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While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity $\mathcal{S}$ that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. Here, we found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.
Reduced-order models (ROMs) are a widely used and powerful approach to reducing the complexity of predictive physics-based numerical simulations for a wide range of applications, including electronics and fluid mechanics such as geologic CO 2 sequestration (GCS). ROMs are critical for optimization, sensitivity analysis, model calibration and uncertainty quantification where full-order models cannot be feasibly executed many times. Traditional approaches generate a single ROM for each simulated response (e.g., CO 2 injection rates, pH changes) based on a set of training simulations. Here, we demonstrate that a single ROM can display excellent overall predictive statistics, but have predictions that dramatically and unacceptably deviate from simulator responses especially when the response variable has a large range (i.e., vary over multiple orders of magnitude). For example, we show that a traditional statistically-high-performing GCS ROM (coefficient of determination R 2 of 0.99) can have average absolute relative errors of over 200%. To address this, we propose a new and novel approach where a set of sub-ROMs are generated to overcome the potential pitfalls in traditional single ROM development. The effectiveness of the proposed approach—the ROMster framework—is demonstrated using a case study of predicted CO 2 injection rates for GCS. We find our approach is a robust and general framework for ROM development, reducing the average “error” from 200% to only 4% in our case study.
Biomass pyrolysis is a promising approach for producing economic and environmentally-friendly fuels and bioproducts. Biomass pyrolysis experiments show that feedstock properties have a significant impact on product yields and composition. Scientists are developing detailed chemical reaction mechanisms to capture the relationships between biomass composition and pyrolysis yields. These mechanisms can be computationally intensive. In this study, we investigate the use of a machine learning reduced order model (ROM) for assessing the costs and emissions of a pyrolysis biorefinery. Here, we developed a Kriging-based ROM to predict pyrolysis yields of 314 feedstock samples based on the results of a detailed chemical kinetic pyrolysis mechanism. The ROM is integrated into a chemical process model for calculating mass and energy yields in a commercial-scale (2000 tonne/day) biorefinery. The ROM estimated biofuel yields of 65 to 130 gallons per ton of dry biomass. This results in biofuel minimum fuel-selling prices of $2.62 to $5.43 per gallon and emissions of -13.62 to 145 kg of CO 2 per MJ. The ROM achieved an average mean square error of 1.8e-20 and a mean absolute error of 0.53%. These results suggest that ROMs can facilitate rapid feedstock screening for biorefinery systems.
Microstructure evolution in the electrodes of solid oxide fuel cell is an important degradation mechanism which reduces active sites for redox reaction and the electric conductivity. Phase field models for microstructure evolution simulation are usually expensive for large scale simulations. In this paper, a reduced-order coarsening model is developed using dynamic discrepancy reduced modeling, which reduces the model order by inserting Gaussian process stochastic functions into the dynamic equations of Ostwald ripening. The reduced order model has been calibrated on a dataset generated by a phase field model that has been well validated to experiments. A validating dataset has also been generated with which the model prediction show good agreement. This model is further applied to predict long term microstructure evolution in different SOFC electrodes. Finally, this work is the first attempt of building a degradation model of SOFC using data science techniques.
Abstract not provided.
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 physicsinformed 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 LSROMs. 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. Finally, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.
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 lowdimensional 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 software 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.
Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problems has been hindered by the computational cost of finding the stationary points of the associated Lagrangian, which requires primal and adjoint solves. This issue can be mitigated by using OBC in conjunction with computationally efficient reduced order models (ROMs). To demonstrate the potential of this combination, in this paper, we develop an optimization-based ROM-ROM coupling for a transient advection-diffusion transmission problem. We pursue the “optimize-then-reduce” path toward solving the minimization problem at each time step and solve reduced space adjoint system of equations, where the main challenge in this formulation is the generation of adjoint snapshots and reduced bases for the adjoint systems required by the optimizer. One of the main contributions of the paper is a new technique for an efficient adjoint snapshot collection for gradient-based optimizers in the context of optimization-based ROM-ROM couplings. In conclusion, we present numerical studies demonstrating the accuracy of the approach along with comparison between various approaches for selecting a reduced order basis for the adjoint systems, including decay of snapshot energy, average iteration counts, and timings.
Not Available
Reduced order models (ROMs) present an opportunity to reduce the computational burden of IES analysis using HYBRID models without significantly sacrificing data accuracy. Other applications of ROMs are digital twins, stochastic optimization studies, model exporting, and protection of proprietary information. In this paper the capability of creating ROMs of the models within the HYBRID repository will be demonstrated. Specifically, a linear regression ROM of a gas turbine and a dynamic mode decomposition with control (DMDc) ROM of a lithium-ion battery are constructed.
Many projection-based reduced order models (pROM) that utilize the governing equation and data to accelerate physical simulations can be applied to nonlinear dynamical systems. To avoid full order model (FOM) scale update for each time step, hyperreduction techniques are developed to sample high dimensional nonlinear terms. Our study aims to investigate if preconditioning the least-squares problem used for the nonlinear approximation can improve the robustness of the condition number of the problem while achieving high accuracy. In our study, we use the row-normalization matrix motivated by the Christoffel function as the preconditioner and solve the corresponding weighted least-squares problem. Numerical results for Lagrangian hydrodynamics examples are analyzed to explore how the preconditioner works compared to existing hyper-reduction techniques.
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Abstract not provided.
Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. An alternative, the pilot-scale model, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. The ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. Here this method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about 15–40 times faster with only ~1% relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation.