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DOE OSTI2020

Efficacy of the Cell Perturbation Method in Large-Eddy Simulations of Boundary Layer Flow over Complex Terrain

A challenge to simulating turbulent flow in multiscale atmospheric applications is the efficient generation of resolved turbulence motions over an area of interest. One approach is to apply small perturbations to flow variables near the inflow planes of turbulence-resolving simulation domains nested within larger mesoscale domains. While this approach has been examined in numerous idealized and simple terrain cases, its efficacy in complex terrain environments has not yet been fully explored. Here, we examine the benefits of the stochastic cell perturbation method (CPM) over real complex terrain using data from the 2017 Perdigão field campaign, conducted in an approximately 2-km wide valley situated between two nearly parallel ridges. Following a typical configuration for multiscale simulation using nested domains within the Weather Research and Forecasting (WRF) model to downscale from the mesoscale to a large-eddy simulation (LES), we apply the CPM on a domain with horizontal grid spacing of 150 m. At this resolution, spurious coherent structures are often observed under unstable atmospheric conditions with moderate mean wind speeds. Results from such an intermediate resolution grid are often nested down for finer, more detailed LES, where these spurious structures adversely affect the development of turbulence on the subsequent finer grid nest. We therefore examine the impacts of the CPM on the representation of turbulence within the nested LES domain under moderate mean flow conditions in three different stability regimes: weakly convective, strongly convective, and weakly stable. In addition, two different resolutions of the underlying terrain are used to explore the role of the complex topography itself in generating turbulent structures. We demonstrate that the CPM improves the representation of turbulence within the LES domain, relative to the use of high-resolution complex terrain alone. During the convective conditions, the CPM improves the rate at which smaller-scales of turbulence form, while also accelerating the attenuation of the spurious numerically generated roll structures near the inflow boundary. During stable conditions, the coarse mesh spacing of the intermediate LES domain used herein was insufficient to maintain resolved turbulence using CPM as the flow develops downstream, highlighting the need for yet higher resolution under even weakly stable conditions, and the importance of accurate representation of flow on intermediate LES grids.

17 WIND ENERGY↗

DOE OSTI2024

Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics

Abstract Advancements in computing power have recently made it possible to utilize machine learning and deep learning to push scientific computing forward in a range of disciplines, such as fluid mechanics, solid mechanics, materials science, etc. The incorporation of neural networks is particularly crucial in this hybridization process. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data are sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multiphysics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multiphysics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities are presented in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers.

Computer Science↗

DOE OSTI2022

When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?

Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power and generalization ability. Recently, extended PINNs (XPINNs) based on domain decomposition methods have attracted considerable attention due to their effectiveness in modeling multiscale and multiphysics problems and their parallelization. However, theoretical understanding of their convergence and generalization properties remains unexplored. In this study, we take an initial step towards understanding how and when XPINNs outperform PINNs. Specifically, for general multilayer PINNs and XPINNs, we first provide a prior generalization bound via the complexity of the target functions in the PDE problem and a posterior generalization bound via the posterior matrix norms of the networks after optimization. Moreover, based on our bounds, we analyze the conditions under which XPINNs improve generalization. Concretely, our theory shows that the key building block of XPINN, namely, the domain decomposition, introduces a tradeoff for generalization. On the one hand, XPINNs decompose the complex PDE solution into several simple parts, which decreases the complexity needed to learn each part and boosts generalization. On the other hand, decomposition leads to less training data being available in each subdomain, and hence such a model is typically prone to overfitting and may become less generalizable. Empirically, we choose five PDEs to show when XPINNs perform better than, similar to, or worse than PINNs, hence demonstrating and justifying our new theory.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A seamless multiscale operator neural network for inferring bubble dynamics

