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DOE OSTI2022

Equation‐Free Surrogate Modeling of Geophysical Flows at the Intersection of Machine Learning and Data Assimilation

Abstract There is a growing interest in developing data‐driven reduced‐order models for atmospheric and oceanic flows that are trained on data obtained either from high‐resolution simulations or satellite observations. The data‐driven models are non‐intrusive in nature and offer significant computational savings compared to large‐scale numerical models. These low‐dimensional models can be utilized to reduce the computational burden of generating forecasts and estimating model uncertainty without losing the key information needed for data assimilation (DA) to produce accurate state estimates. This paper aims at exploring an equation‐free surrogate modeling approach at the intersection of machine learning and DA in Earth system modeling. With this objective, we introduce an end‐to‐end non‐intrusive reduced‐order modeling (NIROM) framework equipped with contributions in modal decomposition, time series prediction, optimal sensor placement, and sequential DA. Specifically, we use proper orthogonal decomposition (POD) to identify the dominant structures of the flow, and a long short‐term memory network to model the dynamics of the POD modes. The NIROM is integrated within the deterministic ensemble Kalman filter (DEnKF) to incorporate sparse and noisy observations at optimal sensor locations obtained through QR pivoting. The feasibility and the benefit of the proposed framework are demonstrated for the NOAA Optimum Interpolation Sea Surface Temperature (SST) V2 data set. Our results indicate that the NIROM is stable for long‐term forecasting and can model dynamics of SST with a reasonable level of accuracy. Furthermore, the prediction accuracy of the NIROM gets improved by almost one order of magnitude by the DEnKF algorithm.

Pawar, Suraj↗

NASA NTRS1986

Control of elastic robotic systems by nonlinear inversion and modal damping

Energy efficient, lightweight robot arms for space applications have considerable structural flexibility. For large and fast motions, both the nonlinear coupled dynamics and the elastic behavior of the robots must be considered in control system designs. This paper presents an approach to the control of a class of flexible robotic systems. A control law is derived which decouples the joint-angle motion from the flexible motion and asymptotically decomposes the elastic dynamics into two subsystems, representing the transverse vibrations of the elastic link in two orthogonal planes. This decomposition allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertainty in system parameters. Simulation results are presented to show that large, fast control of joint angles can be performed in spite of space vehicle motion and uncertainty in the payload.

Singh, S. N.↗

DOE OSTI2019

Intelligent load pattern modeling and denoising using improved variational mode decomposition for various calendar periods

This paper proposes a novel approach to identify the load patterns considering calendar impact and denoising process, which advances the state of art of load identification and load forecasting to a more flexible and adaptive extent by revealing the correlation between load profile and the substantial influence factors. With the rapid development and the promising application of energy intemet and grid modernization, the accurate load modeling and forecasting especially by load pattern modeling (LPM) have become more and more critical to observe and estimate load profile so as to optimize the operation efficiency of the power grid. Traditional methods mostly focus on the static LPM itself which are unable to account the non-linear and highly dynamic load fluctuations in order to balance the demand of the power grid during various calendar period (VCP) scheduling. In this paper, a load pattern modeling method for power grid considering the impact of typical calendar effects is proposed using a combination of improved variational mode decomposition (IVMD) and deep belief network (DBN) algorithm. Firstly, an index of load curve curvature (LCC) is proposed to improve the selection of value K in the conventional VMD algorithm. The value K of the intrinsic modality is determined by adopting LCC to better quantify the average instantaneous frequency of the modal decomposition of the VMD and to reduce the elevated stochasticity of k. Secondly, an optimization formulation is developed based on adaptive segmented loop decomposition of the typical correlation coefficient to suppress the edge effect in VMD decomposition, which would enable the reconstructed curve to incorporate the variabilities from the initial data. Finally, the IVMD and DBN algorithms are jointly implemented to optimize the accuracy of VCP load pattern modeling curve regression. Numerical examples have been performed with the results proving that the proposed method significantly outperforms the state-of-art in reducing the modeling error of VCP load curve, improving the overall forecasting accuracy, and reducing load dispatching cost.

