsequently augments this learning via retraining with a higher-fidelity first-principles training data set to concurrently capture both the nanoscale and bulk PES. Our workflow departs from status-quo in its ability to learn from a sparsely sampled data set that nonetheless covers a diverse range of cluster configurations from near-equilibrium to highly nonequilibrium as well as learning strategies that iteratively improve the fingerprinting depending on model fidelity. All the developed models are rigorously tested against an extensive first-principles data set of energies and forces of cluster configurations as well as several properties of bulk configurations for 10 different transition metals. Our approach is material agnostic and provides a methodology to transfer and build upon the learnings from decades of seminal work in molecular simulations on to a new generation of ML-trained potentials to accelerate materials discovery and design.

36 MATERIALS SCIENCE↗
NASA NTRS1992

A Reevaluation of the Vestibulo-Ocular Reflex: New Ideas of its Purpose, Properties, Neural Substrate, and Disorders

Conventional views of the Vestibulo-Ocular Reflex (VOR) have emphasized testing with caloric stimuli and by passively rotating patients at low frequencies in a chair. The properties of the VOR tested under these conditions differ from the performance of this reflex during the natural function for which it evolved-locomotion. Only the VOR (and not visually mediated eye movements) can cope with the high-frequency angular and linear perturbations of the head that occur during locomotion; this is achieved by generating eye movements at short latency (less than 16 msec). Interpretation of vestibular testing is enhanced by the realization that, although the di- and trisynaptic components of the VOR are essential for this short-latency response, the overall accuracy and plasticity of the VOR depend upon a distributed, parallel network of neurons involving the vestibular nuclei. Neurons in this network variously encode inputs from the labyrinthine semicircular canals and otoliths, as well as from the visual and somatosensory systems. The central vestibular pathways branch to contact vestibular cortex (for perception) and the spinal cord (for control of posture). Thus, the vestibular nuclei basically coordinate the stabilization of gaze and posture, and contribute to the perception of verticality and self-motion. Consequently, brainstem disorders that disrupt the VOR cause not just only nystagmus, but also instability of posture (eg, increased fore-aft sway in patients with downbeat nystagmus) and disturbance of spatial orientation (eg, tilt of the subjective visual vertical in Wallenberg's syndrome).

Leigh, R. John↗
NASA NTRS1993

A reevaluation of the vestibulo-ocular reflex: new ideas of its purpose, properties, neural substrate, and disorders

Conventional views of the vestibulo-ocular reflex (VOR) have emphasized testing with caloric stimuli and by passively rotating patients at low frequencies in a chair. The properties of the VOR tested under these conditions differ from the performance of this reflex during the natural function for which it evolved--locomotion. Only the VOR (and not visually mediated eye movements) can cope with the high-frequency angular and linear perturbations of the head that occur during locomotion; this is achieved by generating eye movements at short latency (< 16 msec). Interpretation of vestibular testing is enhanced by the realization that, although the di- and trisynaptic components of the VOR are essential for this short-latency response, the overall accuracy and plasticity of the VOR depend upon a distributed, parallel network of neurons involving the vestibular nuclei. Neurons in this network variously upon a distributed, parallel network of neurons involving the vestibular nuclei. Neurons in this network variously encode inputs from the labyrinthine semicircular canals and otoliths, as well as from the visual and somatosensory systems. The central vestibular pathways branch to contact vestibular cortex (for perception) and the spinal cord (for control of posture). Thus, the vestibular nuclei basically coordinate the stabilization of gaze and posture, and contribute to the perception of verticality and self-motion. Consequently, brainstem disorders that disrupt the VOR cause not just only nystagmus, but also instability of posture (eg, increased fore-aft sway in patients with downbeat nystagmus) and disturbance of spatial orientation (eg, tilt of the subjective visual vertical in Wallenberg's syndrome).

Review↗
NASA NTRS1998

Quantum Analog Computing

Quantum analog computing is based upon similarity between mathematical formalism of quantum mechanics and phenomena to be computed. It exploits a dynamical convergence of several competing phenomena to an attractor which can represent an externum of a function, an image, a solution to a system of ODE, or a stochastic process.

