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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Physics-informed machine learning for fault-leakage reduced-order modeling

Geologic carbon storage (GCS) is a promising technology for mitigating CO 2 emissions. The overall success of GCS depends on safe operations that are informed by risk assessment and have proper mitigation plans in place. Performing quantitative probabilistic risk assessment for a GCS site using traditional reservoir simulators can be challenging due to the high computational costs. To overcome this challenge, the US Department of Energy’s National Risk Assessment Partnership (NRAP) project has developed an integrated assessment modeling approach that utilizes computationally efficient reduced-order models (ROM) for simulating various parts of a GCS storage site to quantify uncertainty. Here, in this study, we develop a reduced-order model for fault leakage risk assessment. We use a deep learning approach to build the reduced-order model. We perform a sensitivity analysis and find that the deep learning model yields high accuracy with a much smaller computational cost than full-physics simulation. We also evaluate the performance of the model in scenarios where simulations are not possible to run, providing analysis not previously performed in fault-leakage ROM analyses. Based on a sensitivity analysis of the model, we suggest a simplified conceptual model for fault leakage and site monitoring.

58 GEOSCIENCES↗
DOE OSTI2024

Reduced Order Model for Guided Wave Propagation on Gas Pipelines to Enable Real-Time Simulation

Reduced order model for simulation of Guided wave propagation is presented here. The utilization of reduced order models ensures efficient data generation for a variety of parameters where it takes huge computational effort to simulate, crucial for timely monitoring and decision-making. Autoencoder based reduced order models are proposed here, which are trained on simulated data from open-source finite element framework, Firedrake.

Bukka, Sandeep Reddy↗
DOE OSTI2024

Reduced Order Model for Guided Wave Propagation on Gas Pipelines to Enable Real-Time Simulation

Reduced order model for simulation of Guided wave propagation is presented here. The utilization of reduced order models ensures efficient data generation for a variety of parameters where it takes huge computational effort to simulate, crucial for timely monitoring and decision-making. Autoencoder based reduced order models are proposed here, which are trained on simulated data from open-source finite element framework, Firedrake.

Bukka, Sandeep Reddy↗
DOE OSTI2021

A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Lastly, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Domain-decomposition nonlinear manifold reduced order model

This software combines nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD) techniques. NM-ROMs, which utilize a shallow, sparse autoencoder trained with full order model (FOM) snapshot data, approximate the FOM state on a nonlinear manifold. These models offer advantages over linear-subspace ROMs (LS-ROMs) particularly in scenarios with slowly decaying Kolmogorov n-width. However, the training of NM-ROMs involves a number of parameters that scale with the size of the FOM, and storing high-dimensional FOM snapshots can significantly increase the cost of ROM training for extreme-scale problems. To mitigate these costs, the software employs DD to partition the FOM into smaller subdomains, computes NM-ROMs for each, and then integrates these to form a global NM-ROM. This strategy offers multiple benefits: it enables parallel training of subdomain NM-ROMs, reduces the number of parameters needed, decreases the dimensional requirements of subdomain FOM training data, and allows for customization to the unique characteristics of each FOM subdomain. The use of a shallow, sparse autoencoder architecture in each subdomain NM-ROM facilitates the application of hyper-reduction (HR), simplifying the nonlinear complexities and enhancing computational speed. This software marks the inaugural application of NM-ROM combined with HR to a DD problem. It features an algebraic DD reformulation of the FOM, training of NM-ROMs with HR for each subdomain, and employs a sequential quadratic programming (SQP) solver for the evaluation of the coupled global NMROM. The effectiveness of the DD NM-ROM with HR is numerically demonstrated on the 2D steady-state Burgers' equation, showing an order of magnitude improvement in accuracy over the DD LS-ROM with HR.

Diaz, AlejandroN↗
DOE OSTI2024

A fast and accurate domain decomposition nonlinear manifold reduced order model

Here, this paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each sub domain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Sensitivity Analysis, Reduced-order Modeling, and Optimization of a Gas-Cooled Pebble Bed Reactor using Equilibrium-Core and DLOFC Performance

This work presents and applies a workflow for performing design optimization on gas-cooled pebble-bed reactors. Based on previous research, a representative equilibrium core of a pebble-bed reactor and a depressurized loss-of-forced-cooling model are created. These applications are built using the Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically utilizing Griffin, Pronghorn, and Bison. After defining design-related parameters and quantities of interest regarding reactor safety and efficiency, this multiphysics model is sampled using the MOOSE stochastic tools module. The result is a comprehensive dataset of configurations, enabling sensitivity analysis and the generation of reduced-order models. Subsequently, the dataset and reduced-order models are employed in an optimization study aimed at maximizing fuel utilization while adhering to safety and operational constraints. The optimization process leads to an improvement of fuel utilization by approximately 10\%, compared to engineering-judgment-based nominal conditions.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Scalable Reduced‐Order Model for the Steady Navier–Stokes Equations

