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At least 55 records · Page 3

Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

Abstract Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $$10^3{\times }$$ 10 3 × in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs. The domain of applications include both parabolic and hyperbolic PDEs, regardless of the dimension of full-order models (FOMs).

42 ENGINEERING↗

Optimization to Generate Equations of State for Hydrogen Production

On a high level, the larger project in question, HydroGEN, aims to develop software used for finding equations of state (EOS) to optimize catalyst configuration for H 2 production through water splitting. In particular, this summer project focused on solving the nonlinear equations used in fitting the equations. This problem involved using Python to solve a linear system with nonlinear constraints. In order for this to be achieved, Pyomo was used to build a model and the solver Ipopt, interior point optimizer, was used. Pyomo is a Python-based language developed at Sandia; it is an optimization modeling language. Rather than solving the entire problem at once, a toy problem was created, simplifying the problem down to the most important focus. This problem had a known solution, comparable to the calculated solution to assess accuracy and as progress was made towards finding solutions, complexity was gradually added to the problem. After building and solving the toy problem, it was found that it gave reasonably accurate solutions, better compared to the two existing solvers previously used with this project in terms of functionality. The solver is now ready for implementation into the project’s main software.

08 HYDROGEN↗

Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations

Here, we demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We conduct experiments on 38 cases from the PGLib-OPF library, showing that the LNC strengthen the SOC and CDF relaxations in 100% of the test cases, with average and maximum differences in the optimality gaps of 6.2% and 17.5% respectively. The NF relaxation is strengthened in 46.2% of test cases, with average and maximum differences in the optimality gaps of 1.3% and 17.3% respectively. We also study the trade-off between relaxation quality and solve time, demonstrating that the strengthened CDF relaxation outperforms the strengthened SOC formulation in terms of runtime and number of iterations needed, while the strengthened NF formulation is the most scalable with the lowest relaxation quality improvement due to these LNC.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Gyrokinetic Simulation of Tokamak Fusion Plasmas

The final technical report for project DE‐FG02‐08ER54954 “Gyrokinetic Simulation of Tokamak Fusion Plasmas”. This report covers the entire period of the sponsored project. This grant supported in part the salary, travel, and research supplies for the principal investigator Scott E. Parker, graduate research associate Stefan Tirkas, who is a Ph.D. graduate student in the Physics Department. Postdoctoral Scholar Dr. Neeraj Kumar is also collaborating on this project. The main goals of the project are to investigate the nonlinear saturation of electron scale turbulence using gyrokinetic theory and simulation and to investigate impurity transport in the edge pedestal region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

OC6 phase I: Improvements to the OpenFAST predictions of nonlinear, low-frequency responses of a floating offshore wind turbine platform

We report in the OC5 and OC6 projects, the authors observed a persistent underprediction of the nonlinear, low-frequency responses of an offshore wind semisubmersible with many mid-fidelity engineering models, including the OpenFAST tool developed by the National Renewable Energy Laboratory. Both the low-frequency wave excitation in surge and pitch and the resulting resonance motions were severely underpredicted. In response, we developed several modifications to the OpenFAST model from the OC5/6 projects to improve the predictions of the low-frequency wave loads and responses. All modifications are in the modeling of the viscous drag forces. Efforts were made to provide physical justifications to the changes and to limit the number of additional parameters requiring tuning, so that the modified model can be applied to other floating wind systems. With the proposed modifications, the predictions of the low-frequency surge and pitch wave loads on a fixed floater and the resonance responses of a floating structure are both significantly improved with a single set of model coefficients, which leads to good agreement with the measurements from the OC6 wave-basin experimental campaign.

