Optimization with missing data

The 1st AIAA Geometry and Mesh Generation Workshop (GMGW-1) was held in conjunction with the AIAA Aviation Forum and Exposition 2017 and in collaboration with the 3rd AIAA Computational Fluid Dynamics (CFD) High Lift Prediction Workshop (HiLiftPW-3). As the first AIAA workshop on these topics, GMGW-1's broad objectives were to assess the current state-of-the art in geometry preprocessing and mesh generation technology as well as software as applied to aircraft and spacecraft systems. The workshop was intended to identify and develop understanding of areas of needed improvement in terms of performance, accuracy, and applicability. It was also to provide a foundation for documenting best practices for geometry preprocessing and mesh generation. The genesis of GMGW-1 is found in the indictments levied against geometry preprocessing and mesh generation - not undeservedly - by the NASA CFD Vision 2030 Study. In order to create a reference against which future progress in geometry preprocessing and mesh generation can be measured, the organizers of GMGW-1, with the assistance of the organizers of HiLiftPW- 3, focused GMGW-1 on generation of meshes of the NASA High Lift Common Research Model (HL-CRM). Some of the generated meshes were provided for use by the participants in HiLiftPW-3. All meshes and the processes by which they were generated were analyzed by GMGW-1 as a first assessment of state of the art practices. The results of GMGW-1 added quantitative detail to known problem areas including geometry modeling, data interoperability, and amount of human intervention. They do provide a clear path toward a vision of geometry preprocessing and mesh generation in the year 2030. The next milepost along this path will be a second workshop.

Seepage criteria based optimal design of water retaining structures with reliability quantification utilizing surrogate model linked simulation-optimization approach

High-speed forming processes, such as electrohydraulic forming, have recently attracted attention with the development of forming technology. However, because the high-speed operation (above 100 m/s) raises safety concerns, most experiments are conducted in a closed die, which hides the forming process. Therefore, the experimental process can only be observed in a numerical simulation with accurate material properties. The conventional quasistatic material properties are improper for high-speed forming simulations with high strain rates (>102 s−1). In this study, the material properties of Al 6061-T6, which reflect the deformation behavior in the high-strain-rate region, were investigated in a numerical approach based on a reduced order model and a surrogate model in which the numerical results resemble the experimental results. The strain rate effect on the material was determined by the Cowper–Symonds constitutive equation, and two strain rate parameters were predicted. The surrogate model takes two material parameters as inputs and outputs a weighting coefficient calculated by the reduced order model. The surrogate model is based on the Kriging method to reduce the simulation cost. Next, the optimal material parameters that minimize the error between the surrogate model and the experiments are estimated by nonlinear least-squares optimization using a genetic algorithm and the constructed surrogate model. The predicted optimal parameters were verified by comparing the results of the experiment, numerical simulation, and surrogate model.

Surrogate modeling of parameterized multi-dimensional premixed combustion with physics-informed neural networks for rapid exploration of design space

Surrogate Models for Optimization of Dynamical Systems

This paper proposes the use of Artificial Neural Networks (ANNs), specifically Physics-Informed Neural Networks (PINNs), for dynamic surrogate modelling of wind turbines. PINNs offer the flexibility to model complex relationships while incorporating physics-based constraints, enabling accurate representation of wind turbine dynamics. In this paper, a PINN-based surrogate model is developed for the Blade Element Momentum (BEM) aerodynamic model used in state-of-the-art numerical wind turbine simulations. The PINN model replaces the time-consuming root-finding process in BEM with high-dimensional regression, significantly improving computational efficiency. The PINN model is trained using data generated from a numerical model of the IEA-15MW reference wind turbine, and its performance is compared against conventional data-driven Neural Network (DDNN) models. The proposed surrogate model provides more efficient and accurate evaluations of wind turbine responses compared with traditional surrogate modelling approaches. A significant computational advantage is obtained by using the developed surrogate models with a forty-fold speedup demonstrated compared to the BEM model. Replacing the BEM model with the PINN-based surrogate model for load computation in the numerical model used for dynamic analysis results in an overall reduction of 35% in computational time for a complete dynamic simulation. This is a substantial improvement in efficiency without sacrificing accuracy — the maximum Mean Absolute Error (MAE) values for the surrogate models are of the order of 10−2, which shows that the surrogate models can predict the angle of attack at any blade node with a discrepancy of less than 0.5°. The surrogate models significantly reduce computational time while maintaining high accuracy, making them a promising approach for simulating wind turbine dynamics, especially in fields such as reliability analysis or fatigue estimation where many simulations are necessary.

