Numerical models for hydraulic fracturing often demand substantial computing resources. Recent advancements like Physics-Informed Neural Networks (PINN) and operator nets (like DeepONet) have ...introduced innovative approaches to partial differential equation solutions. Within the phase-field framework, hydraulic fracturing is viewed as a multi-physics coupling problem. This portrayal of multi-field coupling, where the fracture is regarded as a diffuse field, makes it possible for PINN or DeepONet to solve the governing equations of each field. However, employing PINN or operator nets for fracture mechanics encounters challenges such as the convergence issues and the need for extensive datasets. We developed a Semi-Physics-Informed Multiple Input Operator Net (SPI-MIONet) tailored for phase-field hydraulic fracturing. SPI-MIONet employs a subset of governing equations from the actual physical process to constrain the problem. This strategy effectively combines data-driven and physical constraint mechanisms while circumventing the need for expressing complex governing equations in a multi-physics system. In the context of hydraulic fracturing, the unified governing equation for fluid flow in porous media and fractures presents computational challenges due to the complexity of certain parameters. These complexities often result in time-consuming numerical solving like FEM. With the emergence of operator nets, neural networks can now undergo training without strict adherence to complete physical constraints. The optimization of the pressure field loss function predominantly relies on implicit physical constraints from the phase field and displacement field, complemented by explicit constraints from the original data loss function of operator nets. Moreover, SPI-MIONet inherently handles multiple function inputs, a critical aspect for hydraulic fracturing simulations. The results section presents two scenario studies comparing SPI-MIONet’s predictions to those of the FEM. Notably, SPI-MIONet accurately captures crack propagation paths, even in challenging scenarios involving the interaction of multiple cracks.
•Introducing SPI-MIONet, a surrogate model designed for hydraulic fracturing.•SPI-MIONet solves multi-physics problems with a semi-physics-informed operator net.•SPI-MIONet can predicts field evolution in diverse hydraulic fracturing scenarios.
Intelligent structural design using generative adversarial networks (GANs) is a revolutionary design approach for building structures. Despite its far‐reaching capability, the data quantity and ...quality may have limited the performance of such a data‐driven network. This study proposes to enhance the objectiveness of training processes by innovatively introducing a surrogate model, Physics Estimator, that informs the generator by appraising the physical behavior of the generated design. Dual loss functions evaluated by a traditional data‐driven discriminator and the Physics Estimator collaboratively foster the physics‐enhanced GAN architecture. We further develop a structural mechanics model to train and optimize the inherent accuracy of the Physics Estimator. The comparative study suggests that the proposed physics‐enhanced GAN can generate structural designs from architectural drawings and specified design conditions 44% better than a data‐driven design method and 90 times faster than a competent engineer.
This paper describes an emulator that uses a Stochastic Variational Gaussian process (SVGP) regression model to parameterize radiation in a numerical weather prediction (NWP) model that ...meteorologically models the Earth's weather system. The computation of radiative processes is very large, accounting for most of the total NWP model computation. Statistical emulators are surrogate models that represent simulators and can overcome the computational limitations of very complex simulators such as radiative processes. Recently, artificial neural network-based radiative transfer emulators have been developed, and in this study, a statistical model, GP, is used to develop a radiative transfer emulator. The GP model has the advantage of calculating the uncertainty of the prediction along with the prediction, so the uncertainty of the prediction can be utilized appropriately. However, the computational complexity of the conventional GP model is very high, making it difficult to apply to large data. To solve this problem, an approximate approach, the SVGP model, was utilized. To further reduce the dimensionality of the input variables, we used a combined neural network and SVGP model. As a result, the SVGP-based radiative physics emulator improved its accuracy by about 20% compared to the artificial neural network emulator. However, the computation speed was about 3 to 9 times slower than the neural network emulator, but it was faster than the computation speed of the NWP model. This suggests that statistical emulators can be used to replace NWP model simulators.