17 WIND ENERGY↗

Development of an advanced ultrasonic phased array for the characterization of thick, reinforced concrete components (Final Scientific/Technical Report)

There are no nondestructive evaluation (NDE) tools capable of characterizing microscale damage throughout the thickness of concrete components, due to the multiphase, heterogeneous and multiscale nature of concrete. Ultrasound is only scattered by features at the same length scale, or smaller, than the wavelength of a wave’s dominant frequency. Successful imaging of microscale damage using ultrasound requires that the ultrasonic wavelength be on the order of a few millimeters (or smaller), yet the heterogeneous microstructure of concrete, with its fine and coarse aggregates, is on this same (and higher) micrometer/millimeter length scale, causing excessive ultrasonic wave scattering even in “good” concrete. The proposed solution applies non-collinear wave mixing to spatially image microscale damage, while still maintaining penetration through thick concrete components. This microscale imaging is possible by combining nonlinear wave mixing, with advanced phased array hardware and software to develop a breakthrough tool that will bring revolutionary changes in NDE of concrete infrastructure in terms of image resolution and depth of penetration. This work uses non-collinear wave mixing which exploits the physics that material nonlinearities such as microscale damage, cause interactions between two intersecting ultrasonic waves due to cross-mixing, which can lead to the generation of a third wave with a frequency and wave number of the sum or difference of the incident waves. The concrete material volume at this mixing point is characterized/imaged. This project delivered a single-sided nonlinear ultrasonic phased array imaging device, that can image microscale damage (microcracks of 100 micrometers) through a 0.5 m thick concrete component and assessed the commercial feasibility of such arrays for improved crack detection.

42 ENGINEERING↗

Developing nonlinear laser-plasma instability models for high-fidelity, multi-physics simulation capability for ICF/HED (IC Report) [Slides]

Modeling nonlinear effects of laser plasma instabilities (LPI) is critically important for ICF/HED experiments. Our project has the following goals: • Develop physics-based nonlinear LPI models using PIC simulations • Couple the nonlinear LPI effects to macroscopic modeling of ICF/HED exp. through laser ray-tracing (LRT).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Applying cumulative effects to strategically advance large-scale ecosystem restoration

Programs restoring large terrestrial-aquatic ecosystems are expected to increase in area and number over the next decade. Factors ensuring long-term effectiveness at the program scale differ from those at the individual restoration project scale, necessitating a new synthesis. Here we contextualize hydrological, geomorphological, and biological effects of large-scale ecosystem restoration activities within a cumulative-effects paradigm. Evidence of eight modes of cumulative effects benefiting species and ecosystems was elucidated by reviewing restoration efforts in the greater Florida Everglades, Gulf Coast, lower Columbia River and estuary, Puget Sound estuary, Missouri River, northeastern coastal states, San Francisco Bay and Sacramento Delta. Additive and nonlinear cumulative effects of interacting restoration projects propagated across landscape and regional geographic scales, and throughout trophic levels, affecting population structures. Applying a cumulative-effects paradigm to planning, implementing, and evaluating large-scale restoration will avoid countervailing effects and capitalize on positive feedback, advancing evidence-based programs to recover priority species and ecosystems.

54 ENVIRONMENTAL SCIENCES↗

Nonlinear X-ray Optics

Novel X-ray free-electron lasers (XFELs) are capable of producing radiation with unprecedented properties. Specifically, their ultrashort coherent X-ray pulses can generate extreme peak intensities where ordinary rules of light-matter interaction may no longer apply, and nonlinear processes start to become important. XFELs have made it possible to observe some of the most important coherent non-sequential nonlinearities, including X-ray-optical sum frequency generation (SFG), X-ray second harmonic generation (XSHG), two-photon absorption (TPA) and nonlinear two-photon Compton scattering (2PCS). In particular, the 2PCS experiment has led to unexpected results, namely the observation of a substantial anomalous red shift in the energy of photons generated by nonlinear two-photon X-ray Compton scattering in beryllium. The energy shift is in addition to the predicted nonlinear Compton shift and was neither expected from extrapolations from linear X-ray interactions nor from nonlinear effects at optical wavelengths. Our results suggest a novel nonlinear scattering mechanism that can only be observed at high fields at X-ray wavelengths, where the photon energy is a significant fraction of the electron rest mass (and thus a significant momentum transfer to the electron occurs during the scattering) and where the interaction is not dominated by the quiver motion of the electron in the field (ponderomotive potential) as is usually the case at longer (optical) wavelengths. The goal of this research project was the investigation of fundamental nonlinear X-ray-matter interactions. As these processes are typically weak, part of this research is the exploration of more efficient nonlinear X-ray processes by studying novel mechanisms including solid-state effects, the assistance of optical radiation and novel phase-matching techniques. These experiments require extremely large X-ray field strengths, such as produced by XFELs. Nonlinear X-ray effects can lead to important applications in many research fields. For example, it could lead to instantaneous plasma diagnostics for materials in extreme conditions, as a method for combining atomic-scale structural sensitivity with chemical specificity, or as a probe of electron dynamics in solids on the attosecond (1 as = 10 -18 s) time- and Ångstrom (10 -10 m) length scales. In addition, a detailed understanding of nonlinear X-ray matter interactions is crucial for understanding and extending the limits of structural determination at high intensity such as in serial femto-crystallography. The results could have a profound impact on advanced XFEL light sources such as the LCLS-II.