Significant progress in the oil and gas industry advances the application of pipeline into an intelligent era, which poses rigorous requirements on pipeline safety, reliability, and maintainability, especially when crossing seismic zones. In general, strike-slip faults are prone to induce large deformation leading to local buckling and global rupture eventually. To evaluate the performance and safety of pipelines in this situation, numerical simulations are proved to be a relatively accurate and reliable technique based on the built-in physical models and advanced grid technology. However, the computational cost is prohibitive, so one has to wait for a long time to attain a calculation result for complex large-scale pipelines. In this manuscript, an efficient and accurate surrogate model based on machine learning is proposed for strain demand prediction of buried X80 pipelines subjected to strike-slip faults. Specifically, the support vector regression model serves as a surrogate model to learn the high-dimensionally nonlinear relationship which maps multiple input variables, including pipe geometries, internal pressures, and strike-slip displacements, to output variables (namely tensile strains and compressive strains). The effectiveness and efficiency of the proposed method are validated by numerical studies considering different effects caused by structural sizes, internal pressure, and strike-slip movements.

Transport of contaminant species undergoing chemical reactions in groundwater aquifers is a complex physical and biochemical process. Simulating this transport process involves solving complex nonlinear equations and requires huge computational time for a given aquifer study area. Development of optimal remediation strategies in aquifers may require repeated solution of such complex numerical simulation models. To overcome this computational limitation and improve the computational feasibility of large number of repeated simulations, Genetic Programming based trained surrogate models are developed to approximately simulate such complex transport processes. Transport process of acid mine drainage, a hazardous pollutant is first simulated using a numerical simulated model: HYDROGEOCHEM 5.0 for a study area resembling a mine site. Simulation model solution results for an illustrative contaminated aquifer site is then approximated by training and testing a Genetic Programming (GP) based surrogate model. To decrease the total number of GP formulations, the coordinates of observation locations are implemented as input data in the surrogate models. Comparison of the surrogate models and numerical simulation results show that the surrogate models can provide acceptable approximations of this complex transport process in contaminated groundwater aquifers.

We present a simple and robust Matlab code for polygonal mesh generation that relies on an implicit description of the domain geometry. The mesh generator can provide, among other things, the input needed for finite element and optimization codes that use linear convex polygons. In topology optimization, polygonal discretizations have been shown not to be susceptible to numerical instabilities such as checkerboard patterns in contrast to lower order triangular and quadrilaterial meshes. Also, the use of polygonal elements makes possible meshing of complicated geometries with a self-contained Matlab code. The main ingredients of the present mesh generator are the implicit description of the domain and the centroidal Voronoi diagrams used for its discretization. The signed distance function provides all the essential information about the domain geometry and offers great flexibility to construct a large class of domains via algebraic expressions. Examples are provided to illustrate the capabilities of the code, which is compact and has fewer than 135 lines.

Effective permeability is a key physical property of porous media that defines its ability to transport fluid. Digital rock physics (DRP) combines modern tomographic imaging techniques with advanced numerical simulations to estimate effective rock properties. DRP is used to complement or replace expensive and time‐consuming or impractical laboratory measurements. However, with increase in sample size to capture multimodal and multiscale microstructures, conventional approaches based on direct numerical simulation (DNS) are becoming very computationally intensive or even infeasible. To address this computational challenge, we propose a hierarchical homogenization method (HHM) with a data‐driven surrogate model based on 3‐D convolutional neural network (CNN) and transfer learning to estimate effective permeability of digital rocks with large sample sizes up to billions of voxels. This HHM‐CNN workflow divides a large digital rock into small sub‐volumes and predicts their permeabilities through a CNN surrogate model of Stokes flow at the pore scale. The effective permeability of the full digital rock is then predicted by solving the Darcy equations efficiently on the upscaled model in which the permeability of each cell is assigned by the surrogate model. The proposed method has been verified on micro‐CT scans of both sandstones and carbonates, and applied to the Bentheimer sandstone and a reconstructed high‐resolution carbonate rock obtained by multiscale data fusion. The computed permeabilities of the HHM‐CNN are consistent with the results of DNS on the full digital rock. Compared with conventional DNS algorithms, the proposed hierarchical approach can largely reduce the computational time and memory demand.

