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At least 271 records · Page 15

Multiscale modeling high-order methods and data-driven modeling

Projection-based reduced-order models (ROMs) comprise a promising set of data-driven approaches for accelerating the simulation of high-fidelity numerical simulations. Standard projection-based ROM approaches, however, suffer from several drawbacks when applied to the complex nonlinear dynamical systems commonly encountered in science and engineering. These limitations include a lack of stability, accuracy, and sharp a posteriori error estimators. This work addresses these limitations by leveraging multiscale modeling, least-squares principles, and machine learning to develop novel reduced-order modeling approaches, along with data-driven a posteriori error estimators, for dynamical systems. Theoretical and numerical results demonstrate that the two ROM approaches developed in this work - namely the windowed least-squares method and the Adjoint Petrov - Galerkin method - yield substantial improvements over state-of-the-art approaches. Additionally, numerical results demonstrate the capability of the a posteriori error models developed in this work.

97 MATHEMATICS AND COMPUTING↗

Machine learning for nonintrusive model order reduction of the parametric inviscid transonic flow past an airfoil

Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are computationally expensive to solve because of the high degrees of freedom as well as the coupled nature of the conservation laws. While these issues pose a bottleneck for the use of such models in aerospace design, computational costs can be significantly minimized by constructing special, structure-preserving surrogate models called reduced-order models. In this work, we propose a machine learning method to construct reduced-order models via deep neural networks and we demonstrate its ability to preserve accuracy with a significantly lower computational cost. In addition, our machine learning methodology is physics-informed and constrained through the utilization of an interpretable encoding by way of proper orthogonal decomposition. Application to the inviscid transonic flow past the RAE2822 airfoil under varying freestream Mach numbers and angles of attack, as well as airfoil shape parameters with a deforming mesh, shows that the proposed approach adapts to high-dimensional parameter variation well. Notably, the proposed framework precludes the knowledge of numerical operators utilized in the data generation phase, thereby demonstrating its potential utility in the fast exploration of design space for diverse engineering applications. Comparison against a projection-based nonintrusive model order reduction method demonstrates that the proposed approach produces comparable accuracy and yet is orders of magnitude computationally cheap to evaluate, despite being agnostic to the physics of the problem.

97 MATHEMATICS AND COMPUTING↗

SNS: A Solution-Based Nonlinear Subspace Method for Time-Dependent Model Order Reduction

Several reduced order models have been successfully developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction techniques require the construction of nonlinear term basis, which introduces a computationally expensive offline phase. A novel way of constructing nonlinear term basis within the hyper-reduction process is introduced. In contrast to the traditional hyper-reduction techniques where the collection of nonlinear term snapshots is required, the SNS method avoids collecting the nonlinear term snapshots. Instead, it uses the solution snapshots that are used for building a solution basis, which enables avoiding an extra data compression of nonlinear term snapshots. As a result, the SNS method provides a more efficient offline strategy than the traditional model order reduction techniques, such as the DEIM, GNAT, and ST-GNAT methods. The SNS method is theoretically justified by the conforming subspace condition and the subspace inclusion relation. It is useful for model order reduction of large-scale nonlinear dynamical problems to reduce the offline cost. It is especially useful for ST-GNAT that has shown promising results, such as a good accuracy with a considerable online speed-up for hyperbolic problems in a recent paper by Choi and Carlberg [SIAM J. Sci. Comput., 41 (2019), pp. A26--A58], because ST-GNAT involves an expensive offline cost related to collecting nonlinear term snapshots. Error analysis for the SNS method is presented. Numerical results support that the accuracy of the solution from the SNS method is comparable to the traditional methods and a considerable speed-up (i.e., a factor of two to a hundred) is achieved in the offline phase.