Modelling multiscale systems from nanoscale to macroscale requires the use of atomistic and continuum methods and, correspondingly, different computer codes. Here, we develop a seamless method based on DeepONet, which is a composite deep neural network (a branch and a trunk network) for regressing operators. In particular, we consider bubble growth dynamics, and we model tiny bubbles of initial size from 100 nm to 10 $\mathrm {\mu }\textrm {m}$ , modelled by the Rayleigh–Plesset equation in the continuum regime above 1 $\mathrm {\mu }\textrm {m}$ and the dissipative particle dynamics method for bubbles below 1 $\mathrm {\mu }\textrm {m}$ in the atomistic regime. After an offline training based on data from both regimes, DeepONet can make accurate predictions of bubble growth on-the-fly (within a fraction of a second) across four orders of magnitude difference in spatial scales and two orders of magnitude in temporal scales. The framework of DeepONet is general and can be used for unifying physical models of different scales in diverse multiscale applications.

Mechanics↗

DOE OSTI2024

Multiscale modeling of HBV infection integrating intra- and intercellular viral propagation to analyze extracellular viral markers

Chronic infection with hepatitis B virus (HBV) is caused by the persistence of closed circular DNA (cccDNA) in the nucleus of infected hepatocytes. Despite available therapeutic anti-HBV agents, eliminating the cccDNA remains challenging. Thus, quantifying and understanding the dynamics of cccDNA are essential for developing effective treatment strategies and new drugs. However, such study requires repeated liver biopsy to measure the intrahepatic cccDNA, which is basically not accepted because liver biopsy is potentially morbid and not common during hepatitis B treatment. We here aimed to develop a noninvasive method for quantifying cccDNA in the liver using surrogate markers in peripheral blood. We constructed a multiscale mathematical model that explicitly incorporates both intracellular and intercellular HBV infection processes. The model, based on age-structured partial differential equations, integrates experimental data from in vitro and in vivo investigations. By applying this model, we roughly predicted the amount and dynamics of intrahepatic cccDNA within a certain range using specific viral markers in serum samples, including HBV DNA, HBsAg, HBeAg, and HBcrAg. Our study represents a significant step towards advancing the understanding of chronic HBV infection. The noninvasive quantification of cccDNA using our proposed method holds promise for improving clinical analyses and treatment strategies. By comprehensively describing the interactions of all components involved in HBV infection, our multiscale mathematical model provides a valuable framework for further research and the development of targeted interventions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Data assimilation in operator algebras

We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a nonabelian operator algebra, which provides a representation of observables by multiplication operators and probability densities by density operators (quantum states). In the algebraic approach, the forecast step of data assimilation is represented by a quantum operation induced by the Koopman operator of the dynamical system. Moreover, the analysis step is described by a quantum effect, which generalizes the Bayesian observational update rule. Projecting this formulation to finite-dimensional matrix algebras leads to computational schemes that are i) automatically positivity-preserving and ii) amenable to consistent data-driven approximation using kernel methods for machine learning. Moreover, these methods are natural candidates for implementation on quantum computers. Applications to the Lorenz 96 multiscale system and the El Niño Southern Oscillation in a climate model show promising results in terms of forecast skill and uncertainty quantification.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Multiscale Modeling of Nanoparticle Precipitation in Oxide Dispersion-Strengthened Steels Produced by Laser Powder Bed Fusion

Laser Powder Bed Fusion (LPBF) enables the efficient production of near-net-shape oxide dispersion-strengthened (ODS) alloys, which possess superior mechanical properties due to oxide nanoparticles (e.g., yttrium oxide, Y-O, and yttrium-titanium oxide, Y-Ti-O) embedded in the alloy matrix. To better understand the precipitation mechanisms of the oxide nanoparticles and predict their size distribution under LPBF conditions, we developed an innovative physics-based multiscale modeling strategy that incorporates multiple computational approaches. These include a finite volume method model (Flow3D) to analyze the temperature field and cooling rate of the melt pool during the LPBF process, a density functional theory model to calculate the binding energy of Y-O particles and the temperature-dependent diffusivities of Y and O in molten 316L stainless steel (SS), and a cluster dynamics model to evaluate the kinetic evolution and size distribution of Y-O nanoparticles in as-fabricated 316L SS ODS alloys. The model-predicted particle sizes exhibit good agreement with experimental measurements across various LPBF process parameters, i.e., laser power (110–220 W) and scanning speed (150–900 mm/s), demonstrating the reliability and predictive power of the modeling approach. The multiscale approach can be used to guide the future design of experimental process parameters to control oxide nanoparticle characteristics in LPBF-manufactured ODS alloys. Additionally, our approach introduces a novel strategy for understanding and modeling the thermodynamics and kinetics of precipitation in high-temperature systems, particularly molten alloys.