Quantum analog computing quantum mechanics attract↗
NASA NTRS1990

Distributed memory approaches for robotic neural controllers

The suitability is explored of two varieties of distributed memory neutral networks as trainable controllers for a simulated robotics task. The task requires that two cameras observe an arbitrary target point in space. Coordinates of the target on the camera image planes are passed to a neural controller which must learn to solve the inverse kinematics of a manipulator with one revolute and two prismatic joints. Two new network designs are evaluated. The first, radial basis sparse distributed memory (RBSDM), approximates functional mappings as sums of multivariate gaussians centered around previously learned patterns. The second network types involved variations of Adaptive Vector Quantizers or Self Organizing Maps. In these networks, random N dimensional points are given local connectivities. They are then exposed to training patterns and readjust their locations based on a nearest neighbor rule. Both approaches are tested based on their ability to interpolate manipulator joint coordinates for simulated arm movement while simultaneously performing stereo fusion of the camera data. Comparisons are made with classical k-nearest neighbor pattern recognition techniques.

Jorgensen, Charles C.↗
NASA NTRS1995

Analyzing rocket plume spectral data with neural networks

The Optical Plume Anomaly Detection (OPAD) system is under development to provide early-warning failure detection in support of ground-level testing of the Space Shuttle Main Engine (SSME). Failure detection is to be achieved through the acquisition of spectrally resolved plume emissions and subsequent identification of abnormal levels indicative of engine corrosion or component failure. Two computer codes (one linear and the other non-linear) are used by the OPAD system to iteratively determine specific element concentrations in the SSME plume, given emission intensity and wavelength information. Since this analysis is extremely labor intensive, a study was initiated to develop neural networks that would model the 'inverse' of these computer codes. Optimally connected feed-forward networks with imperceptible prediction error have been developed for each element modeled by the linear code, SPECTRA4. Radial basis function networks were developed for the non-linear code, SPECTRA5, and predict combustion temperature in addition to element concentrations.

Whitaker, Kevin W.↗
NASA NTRS2020

Flare Statistics for Young Stars from a Convolutional Neural Network Analysis of TESS Data

All-sky photometric time-series missions have allowed for the monitoring of thousands of young (t(age) < 800 Myr) stars in order to understand the evolution of stellar activity. Here, we developed a convolutional neural network (CNN), stella, specifically trained to find flares in Transiting Exoplanet Survey Satellite (TESS) short-cadence data. We applied the network to 3200 young stars in order to evaluate flare rates as a function of age and spectral type. The CNN takes a few seconds to identify flares on a single light curve. We also measured rotation periods for 1500 of our targets and find that flares of all amplitudes are present across all spot phases, suggesting high spot coverage across the entire surface. Additionally, flare rates and amplitudes decrease for stars t(age) > 50 Myr across all temperatures T(eff) ≥ 4000 K, while stars from 2300 ≤ T(eff) < 4000 K show no evolution across 800 Myr. Stars of T(eff) ≤ 4000 K also show higher flare rates and amplitudes across all ages. We investigate the effects of high flare rates on photoevaporative atmospheric mass loss for young planets. In the presence of flares, planets lose 4%–7% more atmosphere over the first 1 Gyr. stella is an open-source Python toolkit hosted on GitHub and PyPI.

Adina D. Feinstein↗
DOE OSTI2025

MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities

The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2016

Behavioral, Brain Imaging and Genomic Measures to Predict Functional Outcomes Post - Bed Rest and Spaceflight