97 MATHEMATICS AND COMPUTING↗

Degradation and Modeling of Large-Format Commercial Lithium-Ion Cells as a Function of Chemistry, Design, and Aging Conditions

Demand for large-format (>10 Ah) lithium-ion batteries has increased substantially in recent years, due to the growth of both electric vehicle and stationary energy storage markets. The economics of these applications is sensitive to the lifetime of the batteries, and end-of-life can either be due to energy or power limitations. Despite this, there is little information from cell manufacturers on the sensitivity of cell degradation to environmental conditions or battery use. This work reports accelerated aging test data from four commercial large-format lithium-ion batteries from three manufacturers, with varying design (thickness, casings, ...), chemistry (lithium-iron-phosphate (LFP) or lithium-nickel-manganese-cobalt-oxide positive electrodes (NMC), with graphite (Gr) negative electrodes), and capacity (50 to 250 Amp hours). The tested LFP|Gr cell is found to be relatively insensitive to cycling conditions like temperature or voltage window, while NMC|Gr cells have varying sensitivity. Degradation trends are further investigated by training predictive models: simple polynomial trend lines, a semi-empirical reduced-order model, and an empirical reduced-order model identified using machine-learning based on symbolic regression. Calendar and cycle life are simulated over a variety of conditions to directly compare the various batteries. Cell size and thickness are found to substantially impact sensitivity to temperature during cycle aging, while electrode chemistry impacts depth-of-discharge sensitivity. Real-world battery lifetime is evaluated by simulating residential energy storage and commercial frequency containment reserve systems in several U.S. climate regions. Predicted lifetime across cell types varies from 7 years to 20+ years, though all cells are predicted to have at least 10 year life in certain conditions.

battery lifetime↗

A machine-learning inverse model framework for rapid forecasting and history matching in unconventional reservoirs

Model-based optimization for real-time forecasting in unconventional reser-voirs requires novel methods and work?ows since the strategies and work?ows used in conventional reservoirs are either inapplicable, or prohibitively expen-sive and time-consuming. Insu?cient site data and computational expense of high-?delity simulations mean that work?ows with high-?delity simulations are not ideal for usage in comprehensive uncertainty quanti?cation stud-ies that require 1000s of forward model runs. We present an alternative, novel work?ow for unconventional reservoirs, based on the interplay between reduced-order models and machine-learning. Our physics-informed machine-learning (PIML) work?ow addresses the challenges to real-time reservoir management in uncoventionals, namely lack of data (the time-frame for which the wells have been producing), and computational expense of high-?delity modeling. We use the machine-learning paradigm of transfer-learning to bind together fast but less accurate reduced-order models with slow, but accurate high-?delity models and circumvent the di?culties inherent in the current state-of-the-art for unconventionals. Such a PIML work?ow, grounded in physics, is a viable candidate for real-time history matching and production forecasting in a fractured shale gas reservoir. The signi?cance of our approach is that while it is developed for a particu-lar well and site in the Marcelus Shale gas reservoir of the Appalachian basin (MSEEL), it is not wedded to it. We expect the same work?ow can be ap-plied to other shale formations (e.g., Woodford, Barnett, Utica, EagleFord) should site-data become available, using the same set of machine-learning techniques from transfer learning. Some ?ne-tuning (or minimal retraining of the neural networks) will be required to transfer knowledge across shale gas sites/formations but it is a clearly superior alternative to developing a new machine-learning model altogether when considering a di?erent site.

Srinivasan, Shriram↗

A novel construct for scaling groundwater–river interactions based on machine-guided hydromorphic classification

Hydrologic exchange between river channels and adjacent subsurface environments is a key process that influences water quality and ecosystem function in river corridors. Predictive numerical models are needed to understand responses of river corridors to environmental change and to support sustainable watershed management. We posit that systematic hydromorphic classification provides a scaling construct that facilitates extrapolation of outputs from local-scale mechanistic models to reduced-order models applicable at reach and watershed scales. This in turn offers the potential to improve large-scale predictions of river corridor hydrobiogeochemical processes. Here we present a new machine-guided hydromorphic classification methodology that addresses the key requirements of this objective, and we demonstrate its application to a segment of the Columbia River in the northwestern United States. The resulting hydromorphic classes form spatially coherent and physically interpretable hydromorphic units that exhibit distinct behaviors in terms of distributions of subsurface residence times (a primary control on critical biogeochemical reactions). This approach forms the basis of ongoing research that is evaluating the formulation of reduced-order models and transferability of results to other river reaches and larger scales.