Wang, Zhengming (ORCID:0000000241627112)↗

DOE OSTI2022

NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems

Physics-informed neural network (PINN) is a data-driven approach to solving equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory when it is used to solve multiscale equations. Homogenization approximates a multiscale equation by a homogenized equation without multiscale property; it includes solving cell problems and the homogenized equation. The cell problems are periodic, and we propose an oversampling strategy that significantly improves the PINN accuracy on periodic problems. The homogenized equation has a constant or slow dependency coefficient and can also be solved by PINN accurately. We hence proposed a 3-step method, neural homogenization based PINN (NH-PINN), to improve the PINN accuracy for solving multiscale problems with the help of homogenization.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Predictive Chemical Kinetic Modeling: Where We Succeed, Where We Struggle, and What Comes Next

Chemical kinetic modeling plays a foundational role in fields ranging from energy to environmental science, pharmaceuticals, and advanced materials. The past two decades have seen remarkable progress, particularly in modeling gas-phase reactions for thermochemical processes, leading to impactful industrial applications such as steam cracking and air quality management. However, new challenges are emerging. The successful development of systematic methodologies for the description of gas-phase kinetics opens the possibility to apply the same approach to the study of more challenging systems. Here, we review recent advances, including ab initio transition state theory-based master equation estimation of elementary rates, automated mechanism generation, machine-learning-assisted kinetics, and uncertainty quantification, and discuss the advances needed to apply the same methodological approach in areas such as heterogeneous catalysis, electrochemistry, liquid-phase and solid-state reactivity, and multiscale model integration. We advocate for the development of targeted tools, especially methods that go beyond empirical tuning toward first-principles-based predictions. We highlight the need for accessible software and AIaugmented workflows to democratize modeling for industry and academia alike. In this perspective, we call attention to not only what has worked but also what remains unsolved, advocating to avoid overemphasizing successes in scientific works at the expense of realism. The next decade should focus on predictive capability, physical accuracy, and community infrastructure (e.g., databases and services) to enable innovation across diverse fields. We argue that kinetic modeling, properly equipped, can accelerate discovery far beyond its traditional domains.

ab initio calculations↗

DOE OSTI2025

Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTi⁢O3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Calibration of RAFM Micromechanical Model for Creep Using Bayesian Optimization for Functional Output

A Bayesian optimization procedure is presented for calibrating a multimechanism micromechanical model for creep to experimental data of F82H steel. Reduced activation ferritic martensitic (RAFM) steels based on Fe(8–9)%Cr are the most promising candidates for some fusion reactor structures. Although there are indications that RAFM steel could be viable for fusion applications at temperatures up to 600°C, the maximum operating temperature will be determined by the creep properties of the structural material and the breeder material compatibility with the structural material. Due to the relative paucity of available creep data on F82H steel compared to other alloys such as Grade 91 steel, micromechanical models are sought for simulating creep based on relevant deformation mechanisms. As a point of departure, this work recalibrates a model form that was previously proposed for Grade 91 steel to match creep curves for F82H steel. Due to the large number of parameters (9) and cost of the nonlinear simulations, an automated approach for tuning the parameters is pursued using a recently developed Bayesian optimization for functional output (BOFO) framework (Huang et al., 2021, “Bayesian optimization of functional output in inverse problems,” Optim. Eng., 22, pp. 2553–2574). Incorporating extensions such as batch sequencing and weighted experimental load cases into BOFO, a reasonably small error between experimental and simulated creep curves at two load levels is achieved in a reasonable number of iterations. In conclusion, validation with an additional creep curve provides confidence in the fitted parameters obtained from the automated calibration procedure to describe the creep behavior of F82H steel.

