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DOE OSTI2023

Difference in load predictions obtained with effective turbulence vs. a dynamic wake meandering modeling approach

Abstract. According to the international standard for wind turbine design, the effects of wind turbine wakes on structural loads can be considered in two ways: (1) by augmenting the ambient turbulence levels with the effective turbulence model (EFF) and then calculating the resulting loads and (2) by performing dynamic wake meandering (DWM) simulations, which compute wake effects and loads for all turbines on a farm at once. There is no definitive answer in scientific literature as to the consequences of choosing one model over the other, but the two approaches are unarguably very different. The work presented here expounds on these differences and investigates to what extent they affect the simulated structural loads. We consider an idealized 4×4 rectangular array of National Renewable Energy Laboratory 5 MW wind turbines with a spacing of 5 by 8 rotor diameters and three wind speed scenarios at high ambient turbulence. Load simulations are performed in OpenFAST with EFF and in FAST.Farm with the DWM implementation. We compare ambient turbulence, wind farm turbulence, and loads between both approaches. When omnidirectional results are compared, EFF wind farm turbulence intensity is consistently higher by 0.2 % (above-rated wind speed) to 2.7 % (below-rated wind speed). However, for certain wind directions, the EFF turbulence can be lower than FAST.Farm by almost 9 %. Wind speeds within the farm were found to differ by up to 3 m s−1 due to the lack of wake deficits in the EFF approach, leading to longer tails toward low values in the FAST.Farm mean load distributions. Consistent with the turbulence results, the median EFF load standard deviations are also consistently higher, by a maximum of 20 % and 17 % for blade-root out-of-plane and tower-base fore-aft moments, respectively.

17 WIND ENERGY↗

DOE OSTI2025

Nonadiabatic dynamics of photoexcited thiopyridone isomers: An interplay between El-Sayed’s conditions and energy gap law

We investigated the non-adiabatic dynamics of photoexcited thiopyridone systems across their ortho-, meta-, and para-isomeric forms. The relaxation pathways of the three isomers in both gas phase and solvent environments are mapped using surface hopping dynamics based on time-dependent density functional theory. Our analysis highlights the influence of isomeric structures on photophysical behavior, offering insights into design principles to control photochemical phenomena. The simulations suggest a systematic reduction in the rate of intersystem crossing (ISC) from ortho- to meta- to para-isomer. Comparisons with multiconfigurational wave function methods in the gas phase further demonstrate how electronic structure influences the predicted dynamical pathways. The simulated dynamics demonstrates that the spin–orbit coupling strength alone does not determine the rate of ISC, as both state energetics and underlying electronic and structural features play decisive roles. These aspects explain the much slower ISC in the para-isomer, as well as the non-negligible role of the El-Sayed forbidden pathway in the computed ISC dynamics.

Complete-active space self-consistent field↗

DOE OSTI2024

ELECTRONIC STRUCTURE METHODS AND PROTOCOLS WITH APPLICATION TO DYNAMICS, KINETICS AND THERMOCHEMISTRY

Hydrocarbon combustion involves the reaction dynamics of a tremendous number of species beginning with many-component fuel mixtures and proceeding via a complex system of intermediates to form primary and secondary products. Combustion conditions corresponding to new advanced engines and/or alternative fuels rely increasingly on autoignition and low-temperature-combustion chemistry. In these regimes various transient radical species such as HO2, ROO·, ·QOOH, HCO, NO2, HOCO, and Criegee intermediates play important roles in determining the detailed as well as more general dynamics. A clear understanding and accurate representation of these processes is needed for effective modeling. Given the difficulties associated with making reliable experimental measurements of these systems, computation can play an important role in developing these energy technologies. Accurate calculations have their own challenges since even within the simplest dynamical approximations such as transition state theory, the rates depend exponentially on critical barrier heights and these may be sensitive to the level of quantum chemistry. Moreover, it is well-known that in many cases it is necessary to go beyond statistical theories and consider the dynamics. Quantum tunneling, resonances, radiative transitions, and non-adiabatic effects governed by spin-orbit or derivative coupling can be determining factors in those dynamics. Building upon progress made during a period of prior support through the DOE Early Career Program, this project combines developments in the areas of potential energy surface (PES) fitting and multistate multireference quantum chemistry to allow spectroscopically and dynamically/kinetically accurate investigations of key molecular systems (such as those mentioned above), many of which are radicals with strong multireference character and have the possibility of multiple electronic states contributing to the observed dynamics. An ongoing area of investigation is to develop general strategies for robustly convergent electronic structure theory for global multichannel reactive surfaces including diabatization of energy and other relevant surfaces such as dipole transition. Combining advances in ab initio methods with automated interpolative PES fitting allows the construction of high-quality PESs (incorporating thousands of high-level data) to be done rapidly through parallel processing on high-performance computing (HPC) clusters. In addition, new methods and approaches to electronic structure theory will be developed and tested through applications. This project will explore limitations in traditional multireference calculations (e.g., MRCI) such as those imposed by internal contraction, lack of high-order correlation treatment and poor scaling. Methods such as DMRG-based extended active-space CASSCF and various Quantum Monte Carlo (QMC) methods will be applied (including VMC/DMC and FCIQMC). Insight into the relative significance of different orbital spaces and the robustness of application of these approaches on leadership class computing architectures will be gained. Synergy with other components of this research program such as automated PES fitting and multireference quantum chemistry will be used to address challenges encountered by the standard approaches to computational thermochemistry (those being single-reference quantum chemistry and perturbative treatments of the anharmonic vibrational energy, which break down for some cases of electronic structure or floppy strongly coupled vibrational modes).