54 ENVIRONMENTAL SCIENCES↗

Directed Energy Deposition Process Modeling, Validation, and Process-Informed Optimization

The directed energy deposition (DED) process, one of the most popular additive manufacturing techniques in use today, involves various complex physical mechanisms that are not yet well understood. In this regard, computational tools show promise for elucidating the manufacturing process and enabling nondestructive performance evaluations of manufactured parts. To better control and optimize the DED process?thereby improving the manufactured product? the present work develops and demonstrates a novel artificial intelligence (AI)-based process control and optimization technique. Specifically, a geometry-free thermo-mechanical model with adaptive subdomain construction is developed to accurately capture the material?s thermo-mechanical response under cyclical reheating and high cooling rates [1]. The model is demonstrated and validated with experimental measurements, in light of various geometries and processing parameters. Moreover, based on this thermo-mechanical model, a physics-informed reduced-order model is developed to enable quick predictions of the temperature field at every time step. Furthermore, an AI-based controller is developed that can adapt to the ever-changing system states by automatically adjusting the manufacturing process parameters. This entire work is based on the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) [2] and its recent integration with Libtorch (the C++ frontend of PyTorch [3]). The combined development of the adaptive material deposition scheme, thermo-mechanical model, associated reduced-order model, and AI-based process controller carries great potential for improving advanced manufacturing processes.

36 MATERIALS SCIENCE↗

Improving Grid Awareness by Empowering Utilities with Machine Learning and Artificial Intelligence

Gap filling time series data typically depends on linear interpolation. More recently gap filling advancements include machine learning techniques. However, none leverage advanced learning approach that uses cohort training or a neighborhood informed approach, which is described in this report. The report also describes a physics informed approach using Reduced Order Models (ROM). There are several methods to capture the nature of the detailed system in aggregated models, however there is a trade-off for these methods developed for multiple applications. These methods have specific requirements and applications that includes consideration of dynamics or covering a larger range of operating conditions, etc. The various methods of aggregation are: 1) Thevenin equivalents for downstream networks 2) Equivalent feeder representation to capture downstream network losses accurately 3) Structured reduced order models for dynamics 4) System identification-based ROM (abstract dynamical model) Methods described in items 1 and 2 above are ideal for steady-state models and useful for this application. Of these two methods, based on the data availability, the targeted application, the reduced order model that is proposed to be developed is the equivalent feeder model representation. This includes a structure of the reduced order model whose parameters can be determined by the system load and losses with the meter measurements.

14 SOLAR ENERGY↗

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↗

Predictive multiscale modeling for Unidirectional Carbon Fiber Reinforced Polymers

This paper presents a predictive multiscale modeling scheme for Unidirectional (UD) Carbon Fiber Reinforced Polymers (CFRP). A bottom-up modeling procedure is discussed for predicting the performance of UD structures. UD material responses are computed from high fidelity Representative Volume Elements (RVEs). A data-driven Reduced Order Modeling approach compresses RVEs into Reduced Order Models so material responses can be computed in a concurrent fashion along with the structural level simulation. The approach presented in this paper is validated against experimental data and is believed to provide design guidance for future fiber reinforced polymers development.

36 MATERIALS SCIENCE↗

Self-supervised learning of spatiotemporal thermal signatures in additive manufacturing using reduced order physics models and transformers

Microstructure control via additive manufacturing has enormous potential as manufacturers, materials scientists, and designers alike seek to exploit novel fabrication technologies to improve component performance. Recent works have demonstrated the feasibility of producing materials with controlled microstructures across various length scales. However, the experimental approach towards exploring the process-structure space can be laborious and costly. This is particularly true if also considering scan pattern optimization which is well suited for processes such as powder bed fusion electron beam melting. In this work we propose an approach for encoding additive manufacturing layer-wise thermal response signatures using self-supervised representation learning. Thermal simulations from a reduced order model are utilized to estimate the spatiotemporal response during printing. A machine learning framework, using video-transformers, is utilized to efficiently distill spatiotemporal patterns into a compact latent space representation. This latent state representation encodes the relevant physics which is then utilized to establish a data-driven process-structure model for an additively manufactured Ni-based superalloy. In conclusion, the proposed methodology could potentially be used towards in-situ process monitoring, scan pattern experimental design, and component qualification.