Surrogate model for energy release rate and structure optimization of double-ceramic-layers thermal barrier coatings system

Production from multi-bench unconventional development is time-consuming to model in physics-based simulators, requiring multiple runs. Each simulation takes minutes to hours, even with enhanced cloud computing power. This limits history matching to a single deterministic solution, as multi-scenario algorithms need significantly more simulations. An AI-based surrogate model expedites forecasting, enabling efficient multi-scenario algorithms. The AI surrogate relies on a large dataset of high-fidelity physics-based simulations created using modern high-performance computing (HPC) infrastructure. Simulations were based on Latin-hypercube sampling of over 100 parameters, covering geology, reservoir properties, well placements, and completion designs. Results were processed on HPC to extract features and train a surrogate model using advanced AI techniques. The model was iteratively trained to meet user-defined error metrics. The final surrogate was integrated with an automated history matching (AHM) package using a Gauss-Newton trust region optimizer to obtain multiple scenarios that align with field production. Developing a surrogate model with the desired fidelity was a challenging task. Reservoir models include several highly non-linear input-output relationships from various physical processes. Training a surrogate with an acceptable level of fidelity requires both a massive dataset and specialized AI techniques to enforce physical relationships in deep learning algorithms. The latter was critical to obtain correct physical trends from the surrogate model predictions. The final surrogate model's production forecasts accurately match the trends and magnitudes of the computationally expensive, high-fidelity numerical simulations across several real examples of multi-well and multi-bench developments. The surrogate model integration within the AHM package was straightforward and enabled the efficient determination of multiple scenarios in about one hour for a typical unconventional case. This expedites the determination of plausible scenarios, empowering end-users to better optimize the development plan. A fast reservoir surrogate model significantly reduces the cycle time for using physics-based models and workflows, capturing subsurface uncertainty more holistically. The surrogate model workflow benefits from standard features of machine learning systems, including interpretability and confidence scores, providing the user with richer information before making decisions. In particular, the work demonstrates that determining multiple reservoir scenarios matching production history is practically achievable by leveraging cutting-edge AI technologies.