47 OTHER INSTRUMENTATION↗

IC Project: w19_hossfault “Modelling of stick-slip behavior in sheared granular fault gouge & nonlinear elasticity behavior in cracked solid”

Low frequency earthquakes, non-volcanic tremor, and acoustic emissions are examples of weak seismic signals that may help detect major seismic events, i.e., earthquakes. In a laboratory setting, in which stick-slip events are simulated, acoustic emissions are detected far from the stick-slip events. In both, field and laboratory scale cases, the acoustic emission signals are sourced or detected in a volume remote from the volume that spawns the earthquake. Therefore, it is relevant to establish the causal relationship between signals detected on passive, remote monitors and the dynamics of the elastic structures that launch important seismic events. The work conducted under this IC allocation allowed us to utilize a numerical model that let us follow this causality, i.e., examine and connect the dynamics in a granular system (fault gouge), to signals detected on passive remote monitors. It was demonstrated that stress chains are key in the dynamics of granular systems and that their evolution is the source of the acoustic emission.

58 GEOSCIENCES↗

Advanced Laboratory and Field Arrays (ALFA)/Lab Collaboration Project (LCP) for Marine Energy (Final Scientific/Technical Report)

The objective of the Advanced Laboratory and Field Arrays (ALFA) project was to reduce the Levelized Cost of Energy (LCOE) of Marine and Hydrokinetic (MHK) energy by leveraging research, development, and testing capabilities at Oregon State University, University of Washington, and the University of Alaska, Fairbanks. ALFA is a project within the Pacific Marine Energy Center (PMEC; formerly NNMREC), a multi-institution entity with a diverse funding base that focuses on research and development for marine renewables. The ALFA project aimed to accelerate the development of next-generation arrays of wave energy conversion (WEC) and tidal energy conversion (TEC) devices through a suite of field-focused R&D activities spanning a broad range of strategic opportunity areas identified in the Funding Opportunity Announcement: • Device and/or array operation and maintenance (O&M) logistics development; • High-fidelity resource characterization and/or modeling technique development and validation; • Array-specific component technology development (e.g. moorings and foundations, transmission, and other offshore grid components); • Array performance testing and evaluation; and • Novel cost-effective environmental monitoring techniques and instrumentation testing and evaluation. The objective of the Lab Collaboration Project (LCP) was to accelerate the development of next-generation marine energy conversion systems. The LCP aimed to achieve these project objectives in collaboration with the national laboratories by: • Developing concept generation and assessment tools; • Improving access to existing testing resources; • Validating collision risk models between fish and turbines; and • Advancing analysis and simulation capabilities for wave-WEC interactions and PTO analysis in nonlinear ocean waves. The ALFA portion of the project was comprised of six overarching technical tasks: • Task 1: Debris Modeling, Detection and Mitigation; • Task 2: Autonomous Monitoring & Intervention; • Task 3: Resource Characterization for Extreme Conditions; • Task 4: Robust Models for Design of Offshore Anchoring and Mooring Systems; • Task 5: Performance Enhancement for Marine Energy Converter (MEC) Arrays; and • Task 6: Evaluating Sampling Techniques for MHK Biological Monitoring. The LCP was divided into four overarching technical tasks: • Task 7: Project Management and Reporting • Task 8: Novel Design and Assessment Methodologies for Wave Energy Converter Design (Wave- SPARC) • Task 9: Testing Access for Commercial Marine Renewable Energy Technology Developers • Task 10: Quantifying Collision Risk for Fish and Turbines • Task 11: Nonlinear Ocean Waves and PTO Control Strategy Each ALFA/LCP task listed above functioned as a separate and discreet project. A final Technical Report was written for each individual task and these reports were uploaded to OSTI, after receiving DOE approval. The following document is a compilation of each of these final, approved reports arranged as individual chapters.