97 MATHEMATICS AND COMPUTING↗

Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems

Abstract A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data. On the other hand, reinforcement learning (RL) is a powerful yet relatively uncharted method in spatiotemporally extended systems. In this study, we put forth a modular dynamic closure modeling and discovery framework to stabilize the Galerkin projection based reduced order models that may arise in many nonlinear spatiotemporal dynamical systems with quadratic nonlinearity. However, a key element in creating a robust RL agent is to introduce a feasible reward function, which can be constituted of any difference metrics between the RL model and high fidelity simulation data. First, we introduce a multi-modal RL to discover mode-dependant closure policies that utilize the high fidelity data in rewarding our RL agent. We then formulate a variational multiscale RL (VMRL) approach to discover closure models without requiring access to the high fidelity data in designing the reward function. Specifically, our chief innovation is to leverage variational multiscale formalism to quantify the difference between modal interactions in Galerkin systems. Our results in simulating the viscous Burgers equation indicate that the proposed VMRL method leads to robust and accurate closure parameterizations, and it may potentially be used to discover scale-aware closure models for complex dynamical systems.

97 MATHEMATICS AND COMPUTING↗

Effects of Reactive Power on Photovoltaic Inverter Reliability and Lifetime

This paper performs research on predicting Photovoltaic (PV) inverters reliability and lifetime based on thermal cycling. Thermal cycling is considered the most important stressors in an inverter system. In order to achieve this, a detailed electro-thermal model of the PV inverter will be developed along with their controllers capable of providing voltage support through reactive power. An in-house inverter was built, and a PV inverter model was developed to match the physical inverter. The PV inverter electrothermal model was validated for different ambient temperatures to match the in-house inverter hardware. The in-house inverter was placed inside a thermal chamber to emulate different ambient temperatures and their losses and temperature rises within the system were measured. After the validation of the model, a reduced order model of the inverter will be implemented to translate the mission profile of ambient temperature and solar irradiance into load profile of junction temperatures of the switches. The junction temperature data will be used to identify the reliability indices and hence predict the useful lifetime of the inverter system. Along with the model to predict useful lifetime of the system, the impact of reactive power on the overall reliability of the system will be studied. The key observation in this paper shows that lifetime of the inverter decreases as the operating power factor moves away from unity.

14 SOLAR ENERGY↗

Editorial: Sorption processes in nuclear waste management: data knowledge management and new methodologies for data acquisition/prediction

A fundamental approach to Nuclear Waste Repository research involves the collection of experimental data in a laboratory setting, development of empirical and/or mechanistic numerical models representing those observations, and application of these models (or Reduced Order Models) into reactive transport and performance assessment models as predictive tools for informing society of impacts and risks associated with nuclear waste repository scenarios (Stevens et al., 2020). Therefore, the assimilation and interpretation of experimental data must take advantage of both new data and the rich historical data available in the literature and apply novel modeling approaches to improve predictive tools, particularly from the standpoint of uncertainty quantification, for nuclear waste repository performance assessment (Zavarin et al., 2022).

sorption↗

Machine-Learned Linear Structural Dynamics

The tension between accuracy and computational cost is a common thread throughout computational simulation. One such example arises in the modeling of mechanical joints. Joints are typically confined to a physically small domain and yet are computationally expensive to model with a high-resolution finite element representation. A common approach is to substitute reduced-order models that can capture important aspects of the joint response and enable the use of more computationally efficient techniques overall. Unfortunately, such reduced-order models are often difficult to use, error prone, and have a narrow range of application. In contrast, we propose a new type of reduced-order model, leveraging machine learning, that would be both user-friendly and extensible to a wide range of applications.

97 MATHEMATICS AND COMPUTING↗

Optimal renormalization of multiscale systems

While model order reduction is a promising approach in dealing with multi-scale time-dependent systems that are too large or too expensive to simulate for long times, the resulting reduced order models can suffer from instabilities. We have recently developed a time-dependent renormalization approach to stabilize such reduced models. In the current work, we extend this framework by introducing a parameter that controls the time-decay of the memory of such models and optimally selecting this parameter based on limited fully resolved simulations. First, we demonstrate our framework on the inviscid Burgers equation whose solution develops a finite-time singularity. Our renormalized reduced order models are stable and accurate for long times while using for their calibration only data from a full order simulation before the occurrence of the singularity. Furthermore, we apply this framework to the 3D Euler equations of incompressible fluid flow, where the problem of finite-time singularity formation is still open and where brute force simulation is only feasible for short times. Our approach allows us to obtain for the first time a perturbatively renormalizable model which is stable for long times and includes all the complex effects present in the 3D Euler dynamics. We find that, in each application, the renormalization coefficients display algebraic decay with increasing resolution, and that the parameter which controls the time-decay of the memory is problem-dependent.

Price, Jacob↗