42 ENGINEERING↗

DOE OSTI2021

Multiscale Patterning from Competing Interactions and Length Scales

We live in an era of complexity marked by impressive new tools powering the scientific method to accelerate discovery, prediction, and control of increasingly complex systems. In common with many disciplines and societal challenges and opportunities, materials and condensed matter sciences are beneficiaries. The volume and fidelity of experimental, computational, and visualization data available, and tools to rapidly interpret them, are remarkable. Conceptual frameworks, including multiscale, multiphysics modeling of this complexity, are fueled by the data and, in turn, guide directions for future experimental and computational strategies. In this spirit, we discuss the importance of competing interactions, length scales, and constraints as pervasive sources of spatio-temporal complexity. We use representative examples drawn from materials and condensed matter, including the important role of elasticity in some technologically important quantum materials.

36 MATERIALS SCIENCE↗

DOE OSTI2022

#COVIDisAirborne: AI-enabled multiscale computational microscopy of delta SARS-CoV-2 in a respiratory aerosol

We seek to completely revise current models of airborne transmission of respiratory viruses by providing never-before-seen atomic-level views of the SARS-CoV-2 virus within a respiratory aerosol. Our work dramatically extends the capabilities of multiscale computational microscopy to address the significant gaps that exist in current experimental methods, which are limited in their ability to interrogate aerosols at the atomic/molecular level and thus obscure our understanding of airborne transmission. We demonstrate how our integrated data-driven platform provides a new way of exploring the composition, structure, and dynamics of aerosols and aerosolized viruses, while driving simulation method development along several important axes. We present a series of initial scientific discoveries for the SARS-CoV-2 Delta variant, noting that the full scientific impact of this work has yet to be realized.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

Simulator for Hydrologic Unstructured Domains (SHUD v1.0): numerical modeling of watershed hydrology with the finite volume method

Abstract. Hydrologic modeling is an essential strategy for understanding and predicting natural flows, particularly where observations are lacking in either space or time or where complex terrain leads to a disconnect in the characteristic time and space scales of overland and groundwater flow. However, significant difficulties remain for the development of efficient and extensible modeling systems that operate robustly across complex regions. This paper introduces the Simulator for Hydrologic Unstructured Domains (SHUD), an integrated, multiprocess, multiscale, flexible-time-step model, in which hydrologic processes are fully coupled using the finite volume method. SHUD integrates overland flow, snow accumulation/melt, evapotranspiration, subsurface flow, groundwater flow, and river routing, thus allowing physical processes in general watersheds to be realistically captured. SHUD incorporates one-dimensional unsaturated flow, two-dimensional groundwater flow, and a fully connected river channel network with hillslopes supporting overland flow and baseflow. The paper introduces the design of SHUD, from the conceptual and mathematical description of hydrologic processes in a watershed to the model's computational structures. To demonstrate and validate the model performance, we employ three hydrologic experiments: the V-catchment experiment, Vauclin's experiment, and a model study of the Cache Creek Watershed in northern California. Ongoing applications of the SHUD model include hydrologic analyses of hillslope to regional scales (1 m2 to 106 km2), water resource and stormwater management, and interdisciplinary research for questions in limnology, agriculture, geochemistry, geomorphology, water quality, ecology, climate and land-use change. The strength of SHUD is its flexibility as a scientific and resource evaluation tool where modeling and simulation are required.

