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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

CONNECTING THE GAMMA RAY BURST RATE AND THE COSMIC STAR FORMATION HISTORY: IMPLICATIONS FOR REIONIZATION AND GALAXY EVOLUTION

The contemporary discoveries of galaxies and gamma ray bursts (GRBs) at high redshift have supplied the first direct information on star formation when the universe was only a few hundred million years old. The probable origin of long duration GRBs in the deaths of massive stars would link the universal GRB rate to the redshift-dependent star formation rate (SFR) density, although exactly how is currently unknown. As the most distant GRBs and star-forming galaxies probe the reionization epoch, the potential reward of understanding the redshift-dependent ratio {Psi}(z) of the GRB rate to SFR is significant and includes addressing fundamental questions such as incompleteness in rest-frame UV surveys for determining the SFR at high redshift and time variations in the stellar initial mass function. Using an extensive sample of 112 GRBs above a fixed luminosity limit drawn from the Second Swift Burst Alert Telescope catalog and accounting for uncertainty in their redshift distribution by considering the contribution of 'dark' GRBs, we compare the cumulative redshift distribution N(< z) of GRBs with the star formation density {rho}-dot{sub *}(z) measured from UV-selected galaxies over 0 < z <4. Strong evolution (e.g., {Psi}(z){proportional_to}(1 + z){sup 1.5}) is disfavored (Kolmogorov-Smirnov test P < 0.07). We show that more modest evolution (e.g., {Psi}(z){proportional_to}(1 + z){sup 0.5}) is consistent with the data (P Almost-Equal-To 0.9) and can be readily explained if GRBs occur primarily in low-metallicity galaxies which are proportionally more numerous at earlier times. If such trends continue beyond z {approx_equal} 4, we find that the discovery rate of distant GRBs implies an SFR density much higher than that inferred from UV-selected galaxies. While some previous studies of the GRB-SFR connection have concluded that GRB-inferred star formation at high redshift would be sufficient to maintain cosmic reionization over 6 4 measured from rest-frame optical surveys. The resolution of this important disagreement is currently unclear, and the GRB production rate at early times is likely more complex than a simple function of SFR and progenitor metallicity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Angle dependence of strong-field single and double ionization of carbonyl sulfide

We have studied, experimentally and theoretically, the ionization probability of carbonyl sulfide (OCS) molecules in intense linearly polarized 800-nm laser pulses as a function of the angle between the molecular axis and the laser polarization. Experimentally, the molecules are exposed to two laser pulses with a relative time delay. The first, weaker pulse induces a nuclear rotational wave packet within each molecule such that the ensemble exhibits preferential alignment in the laboratory frame at specific times. The second, stronger pulse induces ionization, and the variation in single and double ionization yields is measured as a function of the delay between the two pulses. The angular dependence of the ionization yield is extracted by fitting the delay-dependent yields to a sum of delay-dependent moments of the rotational wave packet's angular distribution. We compute these same angular-dependent strong-field ionization yields for OCS using time-dependent density-functional theory (TDDFT). For the single-ionization case, our measurements agree well with TDDFT calculations and with previous experiments. Furthermore, analysis of the simulated one-body density reveals that, when averaged over a laser cycle, the resulting hole is delocalized across the molecule for light polarized perpendicular to the molecular axis and mostly localized on the sulfur for parallel polarization. Furthermore, this suggests that preferential molecular alignment is a key parameter for controlling charge migration dynamics initiated by strong-field ionization. For double ionization, the agreement between experiment and theory is less compelling, reflecting the substantial challenges of computing double-ionization yields using TDDFT methods.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

Dissociation of chloromethanes upon resonant σ{sup *} excitation studied by x-ray scattering

The dissociation process following the Cl K-shell excitation to σ{sup *} resonances is studied by high resolution spectroscopy of resonant elastic and inelastic x-ray scattering on CH{sub 3}Cl, CH{sub 2}Cl{sub 2}, CHCl{sub 3}, and CCl{sub 4} molecules. Calculations employing the transition potential and Delta-Kohn-Sham DFT approach are in good agreement with the measured total fluorescence yield and show the presence of a second quasidegenerate group of states with σ{sup *} character above the lowest σ{sup *} unoccupied molecular orbital for molecules with more than one Cl atom. A bandwidth narrowing and a nonlinear dispersion behavior is extracted from the Kα spectral maps for both σ{sup *} resonances. The fitted data indicate that the widths of the Franck-Condon distributions for the first and second σ{sup *} resonances are comparable for all the molecules under study. In addition, an asymmetric broadening of the emission peaks is observed for resonant elastic x-ray scattering with zero detuning on both σ{sup *} resonances. This is attributed to the fast dissociation, transferring about 0.15 of the scattering probability into higher vibrational modes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Transfer Learning-Based Independent Component Analysis