deep belief network↗

NASA NTRS2015

A Structural Model Decomposition Framework for Hybrid Systems Diagnosis

Nowadays, a large number of practical systems in aerospace and industrial environments are best represented as hybrid systems that consist of discrete modes of behavior, each defined by a set of continuous dynamics. These hybrid dynamics make the on-line fault diagnosis task very challenging. In this work, we present a new modeling and diagnosis framework for hybrid systems. Models are composed from sets of user-defined components using a compositional modeling approach. Submodels for residual generation are then generated for a given mode, and reconfigured efficiently when the mode changes. Efficient reconfiguration is established by exploiting causality information within the hybrid system models. The submodels can then be used for fault diagnosis based on residual generation and analysis. We demonstrate the efficient causality reassignment, submodel reconfiguration, and residual generation for fault diagnosis using an electrical circuit case study.

structural model decomposition↗

DOE OSTI2015

Simulation of injector dynamics during steady inductive helicity injection current drive in the HIT-SI experiment

We present simulations of inductive helicity injection in the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI) device that treats the entire plasma volume in a single dynamic MHD model. A new fully 3D numerical tool, the PSI-center TETrahedral mesh code, was developed that provides the geometric flexibility required for this investigation. Implementation of a zero-β Hall MHD model using PSI-TET will be presented including formulation of a new self-consistent magnetic boundary condition for the wall of the HIT-SI device. Results from simulations of HIT-SI are presented focusing on injector dynamics that are investigated numerically for the first time. Asymmetries in the plasma loading between the two helicity injectors and progression of field reversal in each injector are observed. Analysis indicates cross-coupling between injectors through confinement volume structures. Injector impedance is found to scale with toroidal current at fixed density, consistent with experimental observation. Comparison to experimental data with an injector drive frequency of 14.5 kHz shows good agreement with magnetic diagnostics. Global mode structures from Bi-Orthogonal decomposition agree well with experimental data for the first four modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

Energetics and Dynamics of Dissociation of Deprotonated Peptides: Fragmentation of Angiotensin Analogs

We present a first study of the energetics and dynamics of dissociation of deprotonated peptides using time- and collision-energy resolved surface-induced dissociation (SID) experiments. SID of four model peptides: RVYIHPF, HVYIHPF, DRVYIHPF, and DHVYIHPF was studied using a specially designed Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR MS) configured for studying ion-surface collisions. Energy and entropy effects for the overall decomposition of the precursor ion were deduced by modeling the time- and collision energy-resolved survival curves using an RRKM based approach developed in our laboratory. The results were compared to the energetics and dynamics of dissociation of the corresponding protonated species. We demonstrate that acidic peptides are less stable in the negative mode because of the low threshold associated with the kinetically hindered loss of H2O from [M-H]- ions. Comparison between the two basic peptides indicates that the lower stability of the [M-H]- ion of RVYIHPF as compared to HVYIHPF towards fragmentation is attributed to the differences in fragmentation mechanisms. Specifically, threshold energy associated with losses of NH3 and NHCNH from RVYIHPF is lower than the barrier for backbone fragmentation that dominates gas-phase decomposition of HVYIHPF. The results provide a first quantitative comparison between the energetics and dynamics of dissociation of [M+H]+ and [M-H]- ions of acidic and basic peptides.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2016

Exploration of laser-driven electron-multirescattering dynamics in high-order harmonic generation