58 GEOSCIENCES↗

DOE OSTI2020

Revealing Molecular Mechanisms in Hierarchical Nanoporous Carbon via Nuclear Magnetic Resonance

Hierarchical nanoporous carbons (HNC) have been proven to be an effective adsorbent for the adsorption of volatile organic compounds (VOCs) and CO 2 . However, questions remain regarding the hierarchical structure regulation, the adsorption mechanisms of adsorbate uptake, and interactions within the HNC. Here, we synthesize HNC from wood, using a microwave-induced heating method incorporating K 2 CO 3 activation. Our HNC exhibit Murray's law multiscale structures, prompting a molecular-scale study of adsorbate adsorption via nuclear magnetic resonance (NMR). NMR chemical shifts are consistent with ring-current effects from the adsorbent. Our NMR technique provides a convenient way to quantitate adsorption of adsorbate in HNC. VOC vapor adsorption results show NMR chemical-shift changes with time, suggesting initial adsorption into mesopores, followed by diffusion into micropores. Schroeder's paradox is demonstrated by differences in observed shifts for adsorbed liquid vis-à-vis vapor phase in these HNC. These HNC show high CO 2 adsorption capacity, portending applications to carbon capture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Explicit modeling of pebble temperature in the porous-media model for pebble-bed reactors

In this study, we developed a multiscale model to include an explicit pebble-temperature model nested in the porous-media model for pebble-bed reactor applications. The multiscale solid-phase energy balance model, including the pebble surface energy balance equation and an explicit modeling of pebble temperature, can predict the macroscopic (pebble bed) and microscopic (pebble) temperature distributions under both steady-state and transient conditions. The proposed multiscale model is solved in a fully coupled manner using the Newton- Krylov method, and therefore iterations between the macroscopic (pebble-bed-scale) and microscopic (pebble- scale) model are avoided. Extensive code verifications, validation, and demonstrations have been performed for this newly developed model. By explicitly modeling pebble temperatures, this new model addresses a major deficiency of the basic porous-media model, which assumes homogeneous solid-phase temperature and is not appropriate for pebble-bed reactor design and safety analyses.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Revealing Mesoscale Ionomer Membrane Structure by Tender Resonant X-ray Scattering

Nafion, a perfluorosulfonic acid ionomer, has been well-studied for decades due to its key role as an ion-conductive membrane in electrochemical energy conversion and storage applications. When hydrated, this membrane phase separates into a complex hierarchical nanostructure with hydrophilic domains that facilitate ion transport. Hard X-ray scattering has been a powerful technique in understanding Nafion due to its capabilities in capturing the ionomer’s nanophase separated structure, which gives rise to contrast between polymer and water domains. More recently, resonant X-ray scattering, which tunes to elemental absorption edges to provide specificity on constituent elements, has been explored to highlight key interactions related to the sulfonic acid groups within its structure. Here, in this work, we study the Nafion nanostructure by combining hard X-ray scattering and tender resonant X-ray scattering (TReXS) at the sulfur K-edge to reveal a mesoscopic feature corresponding to a correlation length of approximately 40 nm that has been challenging to resolve with hard X-ray studies. Additionally, we study the effect of the dispersion solvent composition that plays a key role in the formation of this mesoscale feature. Notably, TReXS can attain high contrast to decipher this mesoscale morphology even for dry polymer membranes under a vacuum, which typically have reduced contrast for hard X-rays. We find that the correlation length of this mesoscale feature decreases with increasing water fraction in the dispersion, which is the opposite trend exhibited by the smaller intercrystalline feature in the same membranes. This study showcases the utility of TReXS to uncover multiscale morphological details in functional polymers that are not always revealed by other methods like hard X-ray scattering. We illustrate this with Nafion, which is a relevant ion-conducting polymer for electrochemical technologies.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Anomalous phase separation in a correlated electron system: Machine-learning–enabled large-scale kinetic Monte Carlo simulations

Significance Phase separation is crucial to the functionalities of many correlated electron materials with notable examples including colossal magnetoresistance in manganites and high- T c superconductivity in cuprates. However, the nonequilibrium phase-separation dynamics in such systems are poorly understood theoretically, partly because the required multiscale modeling is computationally very demanding. With the aid of machine-learning methods, we have achieved large-scale dynamical simulations in a representative correlated electron system. We observe an unusual relaxation process that is beyond the framework of classical phase-ordering theories. We also uncover a correlation-induced freezing behavior, which could be a generic feature of phase separation in correlated electron systems.

Zhang, Sheng↗