13 HYDRO ENERGY↗

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗

Augmented reduced order models for turbulence

The authors introduce an augmented-basis method (ABM) to stabilize reduced-order models (ROMs) of turbulent incompressible flows. The method begins with standard basis functions derived from proper orthogonal decomposition (POD) of snapshot sets taken from a full-order model. These are then augmented with divergence-free projections of a subset of the nonlinear interaction terms that constitute a significant fraction of the time-derivative of the solution. The augmenting bases, which are rich in localized high wavenumber content, are better able to dissipate turbulent kinetic energy than the standard POD bases. Several examples illustrate that the ABM significantly out-performs L 2 -, H 1 - and Leray-stabilized POD ROM approaches. The ABM yields accuracy that is comparable to constraint-based stabilization approaches yet is suitable for parametric model-order reduction in which one uses the ROM to evaluate quantities of interests at parameter values that differ from those used to generate the full-order model snapshots. Several numerical experiments point to the importance of localized high wavenumber content in the generation of stable, accurate, and efficient ROMs for turbulent flows.

Kaneko, Kento↗

The Schwarz Alternating Method for the Seamless Coupling of Nonlinear Reduced Order Models and Full Order Models

Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of a set of partial differential equations (PDEs) using conventional techniques (e.g., finite element, finite volume, finite difference methods) where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the “plug-and-play” integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method [41]. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multiscale coupling of finite element FOMs in solid mechanics [35, 36], we present a new extension of the Schwarz framework that enables FOM-ROM and ROM-ROM coupling, following a domain decomposition of the physical geometry on which a PDE is posed. In order to maintain efficiency and achieve computation speed-ups, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting (ECSW) approach [13]. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.

97 MATHEMATICS AND COMPUTING↗

The Response of Precipitation Extremes to the Twentieth- and Twenty-First-Century Global Temperature Change in a Comprehensive Suite of CESM1 Large Ensemble Simulation: Revisiting the Role of Forcing Agents Vs. the Role of Forcing Magnitudes

The response of precipitation extremes (PEs) to global warming is found to be nonlinear in Community Earth System Model version 1 (CESM1) and other global climate models (Pendergrass et al., 2019), which led to the concern that it is not accurate to approximate the response of PE to a single forcing as the difference between simulations with all forcing agents and those that exclude one specific forcing. This calls into question previous model-based results that the sensitivity of PE with warming due to aerosol forcing is significantly larger than that due to greenhouse gases (GHGs). We reevaluate the PE sensitivity to GHGs and aerosols using available CESM1 ensemble simulations. We show that although the PE response to warming is nonlinear in CESM1, especially for the high warming projected in the twenty-first-century, PE sensitivity to aerosols is still significantly stronger than that due to GHGs when the comparison is made within similar warming regimes to avoid the bias induced by the nonlinear behavior. But the difference is smaller than previously estimated. We also conclude that the additivity assumption is largely valid to isolate the PE response due to aerosol forcing from the paired simulations including the “all forcing” experiment when the warming regime is small (e.g., 1°C–2°C in the next few decades when aerosol forcing is projected to decline and becomes a major source of uncertainty for model projection).