Multiple rescattering processes play an important role in high-order harmonic generation (HHG) in an intense laser field. However, the underlying multi-rescattering dynamics are still largely unexplored. Here we investigate the dynamical origin of multiple rescattering processes in HHG associated with the odd and even number of returning times of the electron to the parent ion. We perform fully ab initio quantum calculations and extend the empirical mode decomposition method to extract the individual multiple scattering contributions in HHG. We find that the tunneling ionization regime is responsible for the odd number times of rescattering and the corresponding short trajectories are dominant. On the other hand, the multiphoton ionization regime is responsible for the even number times of rescattering and the corresponding long trajectories are dominant. Moreover, we discover that the multiphoton- and tunneling-ionization regimes in multiple rescattering processes occur alternatively. Our results uncover the dynamical origin of multiple rescattering processes in HHG for the first time. As a result, it also provides new insight regarding the control of the multiple rescattering processes for the optimal generation of ultrabroad band supercontinuum spectra and the production of single ultrashort attosecond laser pulse.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2026

Local reduced-order modeling for electrostatic plasmas by physics-informed solution manifold decomposition

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.

Electrostatic plasmas↗

NASA NTRS2015

Integrated Physics-based Modeling and Experiments for Improved Prediction of Combustion Dynamics in Low-Emission Systems

Concurrent simulation and experiment was undertaken to assess the ability of a hybrid RANS-LES model to predict combustion dynamics in a single-element lean direct-inject (LDI) combustor showing self-excited instabilities. High frequency pressure modes produced by Fourier and modal decomposition analysis were compared quantitatively, and trends with equivalence ratio and inlet temperature were compared qualitatively. High frequency OH PLIF and PIV measurements were also taken. Submodels for chemical kinetics and primary and secondary atomization were also tested against the measured behavior. For a point-wise comparison, the amplitudes matched within a factor of two. The dependence on equivalence ratio was matched. Preliminary results from simulation using an 18-reaction kinetics model indicated instability amplitudes closer to measurement. Analysis of the simulations suggested a band of modes around 1400 Hz were due to a vortex bubble breakdown and a band of modes around 6 kHz were due to a precessing vortex core hydrodynamic instability. The primary needs are directly coupled and validated ab initio models of the atomizer free surface flow and the primary atomization processes, and more detailed study of the coupling between the 3D swirling flow and the local thermoacoustics in the diverging venturi section.

combustion↗

NASA NTRS2012

Flexible Launch Vehicle Stability Analysis Using Steady and Unsteady Computational Fluid Dynamics

Launch vehicles frequently experience a reduced stability margin through the transonic Mach number range. This reduced stability margin can be caused by the aerodynamic undamping one of the lower-frequency flexible or rigid body modes. Analysis of the behavior of a flexible vehicle is routinely performed with quasi-steady aerodynamic line loads derived from steady rigid aerodynamics. However, a quasi-steady aeroelastic stability analysis can be unconservative at the critical Mach numbers, where experiment or unsteady computational aeroelastic analysis show a reduced or even negative aerodynamic damping.Amethod of enhancing the quasi-steady aeroelastic stability analysis of a launch vehicle with unsteady aerodynamics is developed that uses unsteady computational fluid dynamics to compute the response of selected lower-frequency modes. The response is contained in a time history of the vehicle line loads. A proper orthogonal decomposition of the unsteady aerodynamic line-load response is used to reduce the scale of data volume and system identification is used to derive the aerodynamic stiffness, damping, and mass matrices. The results are compared with the damping and frequency computed from unsteady computational aeroelasticity and from a quasi-steady analysis. The results show that incorporating unsteady aerodynamics in this way brings the enhanced quasi-steady aeroelastic stability analysis into close agreement with the unsteady computational aeroelastic results.