This study introduces the application of a spiral structure in pipeline transportation to enhance the pipeline capacity of a slurry shield circulation system. A numerical model of solid–fluid ...coupling in a pipeline with a double spiral structure was established based on computational fluid dynamics and the discrete element method (CFD–DEM) theory, and its validity was confirmed through comparison with experimental data. The characteristics of the spiral pipeline were evaluated by comparing them with those of a conventional smooth straight pipeline. A multi-objective optimization method for determining the structural parameters of a spiral pipeline in a slurry shield circulation system is proposed using the Kriging surrogate model. The optimized design of a spiral pipeline was demonstrated through a specific project, and the impact of the main structural parameters on the slurry transport characteristics of the pipeline was analyzed. The results indicated that the optimized structural parameters led to an 18.65% increase in the average flow rate of the slurry and a 19.13% reduction in the accumulation of stones in the pipeline.
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•The Spiral pipeline with transverse protrusion is applied to slurry-water circulation pipe.•The slag carrying performance of pipeline was evaluated by CFD–DEM method.•The relationship between the structure parameters and the slag carrying performance of the pipeline is studied.•The optimization process is used to optimize the structural parameters.
•Large-scale reservoir operating rules are derived by sensitive analysis and an adaptive surrogate model.•Sensitivity analysis screens out the sensitive parameters of the large-scale reservoir ...operating rules.•The weighted crowding distance of WNSGAII contributes to better performance than the classical NSGAII.•WMO-ASMO outperforms NSGAII and WNSGAII with same original model runs.
The optimization of large-scale reservoir system is time-consuming due to its intrinsic characteristics of non-commensurable objectives and high dimensionality. One way to solve the problem is to employ an efficient multi-objective optimization algorithm in the derivation of large-scale reservoir operating rules. In this study, the Weighted Multi-Objective Adaptive Surrogate Model Optimization (WMO-ASMO) algorithm is used. It consists of three steps: (1) simplifying the large-scale reservoir operating rules by the aggregation-decomposition model, (2) identifying the most sensitive parameters through multivariate adaptive regression splines (MARS) for dimensional reduction, and (3) reducing computational cost and speeding the searching process by WMO-ASMO, embedded with weighted non-dominated sorting genetic algorithm II (WNSGAII). The intercomparison of non-dominated sorting genetic algorithm (NSGAII), WNSGAII and WMO-ASMO are conducted in the large-scale reservoir system of Xijiang river basin in China. Results indicate that: (1) WNSGAII surpasses NSGAII in the median of annual power generation, increased by 1.03% (from 523.29 to 528.67billionkWh), and the median of ecological index, optimized by 3.87% (from 1.879 to 1.809) with 500 simulations, because of the weighted crowding distance and (2) WMO-ASMO outperforms NSGAII and WNSGAII in terms of better solutions (annual power generation (530.032billionkWh) and ecological index (1.675)) with 1000 simulations and computational time reduced by 25% (from 10h to 8h) with 500 simulations. Therefore, the proposed method is proved to be more efficient and could provide better Pareto frontier.
The accuracy of predicting the behaviour of structure using finite element (FE) depends widely on the precision of the evaluation of the stiffness matrix. In the present article, an attempt has been ...made to evaluate the stiffness matrix of functionally graded (FG) nanoplate using Gaussian process regression (GPR) based surrogate model in the framework of the layerwise theory. The stiffness matrix comprises various matrix terms corresponding to the membrane, membrane-bending, bending-membrane, and bending and shear. Following two different methodologies are adopted for predicting the stiffness matrix at the elemental level, one in which the final elemental stiffness matrix is evaluated, and the second one in which all the matrix terms as stated are evaluated separately using the GPR surrogate model and then are added to get the final stiffness matrix at the elemental level. The effectiveness of both approaches has been worked out by comparing the present results with those available in the literature. Both the proposed methodologies can predict the behaviour of FG nanoplates with good accuracy. However, the second one is found to be outstanding.
•An active learning method for structural reliability analysis is proposed.•Deep neural network is applied to select candidate experimental points.•A novel weight coefficient of experimental point is ...proposed.•The active learning method can be used for other surrogate models.