Understanding the underlying component structure is crucial for multivariate signal analysis. Among all the techniques that try to learn the latent structure, independent component analysis (ICA) is one of the most important and popular methods, which aims to extract independent components from multivariate signals and enables further analysis. For example, in electroencephalogram (EEG) analysis, artifacts filtering and disease detection are conducted based on the independent components of the signals. One critical challenge in existing ICA approaches is that the component extraction accuracy may degrade when the available data of a unit are limited. To address this issue, this paper proposes a transfer learning-based ICA method by innovatively transferring component distribution from a source domain, so that accurate component extraction results can be achieved even when only limited data are available in the target domain. To the best of our knowledge, this is the first work that leverages transfer learning to improve ICA accuracy with limited available data. In particular, we first extract all the independent components from the source domain by maximizing the log-likelihood function with a Newton-like method on a smooth manifold. Then for the target domain, the component with the largest negentropy is extracted in each round. To effectively leverage the knowledge from the source domain and to prevent the negative transfer, we try to find a component in the source domain that matches the component we are extracting. The probability density function of the matched component will then be used to improve the component extraction accuracy if such matched component can be found; otherwise, no knowledge will be transferred. Finally, numerical simulations and a case study with electrocardiogram (ECG) data are conducted, showing the effectiveness of the proposed method in transferring knowledge and reducing negative transfer.

42 ENGINEERING↗
DOE OSTI2015

Computational study on the behaviors of granular materials under mechanical cycling

Considering that fusion pebble beds are probably subjected to the cyclic compression excitation in their future applications, we presented a computational study to report the effect of mechanical cycling on the behaviors of granular matter. The correctness of our numerical experiments was confirmed by a comparison with the effective medium theory. Under the cyclic loads, the fast granular compaction was observed to evolve in a stretched exponential law. Besides, the increasing stiffening in packing structure, especially the decreasing moduli pressure dependence due to granular consolidation, was also observed. For the force chains inside the pebble beds, both the internal force distribution and the spatial distribution of force chains would become increasingly uniform as the external force perturbation proceeded and therefore produced the stress relief on grains. In this case, the originally proposed 3-parameter Mueth function was found to fail to describe the internal force distribution. Thereby, its improved functional form with 4 parameters was proposed here and proved to better fit the data. These findings will provide more detailed information on the pebble beds for the relevant fusion design and analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Nuclear Data Uncertainty Quantification for Adjoint-Weighted Quantities via XGPT in Monte Carlo Codes