58 GEOSCIENCES↗

Laboratory Study of Nonlinear QED in Intense Laser-Matter Interactions

The goal of the project was to investigate the interaction of powerful laser light with matter, which is of fundamental interest to electrodynamics, thermonuclear fusion plasmas, and high-energy-density physics for DOE. Experiments on highly nonlinear relativistic interactions were performed using the state-of-the-art DIOCLES laser at the Extreme Light Laboratory of the University of Nebraska–Lincoln (UNL). We have demonstrated a novel testbed for laser-plasma interactions in which laser pulses collided in plasma with femtosecond and micron-scale accuracy under extreme experiment conditions. This capability is crucial for future radiation reaction experiments and nonlinear QED studies. Moreover, this is also a milestone towards the efficient generation of GeV electron beams via travelling wave laser wakefield accelerator. We proposed a novel idea for measuring the radiation reaction process using travelling wave Thomson scattering, which was studied in numerical simulations. This method allows unambiguous measurement of radiation reaction in a single shot, therefore, surpassing the conventional methods, which suffer severely from the shot-to-shot fluctuations, due to the instability of laser wavefield acceleration.

74 ATOMIC AND MOLECULAR PHYSICS↗

Assessment of Survey Results from Advanced Reactor Industry Domain Experts on Nonlinear Soil-Structure Interaction Analysis Software Verification and Validation

The seismic load case has a significant impact on the design and cost of nuclear power plants. Given the need to substantially reduce cost, advanced reactor designers are looking to leverage numerical tools that enable seismic analysis of an integrated vessel/support/structure/soil system. Modern nonlinear analysis tools provide a solution, capturing dynamic coupling between components (including soil-structure interaction (SSI)) concurrent with nonlinear behavior in one or more parts of the system. Although these methods have a rich history of technical development and implementation, software quality assurance (SQA) following nuclear industry standards remains a significant burden for those wishing to adopt such methods for advanced reactor design and licensing. To reduce the SQA burden, this project will develop the guidance for SQA verification and validation (V&V) of coupled nonlinear SSI analysis tools, to include a test matrix of software features and test problems to support commercial grade dedication (CGD). The guidance is intended to be technology-neutral: supporting designers of all advanced reactors. To maximize the value of the project to reactor designers, the project team performed focused surveys of and interviews with advanced reactor designers. Additionally, the project surveyed members of the broader industry involved in reactor design and licensing. The aggregated industry feedback consists of written survey responses, live polling responses, focused interviews, and informal feedback provided after outreach presentations, collectively referred to as “survey results”. Herein, the survey results are reported, reviewed, and assessed to inform follow-on project activities. The survey results confirmed the familiarity of the industry with the coupled nonlinear SSI analysis. They also affirm the project need based upon the expressed intent to (1) incorporate nonlinear features and (2) pursue the coupled nonlinear SSI analysis to reduce seismic demands and construction costs. All reactor designers indicated their intent to incorporate two or more nonlinear features, and all reactor designer respondents opined that the coupled nonlinear SSI analysis would allow for the optimization of the reactor design and construction. However, the programmatic challenges, whether real or perceived, present a significant barrier to reactor designers. The barrier most commonly identified by the reactor designer population was regulatory risk, with 70% citing this as a reason not to pursue the approach. The perceived regulatory risk identified by the reactor designers underscores the importance of regulator engagement and dialogue in this project. Additionally, half of the reactor designers identified cost and lack of guidance as a deterrent. The survey results also provide insights to tailor specific aspects of the guidance document and test matrix. The project plans to prepare both a formal referenceable guidance document and a collaborative, web-based test matrix and problem set. The project will focus on more complete test problem definitions for the prioritized nonlinear features over shallower problem descriptions for a larger set of features. The nonlinearities prioritized as high based upon survey feedback include fluid-structure interaction and seismic isolation and energy dissipation devices. The nonlinearities prioritized as intermediate include nonlinear geomaterials, nonlinear concrete, nonlinear steel, and interface/contact nonlinearity. Deep embedment and the associated nonlinear phenomena are assigned the lowest priority based upon survey feedback.

42 ENGINEERING↗