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Non-Empirical and Self-Interaction Corrections for DFTB: Towards Accurate Quantum Simulations for Large Mesoscale Systems (Final Report)

This project was comprised of two complementary (but parallel) thrusts: (1) implementing massively-parallelized computing hardware (with new computational hardware that may replace GPUs) in the density functional tight binding (DFTB) approach and (2) developing new capabilities in DFTB to calculate the electronic structure and dynamics of large chemical systems. While classical molecular dynamics can handle hundreds of thousands of atoms, it cannot provide a first-principles based description of chemical systems at the quantum level. At the other extreme, conventional Kohn-Sham DFT methods can probe the true quantum mechanical nature of chemical systems; however, these methods cannot tackle the large sizes and length scales relevant to dynamics simulations of realistic systems. The DFTB formalism utilized in this project provides a viable approach for probing these large systems at a quantum mechanical level of detail. However, to utilize the DFTB approach for accurate calculations of electronic properties, it is crucial to incorporate quantum-based corrections in DFTB since exchange-correlation effects can still remain very strong in these large systems. At the same time, enhancing the computational efficiency of DFTB is also essential since optimal computational performance is required for addressing the large size scales associated with realistic chemical systems. As such, the new non-empirical corrections and computing hardware enhancements implemented in this project will enable accurate and computationally efficient approaches to directly probe electronic properties in these large, complex systems.

36 MATERIALS SCIENCE↗

DOE OSTI2024

QRCODE: Massively parallelized real-time time-dependent density functional theory for periodic systems

We present a new software module, QRCODE (Quantum Research for Calculating Optically Driven Excitations), for massively parallelized real-time time-dependent density functional theory (RT-TDDFT) calculations of periodic systems in the open-source Qbox software package. Our approach utilizes a custom implementation of a fast Fourier transformation scheme that significantly reduces inter-node message passing interface (MPI) communication of the major computational kernel and shows impressive scaling up to 16,344 CPU cores. In addition to improving computational performance, QRCODE contains a suite of various time propagators for accurate RT-TDDFT calculations. As benchmark applications of QRCODE, we calculate the current density and optical absorption spectra of hexagonal boron nitride (h-BN) and photo-driven reaction dynamics of the ozone-oxygen reaction. We also calculate the second and higher harmonic generation of monolayer and multi-layer boron nitride structures as examples of large material systems. Our optimized implementation of RT-TDDFT in QRCODE enables large-scale calculations of real-time electron dynamics of chemical and material systems with enhanced computational performance and impressive scaling across several thousand CPU cores.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

On the discretization error of the discrete generalized quantum master equation

The transfer tensor method (TTM) [Cerrillo and Cao, Phys. Rev. Lett. 112 , 110401 (2014)] can be considered a discrete-time formulation of the Nakajima–Zwanzig quantum master equation (NZ-QME) for modeling non-Markovian quantum dynamics. A recent paper [Makri, J. Chem. Theory Comput. 21 , 5037 (2025)] raised concerns regarding the consistency of the TTM discretization, particularly a spurious term at the initial time t = 0. Here, this work presents a detailed analysis of the discretization structure of the TTM, clarifying the origin of the initial-time correction and establishing a consistent relationship between the TTM discrete-time memory kernel K N and the continuous-time NZ-QME kernel $\mathscr{K}$( N Δ t ). This relationship is validated numerically using the spin-boson model, demonstrating convergence of reconstructed memory kernels and accurate dynamical evolution as Δ t → 0. While the TTM provides a consistent discretization, we note that alternative schemes are also viable, such as the midpoint derivative/midpoint integral scheme proposed in Makri’s work. The relative performance of various schemes for either computing accurate $\mathscr{K}$( N Δ t ) from exact dynamics or obtaining accurate dynamics from exact $\mathscr{K}$( N Δ t ) warrants further investigation.

Density-matrix↗

DOE OSTI2025

Elucidating the Role of Hydrogen at c‐In 2 O 3 /a‐In 2 O 3− x Interface

Ab initio molecular dynamics simulations and hybrid functional electronic structure calculations are employed to determine the formation, the structural and electronic properties, and the dynamics of covalent (In—OH) and ionic (In—H—In) hydrogen defects at crystalline-In 2 O 3 /amorphous-In 2 O 3−x interface. This comprehensive computational study considers (i) various interstitial and substitutional hydrogen site locations within the crystalline, amorphous, and interfacial regions; (ii) several oxygen-to-hydrogen ratios; and (iii) possible defect charged states. The results reveal hydrogen's inability to fully passivate the undercoordinated under-shared in atoms in amorphous highly substoichiometric oxide, giving rise to the formation of deep electron traps even in net-charge neutral structures. These trap defects are found to be sensitive to photoexcitation, in contrast to In—OH with H's electronic states located below the valence band and to In—H—In, where H is found to maintain its charge state upon illumination. Nevertheless, H plays a critical role in photoinduced conductivity and its relaxation by promoting In—O coordination transformations at the interfacial region, including deterioration of the crystalline layer. Finally, the results help identify mobile H species and metastable H defect complexes (such as In—H—H—In, In—OH–H—In, and In—OH–O—In) that are responsible for long relaxation times of the conductivity decay.

H defects↗

DOE OSTI2024

Recent Advances in X-ray Absorption Near Edge Structure (XANES) Simulation for Catalysis: Theories and Applications

X-ray absorption spectroscopy (XAS) is a powerful spectroscopic technique for characterizing catalytic active sites. In particular, X-ray Absorption Near Edge Structure (XANES) provides insights into the oxidation state and local coordination environment of the absorbing atom, shedding light on the catalytic structure. Computational XANES simulations provide one-on-one correspondence between the molecular structure and their corresponding spectra, making them an effective approach for interpreting experimental XANES features. This work outlines various theories used to simulate XANES spectra and highlights recent advancements in computational XANES applications for homogeneous, heterogeneous, and single-atom catalysts focusing on identifying the active site structures, the site heterogeneity, and the dynamic evolution of catalysts.

Xu, Jiayi↗

DOE OSTI2024

Improving the precision of forces in real-space pseudopotential density functional theory

The high-order finite difference real-space pseudopotential density functional theory (DFT) approach is a valuable method for large-scale, massively parallel DFT calculations. A significant challenge in the approach is the oscillating “egg-box” error introduced by aliasing associated with a coarse grid spacing. To address this issue while minimizing computational cost, we developed a finite difference interpolation (FDI) scheme [Roller et al., J. Chem. Theory Comput. 19, 3889 (2023)] as a means of exploiting the high resolution of the pseudopotential to reduce egg-box effects systematically. Here, we show an implementation of this method in the PARSEC code and examine the practical utility of the combination of FDI with additional methods for improving force precision and/or reducing its computational cost, including orbital-based forces, compensating charges (namely, adding and subtracting a judiciously chosen charge density such that the total density is unaltered), and a modified spatial domain in which the real-space grid is defined. Using selected small molecules, as well as metallic Li, as test cases, we show that a combination of all four aspects leads to a significant reduction in computational cost while retaining a high level of precision that supports accurate structures and vibrational spectra, as well as stable and accurate molecular dynamics runs.

Chemistry↗

DOE OSTI2024

Variation Tolerant and Energy-Efficient Charge Domain Compute-in-Memory Array with Binary and Multi-Level Cell Ferroelectric FET

Here, in this work, we present a variation-tolerant and energy-efficient charge-domain Ferroelectric FET (FeFET) based Compute-in-Memory (CiM) array design that is compatible with both binary and multi-level cell memory sensing. We demonstrate that: 1) by exploiting FeFET as a nonvolatile switch, its high ON/OFF ratio in the subthreshold region can suppress the error introduced by the inaccurate ON state conductance, thus realizing robust CiM operations, unlike the current-domain CiM design where the computation results is highly sensitive to the device conductance variation; 2) by leveraging a dense dynamic random access memory (DRAM)-like 1FeFET1C cell structure, the proposed design benefits from the existing high density DRAM establishment while also significantly relaxing the capacitor retention and transistor leakage requirement; 3) the charge-domain CiM supports both binary FeFET with minimum overhead and MLC FeFET with tolerable latency for MLC state sensing, whose efficacy is validated experimentally on both cell-level and array-level; 4) the proposed CiM shows much better device variation resilience than conventional current-domain CiM, and also improves inference accuracy. Macro-level evaluation results demonstrate significantly higher energy efficiency and area efficiency compared to prior CiM works.

Duan, Jiahui [University of Notre Dame, IN (United↗

DOE OSTI2021

LoTToR: An Algorithm for Missing-Wedge Correction of the Low-Tilt Tomographic 3D Reconstruction of a Single-Molecule Structure (LoTToR) v1.0

The low-tilt tomographic reconstruction (LoTToR) method is a post-processing method to correct the missing-wedge artifact, which contains a model-free iteration process under a set of constraints in real and reciprocal spaces. A proof of concept is conducted by using the LoTToR on a phantom, i.e., a simulated 3D reconstruction from a low-tilt series of images, including that within a tilt range of ±15°. The method is validated by using both negative-staining (NS) and cryo-electron tomography (cryo-ET) experimental data. A significantly reduced missing-wedge artifact verifies the capability of LoTToR, suggesting a new tool to support the future study of macromolecular dynamics, fluctuation and chemical activity from the viewpoint of single-molecule 3D structure determination. Moreover, the software can be used for hospital computer tomography (CT) to reduce the radiation damage to patients without reducing the CT image quality.

Ren, Gang↗

DOE OSTI2024

Spin-Controllable Dynamics in Defect-Engineered Carbon Nanotubes as Single Photon Emitters: Data-Driven Modeling and Computations

Quantum technologies, such as quantum computing and sensing, require efficient single-photon emission (SPE) sources that operate at room temperature in telecom wavelengths. While several materials can serve as SPE sources, no single platform meets all the criteria for efficiency, ambient operation, and scalability. Single-walled carbon nanotubes (SWCNTs) with covalently attached molecules offer a promising solution. Their SPE can be easily tuned via modifications of the SWCNT's diameter, chirality, and bonded molecules, enabling emission across near-IR to telecom wavelengths at ambient conditions. However, to fully realize the potential of SWCNTs and unlock their quantum capabilities, a deeper understanding of how structural defects from molecular adducts affect their emission and competing photoexcited processes is essential. To address this gap in our knowledge, this project combined quantum chemistry calculations with data-driven methods of cheminformatics (QSAR) and machine learning (ML). The developed computational approaches have provided several design strategies for covalent functionalization of SWCNTs to improve their optical response. The collaboration with Los Alamos National Lab (LANL) enabled direct comparison of computational and experimental data, facilitating method validation. This partnership was enhanced through access to LANL's Center for Integrated Nanotechnologies (CINT) utilizing User Facility Program and summer internships, which provided three NDSU graduate students with hands-on experience at LANL. The outcomes of this project included (1) Advancing the current stage of computational methods in accurate modeling of non-adiabatic spin-dependent photoexcited dynamics and its applicability to nanosystems consisting of thousands of atoms, realized as open-access codes linked to existing DFT-based software; (2) Establishing the relationship between the structure of adducts and SWCNTs and intrinsic excitonic and spin properties of defect states for guiding novel synthetic strategies and experimental probes of chemically functionalized SWCNTs as near-IR emitting materials; (3) Generating virtual libraries of hypothetical functionalized SWCNTs for virtual screening of their chemical structures and optical properties, leveraging new functionalities of SWCNTs; (4) Offering a unique experience for NDSU graduate students that prepared them for future scientific careers related to materials modeling and big data processing. These results were summarized in 12 published journal papers and 3 recently submitted papers. One of a key finding is that the position of defect sites on the SWCNT surface primarily drives the emission redshift (up to 100 meV), while the polarity of the defect-inducing molecules has a much smaller effect (~10 meV). However, the electron-donating or withdrawing properties of a molecule influence selecting reactivity of defect sites. These insights important for optimizing synthetic protocols for desired emissions in SWCNTs. We also revealed that the interaction between two defects at various positions on the SWCNT enhances the redshift and optical activity of states, favoring strong near-IR emission. This suggests that manipulations in defect concentrations is a promising strategy for controlling efficient emission. Mostly important, the defect position was found controllable by the spin states of photoexcited intermediates: Excited aromatic molecules form ortho defects with SWCNTs at their singlet states in the presence of oxygen, while oxygen-free conditions favor para defects via the triplet-state mechanism. Additionally, a heat-activated [2+2] cycloaddition reaction facilitates divalent defect formation with fewer bonding positions that narrows emission bands. These groundbreaking findings have been experimentally validated and significantly advance our understanding of defect chemistry in SWCNTs. Using a novel encoding technique and 3D-MoRSE descriptors, we developed highly accurate ML/QSAR models to predict both the 3D structure and optical properties of SWCNTs with chemical defects. This model enabled the creation of a virtual library of 125,556 structures, providing new insights into the relationship between SWCNT-defect structure and emission.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

Numerical assessment of triply periodic minimal surfaces for direct air capture of carbon dioxide

Direct air capture (DAC) systems often consist of packing material wetted by a capture fluid that reacts with CO 2 in the airstream. The efficiency of the contactor is determined by a complex relationship of fluid dynamics, heat and mass transfer, contactor geometry, and chemical properties. The efficiency of the contactor must be balanced with other factors, primarily pressure drop through the system. Triply periodic minimal surfaces (TPMS) are a class of differential surfaces that have been explored in multiple engineering applications and have been shown to exhibit excellent performance when used in heat exchangers. Their tortuous path provides a high surface-to-volume ratio and favorable trade-off between contact area and pressure drop. In this work, a gyroid-type TPMS contactor was evaluated using computational fluid dynamics for a variety of geometric parameters to explore the potential benefit of TPMS shapes for DAC applications. A thin-film model was employed to model the flow and distribution of the capture solvent, allowing efficient simulations of TPMS structures at scale by eliminating the need for a computationally intensive interface capturing method. A liquid-gas mass transfer model was implemented in the commercial software STAR-CCM+ and used to predict the CO 2 capture efficiency and study the trade-off between capture performance and pressure drop through analysis of capture rates, mass transfer coefficients, and other relevant variables. TPMS contactors with a variety of geometric parameters and two capture solvent options were investigated to determine the effect of design choices on the operational performance of DAC systems. In conclusion, results showed that while contactor geometry is the dominant factor in efficiency and pressure drop, the physiochemical properties of the solvent are an important secondary influence on the contactor performance.

CFD↗

DOE OSTI2021

A metabolic modeling platform for the computation of microbial ecosystems in time and space (COMETS)

Genome-scale stoichiometric modeling of metabolism has become a standard systems biology tool for modeling cellular physiology and growth. Extensions of this approach are emerging as a valuable avenue for predicting, understanding and designing microbial communities. Computation of microbial ecosystems in time and space (COMETS) extends dynamic flux balance analysis to generate simulations of multiple microbial species in molecularly complex and spatially structured environments. Here we describe how to best use and apply the most recent version of COMETS, which incorporates a more accurate biophysical model of microbial biomass expansion upon growth, evolutionary dynamics and extracellular enzyme activity modules. In addition to a command-line option, COMETS includes user-friendly Python and MATLAB interfaces compatible with the well-established COBRA models and methods, as well as comprehensive documentation and tutorials. Overall, this protocol provides a detailed guideline for installing, testing and applying COMETS to different scenarios, generating simulations that take from a few minutes to several days to run, with broad applicability to microbial communities across biomes and scales.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