The Total Monte Carlo method (TMC) is an innovative approach to nuclear data uncertainty propagation. In TMC, a large number of independent ENDF files are randomly generated starting from nuclear models parameters and their uncertainties. These files are then processed with NJOY or similar codes to produce a set of formatted continuous-energy cross sections (i.e., ACE files), and independent Monte Carlo neutron transport simulations are run with these different ACE files as input. Finally the distributions of the considered response functions are obtained directly from the results of the Monte Carlo runs. Despite several improvements of the TMC method, this approach is often considered an inefficient way of propagating nuclear data uncertainties, as it requires several computationally expensive Monte Carlo runs. Covariance-based methods present important advantages for several applications, especially when different sources of uncertainties are to be investigated. For this reason, sensitivity analysis and uncertainty quantification capabilities are being implemented in several Monte Carlo neutron transport codes. On the other hand, the fact that no artificial multi-group covariance matrices are required and that higher moments of the responses distributions can be easily obtained, are definite advantages of the TMC method. In an effort to overcome the limitations of both approaches, a new method, called eXtended Generalized Perturbation Theory (XGPT) is under development. When performing nuclear data uncertainty propagation, such XGPT approach does not require generating discretized (i.e., multigroup) covariance matrices, and allows to estimate higher moments of the response probability distributions, via linear perturbation theory. One of the promising applications of the XGPT method involves its adoption in conjunction with the Proper Orthogonal Decomposition (POD) of nuclear data, to build a Reduced Order Model (ROM) for the approximation of thousands of independent TMC results in a single criticality source simulation. In the present work, this approach is employed for the first time to evaluate the impact of uncertainty in nuclear data on adjoint-weighted quantities. The method has been implemented in an extended version of the Serpent-2.1.24 Monte Carlo code and is demonstrated on two fast spectrum benchmarks, focusing on {sup 208}Pb nuclear data. A new method for propagating nuclear data uncertainties in criticality source Monte Carlo simulations has been developed. This eXtended Generalized Perturbation Theory (XGPT) approach allows to accurately reproduce reference Total Monte Carlo (TMC) uncertainty estimates in a single criticality source simulation. The present work aims to demonstrate that the proposed method can quantify nuclear data uncertainty based on adjoint-weighted quantities. The XGPT approach was applied to evaluate the impact of {sup 208}Pb nuclear data uncertainties on the effective prompt neutron lifetime (l{sub eff}) in two fast spectrum systems. The obtained XGPT results show a good agreement with the reference TMC results, obtained from independent Monte Carlo runs with {sup 208}Pb nuclear data from random TENDL-2013 evaluations. The XGPT method, implemented in a extended version of the Serpent Monte Carlo code and adopted along with the Proper Orthogonal Decomposition (POD) of the nuclear data, is able to provide an accurate reduced order model to approximate thousands TMC results within a single run, ensuring a large saving in computational requirements. The effect of {sup 208}Pb nuclear data uncertainties appears to be rather large. This is consistent with previous studies that adopted the same input random evaluations data from TENDL. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Probability of Loss of Assured Safety in Systems with Multiple Time-Dependent Failure Modes: Incorporation of Delayed Link Failure in the Presence of Aleatory Uncertainty

Probability of loss of assured safety (PLOAS) is modeled for weak link (WL)/strong link (SL) systems in which one or more WLs or SLs could potentially degrade into a precursor condition to link failure that will be followed by an actual link failure after some amount of elapsed time. The descriptor loss of assured safety (LOAS) is used because failure of the WL system places the entire system in an inoperable configuration while failure of the SL system before failure of the WL system, although undesirable, does not necessarily result in an unintended operation of the entire system. Thus, safety is “assured” by failure of the WL system before failure of the SL system. Here, the following topics are considered: (i) Definition of precursor occurrence time cumulative distribution functions (CDFs) for individual WLs and SLs, (ii) Formal representation, approximation and illustration of PLOAS with (a) constant delay times, (b) aleatory uncertainty in delay times, and (c) delay times defined by functions of link properties at occurrence times for link failure precursors, and (iii) Procedures for the verification of PLOAS calculations for the three indicated definitions of delayed link failure.

58 GEOSCIENCES↗
DOE OSTI2015

THE SPITZER INFRARED SPECTROGRAPH DEBRIS DISK CATALOG. II. SILICATE FEATURE ANALYSIS OF UNRESOLVED TARGETS

During the Spitzer Space Telescope cryogenic mission, astronomers obtained Infrared Spectrograph (IRS) observations of hundreds of debris disk candidates that have been compiled in the Spitzer IRS Debris Disk Catalog. We have discovered 10 and/or 20 μm silicate emission features toward 120 targets in the catalog and modeled the IRS spectra of these sources, consistent with MIPS 70 μm observations, assuming that the grains are composed of silicates (olivine, pyroxene, forsterite, and enstatite) and are located either in a continuous disk with power-law size and surface density distributions or thin rings that are well-characterized using two separate dust grain temperatures. For systems better fit by the continuous disk model, we find that (1) the dust size distribution power-law index is consistent with that expected from a collisional cascade, q = 3.5-4.0, with a large number of values outside this range, and (2) the minimum grain size, a {sub min}, increases with stellar luminosity, L {sub *}, but the dependence of a {sub min} on L {sub *} is weaker than expected from radiation pressure alone. In addition, we also find that (3) the crystalline fraction of dust in debris disks evolves as a function of time with a large dispersion in crystalline fractions for stars of any particular stellar age or mass, (4) the disk inner edge is correlated with host star mass, and (5) there exists substantial variation in the properties of coeval disks in Sco-Cen, indicating that the observed variation is probably due to stochasticity and diversity in planet formation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Examining the structural evolution of bicarbonate–water clusters: insights from photoelectron spectroscopy, basin-hopping structural search, and comparison with available IR spectral studies

Bicarbonate serves a crucial biochemical role in the physiological pH buffering system and also has important atmospheric implications. In the current study, HCO 3 $-$ (H 2 O) n (n = 0-13) clusters were successfully produced via electrospray ionization of corresponding bulk salt solution, and were characterized by combining negative ion photoelectron spectroscopy and theoretical calculations. The photoelectron spectra reveal that the electron binding energy monotonically increases with the cluster size up to n = 10 and remains largely the same after n > 10. The photo-detaching feature of the solute HCO3$-$itself, which dominates in the small clusters, diminishes with increase of water coverage. Based on the charge distribution and molecular orbital analyses, the universal high electron binding energy tail that dominates in the larger clusters can be attributed to ionization of water. Thus, the transition of ionization from solute to solvent at the size larger than n=10 has been observed. Extensive theoretical structural search based on the Basin-Hopping unbiased method was carried out, and a plethora of low energy isomers have been obtained for each medium and large size. By comparing the simulated photoelectron spectra and calculated electron binding energies with the experiments, as well as by comparing the simulated infrared spectra with previously reported IR spectra, the probable global minima and the structural evolutionary routes are presented. The nature of bicarbonate-water interactions are mainly electrostatic as implied by the electron localization function (ELF) analysis.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2016

MtSWEET11, a Nodule-Specific Sucrose Transporter of Medicago truncatula

Optimization of nitrogen fixation by rhizobia in legumes is a key area of research for sustainable agriculture. Symbiotic nitrogen fixation (SNF) occurs in specialized organs called nodules and depends on a steady supply of carbon to both plant and bacterial cells. Here we report the functional characterization of a nodule-specific Suc transporter, MtSWEET11 from Medicago truncatula . MtSWEET11 belongs to a clade of plant SWEET proteins that are capable of transporting Suc and play critical roles in pathogen susceptibility. When expressed in mammalian cells, MtSWEET11 transported sucrose (Suc) but not glucose (Glc). The MtSWEET11 gene was found to be expressed in infected root hair cells, and in the meristem, invasion zone, and vasculature of nodules. Expression of an MtSWEET11-GFP fusion protein in nodules resulted in green fluorescence associated with the plasma membrane of uninfected cells and infection thread and symbiosome membranes of infected cells. Two independent Tnt1 -insertion sweet11 mutants were uncompromised in SNF. Furthermore, although MtSWEET11 appears to be involved in Suc distribution within nodules, it is not crucial for SNF, probably because other Suc transporters can fulfill its role(s).

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-informed Deep Generative Models

Here, we propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple “snapshots.” Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots. By training a physics-informed generative model that generates “fake” sample paths, we aim to fit the observed particle ensemble distributions with a curve in the probability measure space, which is induced from the inferred particle dynamics. We employ different metrics to quantify the differences between distributions, e.g., the sliced Wasserstein distances and the adversarial losses in generative adversarial networks. We refer to this method as generative “ensemble-regression” (GER), in analogy to the classic “point-regression,” where we infer the dynamics by performing regression in the Euclidean space. We illustrate the GER by learning the drift and diffusion terms of particle ensembles governed by SODEs with Brownian motions and Lévy processes up to 100 dimensions. We also discuss how to treat cases with noisy or truncated observations. Apart from systems consisting of independent particles, we also tackle nonlocal interacting particle systems with unknown interaction potential parameters by constructing a physics-informed loss function. Finally, we investigate scenarios of paired observations and discuss how to reduce the dimensionality in such cases by proving a convergence theorem that provides theoretical support.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A SUBMILLIMETER CONTINUUM SURVEY OF LOCAL DUST-OBSCURED GALAXIES

We conduct a 350 μ m dust continuum emission survey of 17 dust-obscured galaxies (DOGs) at z = 0.05–0.08 with the Caltech Submillimeter Observatory (CSO). We detect 14 DOGs with S{sub 350μm} = 114–650 mJy and signal-to-noise > 3. By including two additional DOGs with submillimeter data in the literature, we are able to study dust content for a sample of 16 local DOGs, which consist of 12 bump and four power-law types. We determine their physical parameters with a two-component modified blackbody function model. The derived dust temperatures are in the range 57–122 K and 22–35 K for the warm and cold dust components, respectively. The total dust mass and the mass fraction of the warm dust component are 3–34 × 10{sup 7} M {sub ⊙} and 0.03%–2.52%, respectively. We compare these results with those of other submillimeter-detected infrared luminous galaxies. The bump DOGs, the majority of the DOG sample, show similar distributions of dust temperatures and total dust mass to the comparison sample. The power-law DOGs show a hint of smaller dust masses than other samples, but need to be tested with a larger sample. These findings support that the reason DOGs show heavy dust obscuration is not an overall amount of dust content, but probably the spatial distribution of dust therein.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Impact of Emergency Diesel Generator Reliability on Microgrids and Building-Tied Systems