Owing to the tremendous computational cost of simulation for large-scale engineering structures, surrogate model method is widely used as a sample classifier in structural reliability analyses. However, the accuracy and efficiency of the surrogate model methods heavily depend on the selection of the experimental points that are used to train the surrogate model. Most of the traditional selection methods do not consider the location information of the Monte Carlo population, which results in a large number of experimental points being selected in unimportant areas. In this study, an active learning method is proposed to address the issues; the selected experimental points are located in the interface of the safety and failure Monte Carlo populations. The proposed active learning method combines the deep neural network (DNN) model and the weighted sampling method to iteratively select new experimental points and update the DNN model. In each iteration, the DNN model is updated to select candidate experimental points near the limit state surface (LSS), and the weighted sampling method is used to select new experimental points from the candidate experimental points. To make the selected experimental points be uniformly distributed in the sampling space, a novel weight coefficient based on the sample probability density is proposed. The numerical examples demonstrate that the proposed method has high accuracy and efficiency in handling multi-variable, nonlinearity and larger-scale engineering structure problems.
Heterogeneity and uncertainty in a composite microstructure lead to either computational bottlenecks if modeled rigorously or to solution inaccuracies in the stress field and failure predictions if ...approximated. Although methods suitable for analyzing arbitrary and non-linear microstructures exist, their computational cost makes them impractical to use in large-scale structural analysis. Surrogate models or Reduced Order Models (ROMs) commonly enhance efficiencies but are typically calibrated with a single microstructure. Homogenization methods, such as the Mori–Tanaka method, offer rapid homogenization for a wide range of constituent properties. However, simplifying assumptions, like stress and strain averaging in phases, render the consideration of both deterministic and stochastic variations in microstructure infeasible. This paper illustrates a transformer neural network architecture that captures the knowledge of various microstructures and constituents, enabling it to function as a computationally efficient homogenization surrogate model. Given an image or an abstraction of an arbitrary composite microstructure of linearly elastic fibers in an elastoplastic matrix, the transformer network predicts the history-dependent, non-linear, and homogenized stress–strain response. Two methods for encoding microstructure features were tested: calculating two-point statistics using Principal Component Analysis (PCA) for dimensionality reduction and employing an autoencoder with a Convolutional Neural Network (CNN). Both methods accurately predict the homogenized material response. The developed transformer neural network offers an efficient means for microstructure-to-property translation, generalizable and extendable to a variety of microstructures. The paper describes the network architecture, training and testing data generation, and performance under cycling and random loadings.
Understanding wood characteristics is essential for enhancing the economic sustainability of the kraft process. In a recent work, we included wood characteristics in the phenomenological modeling of ...digesters. The developed model allows the optimization of the process. Here, we propose a constrained multi-objective optimization approach to minimize the residual lignin content while maximizing the carbohydrate content in the cellulose pulp, using the Non-dominated Sorting Genetic Algorithm II. In order to reduce computational costs during the optimization, we developed a surrogate model, based on simulated data, to predict key performance indicators. We evaluated two machine learning techniques: Multilayer Perceptron (MLP) and decision tree-based methods, considering single and multiple outputs. The combination between the multiple-output approach and MLP performed well and resulted in a more simplified surrogate model. The results for the simulation and the surrogate model were similar, and the computational cost was approximately 50 times lower for the surrogate model. An uncertainty was associated with the multiplicative factor of the delignification rate as a way to observe how its estimate interferes with the Pareto curve. The present work presents contributions to data-driven modeling and multi-objective optimization of digesters, allowing us to determine the importance of wood characteristics in operation.
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•Two MLP neural networks with multiple outputs were chosen as the surrogate model.•NSGA II was used to solve a multi-objective optimization problem with constraints.•The surrogate model was faster than the phenomenological model, with similar results.•The S/G ratio was the standout wood characteristic, emphasizing its importance.•Uncertainties in a kinetic parameter showed a significant impact on the Pareto curve.
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