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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 OSTI2022

A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Enhanced accuracy through ensembling of randomly initialized auto-regressive models for dynamical systems

Computational mechanics simulations using traditional finite element methods (FEM) require prohibitively expensive computational resources for real-time engineering applications, design optimization, and digital twin implementations. While machine learning (ML) surrogate models offer significant computational speedups, autoregressive ML models for time-dependent mechanical systems suffer from error accumulation that compromises long-term prediction reliability - a critical concern for engineering applications where accuracy over extended time horizons is essential for safety and performance assessments. Here, we propose a deep ensemble framework specifically designed to address this challenge in computational mechanics applications, where multiple ML surrogate models with random weight initializations are trained in parallel and their predictions aggregated during inference. This approach leverages statistical diversity to maximize information gain from a fixed set of training data and to mitigate error propagation, while maintaining the computational efficiency that makes ML surrogates attractive for engineering practice. We validate the framework on three representative problems spanning critical areas of computational mechanics: stress field evolution in heterogeneous microstructures under complex loading (relevant to advanced materials design and composite analysis), planetary-scale shallow water dynamics (applicable to environmental and geotechnical engineering), and Gray-Scott reaction-diffusion systems (relevant to mass transport and chemical process engineering). Across all test cases, the ensemble approach demonstrates consistent error reduction of 15-33% compared to individual models. The codes for this work are available on GitHub (https://github.com/Graham-Brady-Research-Group/AutoregressiveEnsemble_SpatioTemporal_Evolution).

autoregressive prediction↗
DOE OSTI2022

Variational encoder geostatistical analysis (VEGAS) with an application to large scale riverine bathymetry

Estimation of riverbed profiles, also known as bathymetry, plays a vital role in many applications, such as safe and efficient inland navigation, prediction of bank erosion, land subsidence, and flood risk management. The high cost and complex logistics of direct bathymetry surveys, i.e, depth imaging, have encouraged the use of indirect measurements such as surface flow velocities. However, estimating high-resolution bathymetry from indirect measurements is an inverse problem that can be computationally challenging. Here, we propose a reduced-order model (ROM) based approach that utilizes a variational autoencoder (VAE), a type of deep neural network with a narrow layer in the middle, to compress bathymetry and flow velocity information and accelerate bathymetry inverse problems from flow velocity measurements. In our application, the shallow-water equations (SWE) with appropriate boundary conditions (BCs), e.g., the discharge and/or the free surface elevation, constitute the forward problem, to predict flow velocity. Then, ROMs of the SWEs are constructed on a nonlinear manifold of low dimensionality through a variational encoder and the bathymetry inversion problem is derived on the low-dimensional latent space in a Hierarchical Bayesian setting. Further, the reformulation allows variational inference with a small number (e.g., $\mathscr{O}$ (100) of ROM runs and efficient uncertainty quantification. We have tested our inversion approach on a one-mile reach of the Savannah River, GA, USA. Once the neural network is trained (offline stage), the proposed technique can perform the inversion operation orders of magnitude faster than traditional inversion methods that are commonly based on linear projections, such as principal component analysis (PCA), or the principal component geostatistical approach (PCGA). Furthermore, tests show that the algorithm can estimate the bathymetry with good accuracy even with sparse flow velocity measurements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Operator inference with roll outs for learning reduced models from scarce and low-quality data

Data-driven modeling has become a key building block in computational science and engineering. However, data that are available in science and engineering are typically scarce, often polluted with noise and affected by measurement errors and other perturbations, which makes learning the dynamics of systems challenging. Here, in this work, we propose to combine data-driven modeling via operator inference with the dynamic training via roll outs of neural ordinary differential equations. Operator inference with roll outs inherits interpretability, scalability, and structure preservation of traditional operator inference while leveraging the dynamic training via roll outs over multiple time steps to increase stability and robustness for learning from low-quality and noisy data. Numerical experiments with data describing shallow water waves and surface quasi-geostrophic dynamics demonstrate that operator inference with roll outs provides predictive models from training trajectories even if data are sampled sparsely in time and polluted with noise of up to 10%.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Sea cucumber ( Holothuria glaberrima ) intestinal microbiome dataset from Puerto Rico, generated by shotgun sequencing