Lithium-ion batteries (LIBs) have found widespread application in energy storage due to their high energy density, low self-discharge and low maintenance characteristics. However, the stability and longevity of the batteries under extreme operating conditions is yet to be fully understood. Numerous experimental and simulation studies have been performed to elucidate the effect of temperature, current, depth of discharge, and the number of cycles [1,2,3] on the performance of LIBs. These studies show that the solid-electrolyte interface (SEI) layer and gas formation accelerate at high C-rates due to increased electrolyte decomposition [4,5]. Consequently, the cell's internal resistance increases, resulting in ever-increasing irreversible heat generation inside the cell [6]. This heat generation leads to high internal temperature and a corresponding reduction in cell capacity. The data of cell temperature for a wide range of ambient temperatures and cycling rates is limited because cell performance is typically reported at room temperature. The design of battery packs for electric vehicles(EVs) is also based on test data taken at room conditions. Given that the cell's capacity, specific energy, maximum power output is bound to depend on C-rate and ambient temperature, it is necessary to test and design battery packs based on these parameters.The thermal characteristics of a lithium-ion cell can be predicted using a physics-based thermal model or data-driven methods (DDM) relying on empirical data. Experimental determination of internal cell parameters required in physics-based thermal models is challenging and time-consuming for commercial cells. On the other hand, DDM requires only cell cycling data at specific operating conditions, thereby eliminating the need for internal parameter estimation. This model predicts the experimental input and output data pattern and fits the response surface to estimate the unknown output. In this study, surrogate modelling has been employed to estimate the surface temperature, capacity, energy, and average power of commercial lithium-ion cells for different discharge currents and ambient temperatures. Surrogate modelling, a popular data analysis and reduced-order modelling technique, aims to find a global minimum of a particular objective function using a few objective function evaluations [7]. The surrogate-based model divides experimental data into training and test data sets. The training data set is employed to train the algorithm. After that, the testing data set is used to validate the model's accuracy. Experiments were performed to develop a surrogate model, with the number of experiments decided using the design of experiments[8] for a current range of 0.5C to 3C-rate and ambient temperature range of 0°C to 45°C . The cycling of cells was performed using a high current battery cycler (Arbin), and the ambient temperature was maintained using a thermal chamber (Cincinnati). The surface temperature of commercial 18650 (NMC811) lithium-ion cells was recorded using T-type thermocouples and a National Instruments DAQ module. A polynomial response surface was fitted using surrogate modelling on experimentally obtained data. The response surface shown in figure 1. contains nine data points for the preliminary study, sub-divided into a set of seven training and two testing data. The prediction error sum of squares (PRESS) is currently bounded within 10% due to the limited training data set availability and is expected to be within a band of 1% after adding data from ongoing experiments. The estimation of temperature, capacity, and specific energy can be used to optimize and develop an improved thermal management system for electric vehicles that works under various operating conditions. References Waldmann, T., Wilka, M., Kasper, M., Fleischhammer, M., & Wohlfahrt-Mehrens, M. (2014). Journal of Power Sources, 262, 129-135.Guan, T., Sun, S., Yu, F., Gao, Y., Fan, P., Zuo, P., Du,C., & Yin, G. (2018). Electrochimica Acta, 279, 204-212.Simolka, M., Heger, J. F., Traub, N., Kaess, H., & Friedrich, K. A. (2020). Journal of The Electrochemical Society, 167(11), 110502.Xu, B., Diao, W., Wen, G., Choe, S. Y., Kim, J., & Pecht, M. (2021). Journal of Power Sources, 510, 230390.Rashid, M., & Gupta, A. (2017). Electrochimica Acta, 231, 171-184.Leng, F., Tan, C. M., & Pecht, M. (2015). Scientific reports, 5(1), 1-12.Queipo, N. V., Haftka, R. T., Shyy, W., Goel, T., Vaidyanathan, R., & Tucker, P. K. (2005). Progress in aerospace sciences, 41(1), 1-28.Li, W., Xiao, M., Peng, X., Garg, A., & Gao, L. (2019). Applied Thermal Engineering, 147, 90-100. Figure 1

We present the first surrogate model for gravitational waveforms from the coalescence of precessing binary black holes. We call this surrogate model NRSur4d2s. Our methodology significantly extends recently introduced reduced-order and surrogate modeling techniques, and is capable of directly modeling numerical relativity waveforms without introducing phenomenological assumptions or approximations to general relativity. Motivated by GW150914, LIGO's first detection of gravitational waves from merging black holes, the model is built from a set of $276$ numerical relativity (NR) simulations with mass ratios $q \leq 2$, dimensionless spin magnitudes up to $0.8$, and the restriction that the initial spin of the smaller black hole lies along the axis of orbital angular momentum. It produces waveforms which begin $\sim 30$ gravitational wave cycles before merger and continue through ringdown, and which contain the effects of precession as well as all $\ell \in \{2, 3\}$ spin-weighted spherical-harmonic modes. We perform cross-validation studies to compare the model to NR waveforms \emph{not} used to build the model, and find a better agreement within the parameter range of the model than other, state-of-the-art precessing waveform models, with typical mismatches of $10^{-3}$. We also construct a frequency domain surrogate model (called NRSur4d2s_FDROM) which can be evaluated in $50\, \mathrm{ms}$ and is suitable for performing parameter estimation studies on gravitational wave detections similar to GW150914.

In this paper, surrogate models are built iteratively using polynomial chaos expansion (PCE) and detailed numerical simulations of a carbon sequestration system. Output variables from a numerical simulator are approximated as polynomial functions of uncertain parameters. Once generated, PCE representations can be used in place of the numerical simulator and often decrease simulation times by several orders of magnitude. However, PCE models are expensive to derive unless the number of terms in the expansion is moderate, which requires a relatively small number of uncertain variables and a low degree of expansion. To cope with this limitation, instead of using a classical full expansion at each step of an iterative PCE construction method, we introduce a mixed-integer programming (MIP) formulation to identify the best subset of basis terms in the expansion. This approach makes it possible to keep the number of terms small in the expansion. Monte Carlo (MC) simulation is then performed by substituting the va...