Microgrids are an emerging alternative as an energy backup system for critical electric loads and have improved performance compared to the traditional architecture where a single emergency diesel generator is tied to an individual building. Both architectures are dependent on the reliability of their individual generators and a quantitative and realistic comparison of the overall system reliability of the two architectures is lacking. Using recently published work on emergency diesel generator finite reliability, a quantitative methodology is presented to compare the reliability of a microgrid architecture based on centralized emergency diesel generators to the traditional approach of generators tied to individual buildings. Three system reliability performance metrics are calculated as a function of outage duration: (1) probability to meet 100% of the critical load; (2) expected fraction of lost load; and (3) probability to meet the highest priority critical loads. It is shown that stand-alone building-tied emergency diesel generators systems, even when two emergency diesel generators are used per building, cannot provide the reliability required to sustain critical loads for a grid outage lasting multiple days. Due to their network configuration and ability to share load, diesel generator-based microgrid configurations are estimated to have = 93% probability of powering all buildings for a 2-week outage there the individual building-tied emergency diesel generator architecture has a =20% probability. Microgrids do present other susceptibilities that are site specific and should be considered including vulnerabilities associated with the on-campus distribution system and cybersecurity.

backup power↗
DOE OSTI2011

DAMPING OF ELECTRON DENSITY STRUCTURES AND IMPLICATIONS FOR INTERSTELLAR SCINTILLATION

The forms of electron density structures in kinetic Alfven wave (KAW) turbulence are studied in connection with scintillation. The focus is on small scales L {approx} 10{sup 8}-10{sup 10} cm where the KAW regime is active in the interstellar medium, principally within turbulent H II regions. Scales at 10 times the ion gyroradius and smaller are inferred to dominate scintillation in the theory of Boldyrev et al. From numerical solutions of a decaying KAW turbulence model, structure morphology reveals two types of localized structures, filaments and sheets, and shows that they arise in different regimes of resistive and diffusive damping. Minimal resistive damping yields localized current filaments that form out of Gaussian-distributed initial conditions. When resistive damping is large relative to diffusive damping, sheet-like structures form. In the filamentary regime, each filament is associated with a non-localized magnetic and density structure, circularly symmetric in cross section. Density and magnetic fields have Gaussian statistics (as inferred from Gaussian-valued kurtosis) while density gradients are strongly non-Gaussian, more so than current. This enhancement of non-Gaussian statistics in a derivative field is expected since gradient operations enhance small-scale fluctuations. The enhancement of density gradient kurtosis over current kurtosis is not obvious, yet it suggests that modest density fluctuations may yield large scintillation events during pulsar signal propagation. In the sheet regime the same statistical observations hold, despite the absence of localized filamentary structures. Probability density functions are constructed from statistical ensembles in both regimes, showing clear formation of long, highly non-Gaussian tails.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Effects of the Random Crystal Field on the Phase Diagrams and the Magnetic Properties of a Spin-1 Blume-Capel Nanoisland

The phase diagrams and the magnetic properties of a spin-1 Blume-Capel nanoisland are investigated by the use of the effective-field theory based on the probability distribution technique. The influence of the random crystal field and the system parameters on the critical behaviors of the nanoisland are examined. The results show that the system can exhibit a first-order phase transition, a tricritical point, and a re-entrant or even a double re-entrant phenomenon.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

FUNDAMENTAL PARAMETERS AND SPECTRAL ENERGY DISTRIBUTIONS OF YOUNG AND FIELD AGE OBJECTS WITH MASSES SPANNING THE STELLAR TO PLANETARY REGIME