Bartels, Robert E.↗

DOE OSTI2014

Multi-layer Potfit: An accurate potential representation for efficient high-dimensional quantum dynamics

The multi-layer multi-configuration time-dependent Hartree method (ML-MCTDH) is a highly efficient scheme for studying the dynamics of high-dimensional quantum systems. Its use is greatly facilitated if the Hamiltonian of the system possesses a particular structure through which the multi-dimensional matrix elements can be computed efficiently. In the field of quantum molecular dynamics, the effective interaction between the atoms is often described by potential energy surfaces (PES), and it is necessary to fit such PES into the desired structure. For high-dimensional systems, the current approaches for this fitting process either lead to fits that are too large to be practical, or their accuracy is difficult to predict and control. This article introduces multi-layer Potfit (MLPF), a novel fitting scheme that results in a PES representation in the hierarchical tensor (HT) format. The scheme is based on the hierarchical singular value decomposition, which can yield a near-optimal fit and give strict bounds for the obtained accuracy. Here, a recursive scheme for using the HT-format PES within ML-MCTDH is derived, and theoretical estimates as well as a computational example show that the use of MLPF can reduce the numerical effort for ML-MCTDH by orders of magnitude, compared to the traditionally used POTFIT representation of the PES. Moreover, it is shown that MLPF is especially beneficial for high-accuracy PES representations, and it turns out that MLPF leads to computational savings already for comparatively small systems with just four modes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

A generalized framework for reduced-order modeling of a wind turbine wake

A reduced-order model for a wind turbine wake is sought from large eddy simulation data. Fluctuating velocity fields are combined in the correlation tensor to form the kernel of the proper orthogonal decomposition (POD). Proper orthogonal decomposition modes resulting from the decomposition represent the spatially coherent turbulence structures in the wind turbine wake; eigenvalues delineate the relative amount of turbulent kinetic energy associated with each mode. Back-projecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reduced-order model of the wind turbine wake (wakeROM) is defined through a series of polynomial parameters that quantify mode interaction and the evolution of each POD mode coefficients. The resulting system of ordinary differential equations models the wind turbine wake composed only of the large-scale turbulent dynamics identified by the POD. Tikhonov regularization is used to recalibrate the dynamical system by adding additional constraints to the minimization seeking polynomial parameters, reducing error in the modeled mode coefficients. The wakeROM is periodically reinitialized with new initial conditions found by relating the incoming turbulent velocity to the POD mode coefficients through a series of open-loop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%, quantified through the normalized root-mean-square error. Furthermore, a high-level view of the modeling approach is provided as a platform to discuss promising research directions, alternate processes that could benefit stability and efficiency, and desired extensions of the wakeROM.

17 WIND ENERGY↗

DOE OSTI2025

Voltage cycling as a dynamic operation mode for high temperature electrolysis solid oxide cells

Solid Oxide Electrolysis Cells (SOECs) have emerged as a promising technology for the efficient production of H2 via high-temperature electrolysis. However, power input from dynamic energy sources remains a significant challenge for their long-term stability. It is important to analyze the tolerance of cells under dynamic operation conditions. This study focuses on evaluating the impact of voltage cycling on the performance and durability of electrode-supported SOECs. We explore the operational limits and degradation mechanisms of SOECs subjected to various voltage conditions and find that the cells have high tolerance for dynamic voltage. Voltage cycling between 1.3 V and 1.5 V for 9000 cycles does not damage the cell. Conversely, cycling to higher voltages (≥1.7 V) results in accelerated degradation. Advanced characterization is used to screen for various degradation modes post operation. Within the oxygen electrode, XRD and STEM EDS find compositional and phase evolution in all voltage cycled samples including increased decomposition of the air electrode resulting in cation migration. Microstructural analysis of the fuel electrode from nano-CT data shows minimal change throughout the sample set and no evidence of Ni migration, indicating the fuel electrode is stable and not impacted by cycling to higher voltages within the timeframe studied.