ExaWind: Opportunity for Discovery

The predictive simulation of the dynamics of modern wind turbines and wind farms is a high-performance-computing (HPC) grand challenge. Modern wind turbines are the largest rotating machines in the world, with rotor diameters exceeding 200 meters, and with heights well into the atmospheric boundary layer. To address this grand challenge, the U.S. Department of Energy (DOE) Wind Energy Technologies Office and the Exascale Computing Project have been supporting the creation of the ExaWind modeling and simulation environment since 2016. ExaWind is composed of the incompressible-flow computational-fluid-dynamics (CFD) solvers AMR-Wind and Nalu-Wind and the wind-turbine-dynamics solver OpenFAST. In our hybrid CFD approach, Nalu-Wind unstructured-grid models resolve the near-body flow around the turbine; those models are embedded in, and two-way coupled to, an AMR-Wind structured-grid mesh through overset meshes. In this talk I give an overview of ExaWind software stack and describe how it is being used to address important problems in wind energy.

computational fluid dynamics↗

DOE OSTI2021

Structure–Capacitance Relationships of Graphene/Ionic Liquid Electrolyte Double Layers

The differential capacitance profile of electrochemical interfaces reflects the physical properties of the double layer. For carbon electrodes and ionic liquid based electrolytes, these capacitance profiles are not fully understood. In this work, we utilize constant voltage molecular dynamics simulations to compute differential capacitance profiles of ionic liquids [BMIm + ][BF 4 - ] and [BMIm + ][TFSI - ] mixed with acetonitrile and 1,2-dichloroethane, at model graphene electrodes. We find that both pure and 10% mole fraction ionic liquid electrolytes exhibit camel shaped capacitance profiles with two peaks on either side of a minimum centered at the potential of zero charge. This profile shape results from electric field induced rearrangement of ion structure within the inner layer closest to the electrode interface. At low potential, the ionic liquid inner layer is concentrated with non-polar tri-fluoromethyl and butyl functional groups of the anions and cations, corresponding to the minimum of the capacitance profiles. With increasing voltage, electrostatic interactions of polar/charged functional groups with the electrode surface compete with these non-polar interactions, leading to ion rearrangement that increases the inner layer charge density and results in higher capacitance. After the ion restructuring is complete, the response saturates and capacitance diminishes. The presence of organic solvent significantly changes the composition of the inner layer. For example, strong non-polar interactions between dichloroethane molecules and the graphene surface substantially block ion/electrode contact at moderate potentials. Overall, our simulations highlight the dynamic nature of the inner region of organic electrolyte double layers, and the sensitive dependence on electrolyte composition and applied voltage.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Dynamic STEM-EELS for single-atom and defect measurement during electron beam transformations

This study introduces the integration of dynamic computer vision–enabled imaging with electron energy loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM). This approach involves real-time discovery and analysis of atomic structures as they form, allowing us to observe the evolution of material properties at the atomic level, capturing transient states traditional techniques often miss. Rapid object detection and action system enhances the efficiency and accuracy of STEM-EELS by autonomously identifying and targeting only areas of interest. This machine learning (ML)–based approach differs from classical ML in that it must be executed on the fly, not using static data. We apply this technology to V-doped MoS 2 , uncovering insights into defect formation and evolution under electron beam exposure. This approach opens uncharted avenues for exploring and characterizing materials in dynamic states, offering a pathway to increase our understanding of dynamic phenomena in materials under thermal, chemical, and beam stimuli.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Probabilistic evolution of stochastic dynamical systems: A meso-scale perspective

Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features are used to quantify and propagate uncertainties associated with the initial conditions, external excitations, etc. From a probabilistic modeling standing point, two broad classes of methods exist, i.e. macro-scale methods and micro-scale methods. Classically, macro-scale methods such as statistical moments-based strategies are usually too coarse to capture the multi-mode shape or tails of a non-Gaussian distribution. Micro-scale methods such as random samples-based approaches, on the other hand, become computationally very challenging in dealing with high-dimensional stochastic systems. In view of these potential limitations, a meso-scale scheme is proposed here that utilizes a meso-scale statistical structure to describe the dynamical evolution from a probabilistic perspective. The significance of this statistical structure is twofold. First, it can be tailored to any arbitrary random space. Second, it not only maintains the probability evolution around sample trajectories but also requires fewer meso-scale components than the micro-scale samples. To demonstrate the efficacy of the proposed meso-scale scheme, a set of examples of increasing complexity are provided. Connections to the benchmark stochastic models as conservative and Markov models along with practical implementation guidelines are presented.

97 MATHEMATICS AND COMPUTING↗