We combine optical, near-infrared, and mid-infrared spectra and photometry to construct expanded spectral energy distributions for 145 field age (>500 Myr) and 53 young (lower age estimate <500 Myr) ultracool dwarfs (M6-T9). This range of spectral types includes very low mass stars, brown dwarfs, and planetary mass objects, providing fundamental parameters across both the hydrogen and deuterium burning minimum masses for the largest sample assembled to date. A subsample of 29 objects have well constrained ages as probable members of a nearby young moving group. We use 182 parallaxes and 16 kinematic distances to determine precise bolometric luminosities (L{sub bol}) and radius estimates from evolutionary models give semi-empirical effective temperatures (T{sub eff}) for the full range of young and field age late-M, L, and T dwarfs. We construct age-sensitive relationships of luminosity, temperature, and absolute magnitude as functions of spectral type and absolute magnitude to disentangle the effects of degenerate physical parameters such as T{sub eff}, surface gravity, and clouds on spectral morphology. We report bolometric corrections in J for both field age and young objects and find differences of up to a magnitude for late-L dwarfs. Our correction in Ks shows a larger dispersion but not necessarily a different relationship for young and field age sequences. We also characterize the NIR–MIR reddening of low gravity L dwarfs and identify a systematically cooler T{sub eff} of up to 300 K from field age objects of the same spectral type and 400 K cooler from field age objects of the same M{sub H} magnitude.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Construction of the landscape for multi-stable systems: Potential landscape, quasi-potential, A-type integral and beyond

Motivated by the famous Waddington’s epigenetic landscape metaphor in developmental biology, biophysicists and applied mathematicians made different proposals to construct the landscape for multi-stable complex systems. We aim to summarize and elucidate the relationships among these theories from a mathematical point of view. We systematically investigate and compare three different but closely related realizations in the recent literature: the Wang’s potential landscape theory from steady state distribution of stochastic differential equations (SDEs), the Freidlin-Wentzell quasi-potential from the large deviation theory, and the construction through SDE decomposition and A-type integral. We revisit that the quasi-potential is the zero noise limit of the potential landscape, and the potential function in the third proposal coincides with the quasi-potential. We compare the difference between local and global quasi-potential through the viewpoint of exchange of limit order for time and noise amplitude. We argue that local quasi-potentials are responsible for getting transition rates between neighboring stable states, while the global quasi-potential mainly characterizes the residence time of the states as the system reaches stationarity. The difference between these two is prominent when the transitivity property is broken. The most probable transition path by minimizing the Onsager-Machlup or Freidlin-Wentzell action functional is also discussed. As a consequence of the established connections among different proposals, we arrive at the novel result which guarantees the existence of SDE decomposition while denies its uniqueness in general cases. It is, therefore, clarified that the A-type integral is more appropriate to be applied to the decomposed SDEs rather than its primitive form as believed by previous researchers. Our results contribute to a deeper understanding of landscape theories for biological systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness

The challenge of quantifying uncertainty propagation in real-world systems is rooted in the high-dimensionality of the stochastic input and the frequent lack of explicit knowledge of its probability distribution. Traditional approaches show limitations for such problems, especially when the size of the training data is limited. To address these diculties, we have developed a general framework of constructing surrogate models on spaces of stochastic input with arbitrary probability measure irrespective of the mutual dependencies between individual components of the random inputs and the analytical form. The present Data-driven Sparsity-enhancing Rotation for Arbitrary Randomness (DSRAR) framework includes a data-driven construction of multivariate polynomial basis for arbitrary mutually dependent probability measure and a sparsity enhancement rotation procedure. This sparsity-enhancing rotation method was initially proposed in our previous work [1] for Gaussian density distributions, which may not be feasible for non-Gaussian distributions due to the loss of orthogonality after the rotation. To remedy such diculties, we developed a new data-driven approach to construct orthonormal polynomials for polynomials for arbitrary mutually dependent (amdP) randomness, ensuring the constructed basis maintains the orthogonality/near-orthogonality with respect to the density of the rotated random vector, where directly applying the regular polynomial chaos including arbitrary polynomial chaos (aPC) [2] shows limitations due to the assumption of the mutual independence between the components of the random inputs. The developed DSRAR framework leads to accurate recovery, with only limited training data, of a sparse representation of the target functions. The eectiveness of our method is demonstrated in challenging problems such as PDEs and realistic molecular systems within high-dimensional conformational space (O(10)) where the underlying density is implicitly represented by a large collection of sample data, as well as systems with explicitly given non-Gaussian probabilistic measures.

Lei, Huan↗