The sea cucumber (H. glaberrima) is a species found in the shallow waters near coral reefs and seagrass beds in Puerto Rico. To characterize the microbial taxonomic composition and functional profiles present in the sea cucumber, total DNA was obtained from their intestinal system, fosmid libraries constructed, and subsequent sequencing was performed. The diversity profile displayed that the most predominant domain was Bacteria (76.56 %), followed by Viruses (23.24 %) and Archaea (0.04 %). Within the 11 phyla identified, the most abundant was Proteobacteria (73.16 %), followed by Terrabacteria group (3.20 %) and Fibrobacterota, Chlorobiota, Bacteroidota (FCB) superphylum (1.02 %). The most abundant species were Porvidencia rettgeri (21.77 %), Pseudomonas stutzeri (14.78 %), and Alcaligenes faecalis (5.00 %). The functional profile revealed that the most abundant functions are related to transporters, MISC (miscellaneous information systems), organic nitrogen, energy, and carbon utilization. The data collected in this project on the diversity and functional profiles of the intestinal system of the H. glaberrima provided a detailed view of its microbial ecology. These findings may motivate comparative studies aimed at understanding the role of the microbiome in intestinal regeneration.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Analytical population dynamics underlying harmful algal blooms triggered by prey avoidance

A modified version of the NPZD ecosystem model is used to analytically examine the effects of predation avoidance, a possible mechanism for triggering harmful algal blooms (HAB). To resolve HAB development caused by predation avoidance, an additional phytoplankton functional group is considered, one that has slower nutrient uptake and better predation avoidance characteristics than the non-harmful phytoplankton group used in traditional NPZD models. Because the two phytoplankton groups (one non-harmful and one HAB) compete for only one resource within the same system, steady state (equilibrium) conditions cannot occur without the presence of zooplankton; only the non-harmful phytoplankton group, which defeats the HAB group in the resource competition, can survive in the equilibrium. The presence of sufficient zooplankton effectively acts to replenish the nutrient pool by consuming the non-harmful phytoplankton. When this occurs, two equilibrium states are found: one with both phytoplankton groups coexisting, and one that only includes the HAB group. Further, the condition required for equilibrium is that the total nitrogen within the system should be larger than a threshold determined by model coefficients. The threshold and feasibility of the equilibrium are sensitive to the relative HAB predation avoidance coefficient. If the coefficient is larger than the ratio of net growth rates between the HAB and non-harmful phytoplankton group, the threshold becomes infinite, and an equilibrium is not feasible. The time scale for the system to reach an equilibrium state that includes a HAB group is determined asymptotically. The dependence of a threshold condition as a controlling factor may explain the regime shift of dominant species causing HABs. The ecosystem model is fully implemented into the Regional Ocean Modeling System and applied to an idealized coastal embayment (with depths and geometry taken from San Francisco Bay) to show numerically the dominance of prey avoidance dynamics in a natural shallow water environment that includes advection and diffusion. The analytical results improve strategies for HAB modeling and provide guidance for setting model coefficients necessary to resolve a HAB event.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Extremely rapid, Lagrangian modeling of 2D flooding: A rivulet-based approach

Estimates of potential flood inundation areas and depths are critical to informing the preparedness, response, and investment decisions of many government agencies and private sector organizations, especially under a changing climate. The standard modeling approaches, however, are often either computationally intensive or constrained in their accuracy or applicability. A novel, rivulet-based, 2D model of pluvial flooding is described in this article that is 10,000 to 10 million times less computationally complex than the full solution of the shallow water equations, yet achieves inundation area hit rates of between 0.8 and 0.9 and relative absolute mean errors of 10%-20% across a wide range of flow depths. This combination of accuracy and efficiency will enable real-time depth estimates during flood events, detailed sensitivity analyses, and the generation of large ensembles to support broad uncertainty analyses.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A weighted Shifted Boundary Method for free surface flow problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods and was recently introduced for the Poisson, linear advection/diffusion, Stokes, Navier-Stokes, acoustics, and shallow-water equations. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we extend the SBM to the simulation of incompressible Navier-Stokes flows with moving free-surfaces, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach prevents spurious pressure oscillations in time, which would otherwise be produced if the total active fluid volume were to change abruptly over a time step. In fact, the proposed weighted SBM method induces small mass (i.e., volume) conservation errors, which converge quadratically in the case of piecewise-linear finite element interpolations, as the grid is refined. Finally, we present an extensive set of two- and three-dimensional tests to demonstrate the robustness and accuracy of the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations

Data-driven discovery of differential equations has been an emerging research topic. We propose a novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers. The subsampling technique is used for improving the accuracy of the Bayesian learning algorithm. It has two parameters: subsampling size and the number of subsamples. When the subsampling size increases with fixed total sample size, the accuracy of our algorithm goes up and then down. When the number of subsamples increases, the accuracy of our algorithm keeps going up. We demonstrate how to use our algorithm step by step and compare our algorithm with threshold sparse Bayesian regression (TSBR) for the discovery of differential equations. We show that our algorithm produces better results. We also discuss the merits of discovering differential equations from data and demonstrate how to discover models with random initial and boundary condition as well as models with bifurcations. The numerical examples are: (1) predator-prey model with noise, (2) shallow water equations with outliers, (3) heat diffusion with random initial and boundary condition, and (4) fish-harvesting problem with bifurcations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements

Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements, standard finite element discretisations of the vector transport equation typically have a low order of spatial accuracy. This paper describes two schemes that improve the accuracy of transporting such vector-valued fields on two-dimensional curved manifolds. The first scheme that is presented reconstructs the transported field in a higher-order function space, where the transport equation is then solved. The second scheme applies a mixed finite element formulation to the vector transport equation, simultaneously solving for the transported field and its vorticity. In this work, an approach to stabilising this mixed vector-vorticity formulation is presented that uses a Streamline Upwind Petrov-Galerkin (SUPG) method. These schemes are then demonstrated, along with their accuracy properties, through some numerical tests. Two new test cases are used to assess the transport of vector-valued fields on curved manifolds, solving the vector transport equation in isolation. The improvement of the schemes is also shown through two standard test cases for rotating shallow-water models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Manipulation of self-organized multi-vortical states in active magnetic roller suspensions

Ensembles of active magnetic colloids demonstrate complex collective behavior and self-organization when driven out of equilibrium by external magnetic fields. The interplay between magnetic and hydrodynamic interactions often result in spontaneous self-assembly and the emergence of localized vortices in ensembles of ferromagnetic rollers. We report experimental and computational study of the self-organized multi-vortical state in ensembles of magnetic rollers under the imposed external confining potential realized by patterned substrates. We explore the behavior of the system on a substrate patterned with shallow wells ordered in a lattice with square symmetry and lattice spacing smaller than the wells’ diameter. Here we demonstrate, that ensembles of active magnetic rollers evolve in response to changes in the geometry of the confining lattice from a globally correlated state characterized by anti-ferromagnetic vortex ordering to a state with rapidly changing particle flows and self-organized vortical states with a lattice constant larger than one of the confining pattern. Our experimental observations are accompanied by numerical simulations based on phenomenological coarse grained particle dynamics coupled to Navier–Stokes hydrodynamics in shallow water approximation. The reported results provide insights into the collective behavior of active magnetic rollers under confinement and suggest strategies for the manipulation of collective dynamic states in active magnetic liquids.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Comparing numerical accuracy and stability for different horizontal discretizations in MPAS-Ocean

This manuscript investigates the effectiveness of two possible horizontal discretizations for the global ocean model MPAS-Ocean, both applied to Spherical Centroidal Voronoi Tessellations (SCVTs). The first discretization is TRiSK, a C-grid, finite-volume method, that possesses many desirable mimetic properties, but has a low order accuracy. The second discretization was introduced for the first time by Peixoto (2016), and consists of modifications to the TRiSK scheme designed to achieve at least first-order accuracy in the L ∞ norm, with the loss of some of the mimetic properties. Tests on shallow-water and primitive-equation models show that the scheme due to Peixoto is indeed more accurate, but presents stability issues with respect to TRiSK. Here, TRiSK is indeed found to be often more stable in time and more robust with respect to errors in the geometric properties of the grid.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation

Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a low-dimensional emulation framework for systems that may be intrinsically high-dimensional. This is accomplished by utilizing a construction algorithm that is purely data-driven. It is no surprise, therefore, that the algorithmic advances of machine learning have led to non-intrusive ROMs with greater accuracy and computational gains. However, in bypassing the utilization of an equation-based evolution, it is often seen that the interpretability of the ROM framework suffers. This becomes more problematic when black-box deep learning methods are used which are notorious for lacking robustness outside the physical regime of the observed data. In this article, we propose the use of a novel latent-space interpolation algorithm based on Gaussian process regression. Notably, this reduced-order evolution of the system is parameterized by control parameters to allow for interpolation in space. The use of this procedure also allows for a continuous interpretation of time which allows for temporal interpolation. The latter aspect provides information, with quantified uncertainty, about full-state evolution at a finer resolution than that utilized for training the ROMs. This research assesses the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Evaluating the effect of meso/submesoscale current–wave interactions on wave energy resource characterization at northeast U.S. coast

Wave energy is a promising renewable resource, but accurate assessment is difficult in regions with strong currents due to wave–current interactions (WCI). Here, this study develops a two-way coupled WCI model within the Coupled Ocean Atmosphere Wave Sediment Transport (COAWST) framework at 2 km resolution to improve wave energy characterization along the northeastern U.S. coast, including the Mid-Atlantic Bight and Gulf of Maine. The model integrates WaveWatchIII (WWIII) and the Regional Ocean Modeling System (ROMS) to enhance wave hindcasting by accounting for Doppler-shift, refraction, and nonlinear energy exchanges. Validation against buoy and satellite observations confirms model accuracy. Analysis shows that Doppler-shifting can alter wave power density by over 20%, while strong current gradients and shear distort wave crests via focusing/defocusing and stretching/squeezing, modifying wave direction and frequency. These processes together can induce wave power fluctuations of up to 40% on synoptic scales. Applying a 2.5 MW Ocean Energy Converter power matrix shows that WCI may change harvested energy by up to 100% in shallow-waters and 60% in deep-waters. These results underscore the importance of incorporating nonlinear WCI for reliable wave climate predictions and resource assessments in energetic coastal regions.

doppler-shift↗
DOE OSTI2020

Non-autoregressive time-series methods for stable parametric reduced-order models

Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant interest in the use of techniques borrowed from machine learning to reduce the computational expense and/or improve the accuracy of predictions for these systems. These rely on the identification of a basis that reduces the dimensionality of the problem and the subsequent use of time series and sequential learning methods to forecast the evolution of the reduced state. Often, however, machine-learned predictions after reduced-basis projection are plagued by issues of stability stemming from incomplete capture of multiscale processes as well as due to error growth for long forecast durations. To address these issues, we have developed a non-autoregressive time series approach for predicting linear reduced-basis time histories of forward models. In particular, we demonstrate that non-autoregressive counterparts of sequential learning methods such as long short-term memory (LSTM) considerably improve the stability of machine-learned reduced-order models. Further, we evaluate our approach on the inviscid shallow water equations and show that a non-autoregressive variant of the standard LSTM approach that is bidirectional in the principal component directions obtains the best accuracy for recreating the nonlinear dynamics of partial observations. Moreover-and critical for many applications of these surrogates-inference times are reduced by three orders of magnitude using our approach, compared with both the equation-based Galerkin projection method and the standard LSTM approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD-Galerkin technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Potential vorticity conservation for plasma turbulence in an inhomogeneous magnetic field: Theory and implications

The concept and theory of potential vorticity in drift wave turbulence are extended to the case of an inhomogeneous magnetic field. A one-field magnetic potential vorticity conserving equation is derived via the use of conservative gyrokinetics. The similarity between the corresponding systems for drift wave turbulence and shallow water theory is discussed in detail. Zonal flow physics in an inhomogeneous magnetic field is discussed. In particular, a Charney–Drazin type nonacceleration theorem is derived from the novel system, which conserves magnetic potential vorticity. Extensions of the turbulent equipartition theory to the transport of magnetic potential vorticity are proposed.

Physics↗