Zhu, Zhikuan↗

DOE OSTI2021

Discrete Empirical Interpolation Method Based Dynamic Load Model Reduction

Dynamic load models add significant complexity to bulk power system time-domain simulations. The complexity is due to the large number of ordinary differential equations (ODEs) introduced by the dynamic load components such as induction motors. It is challenging to derive reduced-order models (ROMs) for dynamic loads due to the nonlinear functions in their governing equations. This paper applies the discrete empirical interpolation method enhanced proper orthogonal decomposition (DEIM-POD) to approximate the full dynamic load model with the ROM that minimizes the projection error of the nonlinear functions in dynamic load ODEs onto their dominant modes. This approach only requires evaluation of nonlinear functions at selected observation points. The observation points selected by DEIM also provide information for screening critical load buses where dynamic load model parameters contribute the most to the accuracy of ROM across multiple contingencies. The proposed approach is validated on IEEE 9-bus, WECC 179-bus and 2384-bus Polish systems.

bulk power system↗

DOE OSTI2024

Geometry-aware training of factorized layers in tensor Tucker format

Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during train and inference of large networks. Given its easy implementation and flexibility, one promising approach is layer factorization, which reshapes weight tensors into a matrix format and parameterizes it as the product of two rank-r matrices. However, this family of approaches often requires an initial full-model warm-up phase, prior knowledge of a feasible rank, and it is sensitive to parameter initialization.In this work, we introduce a novel approach to train the factors of a Tucker decomposition of the weight tensors. Our training proposal proves to be optimal in locally approximating the original unfactorized dynamics and stable for the initialization. Furthermore, the rank of each mode is dynamically updated during training.We provide a theoretical analysis of the algorithm, showing convergence, approximation and local descent guarantees. The method's performance is further illustrated through a variety of experiments, showing remarkable training compression rates and comparable or even better performance than the full baseline and alternative layer factorization strategies.

Zangrando, Emanuele [Gran Sasso Science Institute ↗

DOE OSTI2017

Fourier imaging of non-linear structure formation

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Parametric reduced-order modeling for component-oriented treatment and localized nonlinear feature inclusion

Abstract We propose coupling a physics-based reduction framework with a suited response decomposition technique to derive a component-oriented reduction (COR) approach, which is suitable for assembly systems featuring localized nonlinearities. Dependencies on influencing parameters are injected into the reduced-order model (ROM), thus ensuring robustness and validity over a domain of parametric inputs, while capturing nonlinear effects. The implemented approach employs individual component modes to capture localized features while additionally relying on reduced modes of a global nature to approximate the system’s dynamics accurately. The global modes are derived from a linear monolithic system, defined as a result of a coordinate separation scheme, which permits the proposed COR-ROM to naturally couple the response between linear and nonlinear subdomains. The derived low-order representation utilizes a proper orthogonal decomposition projection and is additionally reinforced with the inclusion of a hyper-reduction technique to capture the underlying high-fidelity model response while providing accelerated computations. The resulting approach is exemplified in the synthetic case studies of a four-story shear frame with multiple nonlinear regions driven by hysteresis and a large-scale kingpin connection featuring plasticity.

Vlachas, Konstantinos (ORCID:000000029124219X)↗

DOE OSTI2020

Model-Agnostic Algorithm for Real-Time Attack Identification in Power Grid using Koopman Modes

Malicious activities on measurements from sensors like Phasor Measurement Units (PMUs) can mislead the control center operator into taking wrong control actions resulting in disruption of operation, financial losses, and equipment damage. In particular, false data attacks initiated during power systems transients caused due to abrupt changes in load and generation can fool the conventional model-based detection methods relying on thresholds comparison to trigger an anomaly. In this paper, we propose a Koopman mode decomposition (KMD) based algorithm to detect and identify false data attacks in real-time. The Koopman modes (KMs) are capable of capturing the nonlinear modes of oscillation in the transient dynamics of the power networks and reveal the spatial embedding of both natural and anomalous modes of oscillations in the sensor measurements. The Koopman-based spatio-temporal nonlinear modal analysis is used to filter out the false data injected by an attacker. The performance of the algorithm is illustrated on the IEEE 68-bus test system using synthetic attack scenarios generated on GridSTAGE, a recently developed multivariate spatio-temporal data generation framework for simulation of adversarial scenarios in cyber-physical power systems.

Nandanoori, Sai Pushpak↗