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional numerical methods are computationally intractable even for intermediate pilot plant scales. Recently, the component reduced order modeling method has been developed to tackle this challenge by combining projection reduced order modeling and discontinuous Galerkin domain decomposition. However, while many scientific or engineering applications involve nonlinear physics, this method has only been demonstrated for various linear systems. In this work, the component reduced order modeling method is extended to steady Navier–Stokes flow, with application to general nonlinear physics in view. The large‐scale, global domain is decomposed into a combination of small‐scale unit component. Linear subspaces for flow velocity and pressure are identified via proper orthogonal decomposition over sample snapshots collected from each small‐scale unit component. Velocity bases are augmented with a pressure supremizer to satisfy the inf–sup condition for stable pressure prediction. Two different nonlinear reduced order modeling methods are employed and compared for efficient evaluation of nonlinear advection: A third‐order tensor projection operator and the empirical quadrature procedure. The proposed method is demonstrated on the flow over arrays of five different unit objects, achieving a 23‐fold speedup with less than 4% relative error in domains up to 256 times larger than the unit components. Furthermore, a numerical experiment with the pressure supremizer strongly indicates the need for a supremizer for stable pressure prediction. A comparison between the tensorial approach and the empirical quadrature procedure revealed a slight advantage of the empirical quadrature procedure. The framework is compared with an alternating Schwarz‐based reduced‐order approach, demonstrating improved efficiency and robustness for the DG‐based global solver while retaining flexibility for sub‐scale iterative solvers. The method is further extended to a coupled advection–diffusion and Navier–Stokes system, illustrating its applicability to multi‐physics problems and its potential for more general, inter‐coupled nonlinear systems.

42 ENGINEERING↗
DOE OSTI2024

A Reduced-Order Model of a Nuclear Power Plant with Thermal Power Dispatch

This paper presents reduced-order modeling of thermal power dispatch (TPD) from a pressurized water reactor (PWR) for providing heat to nearby heat consuming industrial processes that seek to take advantage of nuclear heat to reduce carbon emissions. The reactor model includes the neutronics of the reactor core, thermal–hydraulics of the primary coolant cycle, and a three-lump model of the steam generator (SG). The secondary coolant cycle is represented with quasi-steady state mass and energy balance equations. The secondary cycle consists of a steam extraction system, high-pressure and low-pressure turbines, moisture separator and reheater, high-pressure and low-pressure feedwater heaters, deaerator, feedwater and condensate pumps, and a condenser. The steam produced by the SG is distributed between the turbines and the extraction steam line (XSL) that delivers steam to nearby industrial processes, such as production of clean hydrogen. The reduced-order simulator is verified by comparing predictions with results from separate validated steady-state and transient full-scope PWR simulators for TPD levels between 0% and 70% of the rated reactor power. All simulators indicate that the flow rate of steam in the main steam line and turbine systems decrease with increasing TPD, which causes a reduction in PWR electric power generation. The results are analyzed to assess the impact of TPD on system efficiency and feedwater flow control. Due to the simplicity of the proposed reduced-order model, it can be scaled to represent a PWR of any size with a few parametric changes. In the future, the proposed reduced-order model will be integrated into a power system model in a digital real-time simulator (DRTS) and physical hardware-in-the-loop simulations.

08 HYDROGEN↗
DOE OSTI2024

Learning physics-based reduced-order models from data using nonlinear manifolds

Here we present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

Conditional VAEs↗
DOE OSTI2021

Component-wise reduced order model lattice-type structure design

Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution of a mathematical model feasible. In this paper, we propose a topology optimization (TO) formulation that approximates the governing physics using component-wise reduced order modeling as introduced in Huynh et al. (2013); Eftang and Patera (2013), which can reduce solution time by multiple orders of magnitude over a full-order finite element model while providing a relative error in the solution of 1%. In addition, the offline training data set from such component-wise models is reusable, allowing its application to many design problems for only the cost of a single offline training phase, and the component-wise method is nearly embarrassingly parallel. We also show how the parameterization chosen in our optimization allows a simplification of the component-wise reduced order model (CWROM) not noted in previous literature, for further speedup of the optimization process. Furthermore, the sensitivity of the compliance with respect to the particular parameterization is derived solely at the component level. In numerical examples, we demonstrate a 1000x speedup over a full-order FEM model with relative error of 1% and show minimum compliance designs for two different cantilever beam examples, one smaller and one larger. Finally, error bounds for the displacement field, compliance, and compliance sensitivity of the CWROM are derived.

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 OSTI2024

Accelerating particle-in-cell kinetic plasma simulations via reduced-order modeling of space-charge dynamics using dynamic mode decomposition

We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. Here, we demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction↗
DOE OSTI2024

Reduced-order model to approximate response matrices for filter stack spectrometers

We present a reduced-order model to calculate response matrices rapidly for filter stack spectrometers (FSSs). The reduced-order model allows response matrices to be built modularly from a set of pre-computed photon and electron transport and scattering calculations through various filter and detector materials. While these modular response matrices are not appropriate for high-fidelity analysis of experimental data, they encode sufficient physics to be used as a forward model in design optimization studies of FSSs, particularly for machine learning approaches that require sampling and testing a large number of FSS designs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2001

Reduced-Order Modeling: New Approaches for Computational Physics

In this paper, we review the development of new reduced-order modeling techniques and discuss their applicability to various problems in computational physics. Emphasis is given to methods ba'sed on Volterra series representations and the proper orthogonal decomposition. Results are reported for different nonlinear systems to provide clear examples of the construction and use of reduced-order models, particularly in the multi-disciplinary field of computational aeroelasticity. Unsteady aerodynamic and aeroelastic behaviors of two- dimensional and three-dimensional geometries are described. Large increases in computational efficiency are obtained through the use of reduced-order models, thereby justifying the initial computational expense of constructing these models and inotivatim,- their use for multi-disciplinary design analysis.

Beran, Philip S.↗