Astronauts experience sensorimotor disturbances during their initial exposure to microgravity and during the re-adaptation phase following a return to an Earth-gravitational environment. These alterations may disrupt crewmembers' ability to perform mission critical functional tasks requiring ambulation, manual control and gaze stability. Interestingly, astronauts who return from spaceflight show substantial differences in their abilities to readapt to a gravitational environment. The ability to predict the manner and degree to which individual astronauts would be affected would improve the effectiveness of countermeasure training programs designed to enhance sensorimotor adaptability. For such an approach to succeed, we must develop predictive measures of sensorimotor adaptability that will allow us to foresee, before actual spaceflight, which crewmembers are likely to experience the greatest challenges to their adaptive capacities. The goals of this project are to identify and characterize this set of predictive measures. Our approach includes: 1) behavioral tests to assess sensory bias and adaptability quantified using both strategic and plastic-adaptive responses; 2) imaging to determine individual brain morphological and functional features, using structural magnetic resonance imaging (MRI), diffusion tensor imaging, resting state functional connectivity MRI, and sensorimotor adaptation task-related functional brain activation; and 3) assessment of genotypic markers of genetic polymorphisms in the catechol-O-methyl transferase, dopamine receptor D2, and brain-derived neurotrophic factor genes and genetic polymorphisms of alpha2-adrenergic receptors that play a role in the neural pathways underlying sensorimotor adaptation. We anticipate that these predictive measures will be significantly correlated with individual differences in sensorimotor adaptability after long-duration spaceflight and exposure to an analog bed rest environment. We will be conducting a retrospective study, leveraging data already collected from relevant ongoing or completed bed rest and spaceflight studies. These data will be combined with predictor metrics that will be collected prospectively (as described for behavioral, brain imaging and genomic measures) from these returning subjects to build models for predicting post-mission (bed rest - non-astronauts or space flight - astronauts) adaptive capability as manifested in their outcome measures. To date we have completed a study on 15 normal subjects with all of the above measures. In this presentation we will discuss the optimized set of tests for predictive metrics to be used for evaluating post mission adaptive capability as manifested in their outcome measures. Comparisons of model performance will allow us to better design and implement sensorimotor adaptability training countermeasures against decrements in post-mission adaptive capability that are customized for each crewmember's sensory biases, adaptive capacity, brain structure and functional capacities, and genetic predispositions. The ability to customize adaptability training will allow more efficient use of crew time during training and will optimize training prescriptions for astronauts to ensure expected outcomes.

Mulavara, A. P.↗
NASA NTRS2003

Analysis of Moessbauer Data from Mars: A Database and Artificial Neural Network for Identification of Iron-bearing Phases

The exploration of the planet Mars is one of the major goals within the Solar system exploration programs of the US-American space agency NASA and the European Space Agency ESA. In particular the search for water and life and understanding of the history of the surface and atmosphere will be the major tasks of the upcoming space missions to Mars. The miniaturized Moessbauer spectrometer MIMOS II has been selected for the NASA Mars-Exploration-Rover twin-mission to Mars in 2003 and the ESA 2003 Mars-Express Beagle 2 mission. Reduced in size and weight, in comparison to ordinary laboratory setup, the sensor head just weights approximately 400 g, with a volume of (50x50x90) cu mm, and holds two gamma-ray sources: the stronger for experiments and the weaker for calibrations. The collimator (in sample direction) also shields the primary radiation off the detectors. Around the drive four detectors are mounted. The detectors are made of Si-PIN-photodiodes in chip form (100 sq mm, thickness of 0.5 mm). The control unit is located in a separate electronics board. This board is responsible for the power supply, generation of the drive's velocity reference signal, read of the detector pulses to record the spectrum, data storage and communication with the host computer. After more than four decades from the discovery of the Moessbauer effect, more than 400 minerals were studied at different temperatures. Their Moessbauer parameters were reported in the literature, and have been recently collected in a data bank. Previous Mars-missions, namely Viking and Mars Pathfinder, revealed Si, Al, Fe, Mg, Ca, K, Ti, S and Cl to be the major constituents in soil and rock elemental composition of the red planet. More than 200 minerals already studied by Moessbauer spectroscopy contain significant amounts of these elements. A considerable number of Moessbauer studies were also carried out on meteorites and on Moon samples. Looking backward in the studies of the whole Moessbauer community, we have built a specific library containing Moessbauer parameters of those possible Mars minerals. The selected minerals, their Moessbauer parameter values (min. max. s.d and number of available data), main site substitution, behavior as a function of temperature and a ranking as expected to be found on Mars were organized. Mars-analogue Fe-bearing minerals not studied by Moessbauer spectroscopy are being collected and investigated. In addition, it an identification system based on Artificial Neural Networks (ANN) was implemented which enables fast and precise mineral identification from the experimental Moessbauer parameters at a given temperature.

P A de Souza Jr.↗
DOE OSTI2025

Exploring the nexus of many-body theories through neural network techniques: the tangent model

Abstract In this paper, we present a physically informed neural network (NN) representation of the effective interactions associated with coupled-cluster downfolding models to describe chemical systems and processes. The NN representation not only allows us to evaluate the effective interactions efficiently for various geometrical configurations of chemical systems corresponding to various levels of complexity of the underlying wave functions, but also reveals that the bare and effective interactions are related by a tangent function of some latent variables. We refer to this characterization of the effective interaction as a tangent model. We discuss the connection between this tangent model for the effective interaction with the previously developed theoretical analysis that examines the difference between the bare and effective Hamiltonians in the corresponding active spaces.

97 MATHEMATICS AND COMPUTING↗