Crystal plasticity (CP) model is a vital tool for understanding structure–property relations, but it is computationally expensive. Hence, data-driven models have been used as surrogate. We proposed a Deep Operator Network (DeepONet) to predict polycrystal stress–strain response. It employs a convolutional network to encode microstructure. To account for different material properties and boundary conditions, we proposed using single-crystal responses as inputs to the branch, furnishing a material-response-informed DeepONet. This is the most novel contribution. We demonstrate that our model can be trained on one material and loading and generalized to new conditions via transfer learning. Results show that using single-crystal responses as input outperforms a similar model using material properties and overcomes limitations with changing boundary conditions. The new model achieved a R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2$$\end{document} value of above 0.99, and over 95% of predicted stresses have a relative error of ≤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\le $$\end{document} 5%, indicating superior accuracy. With as few as 20 new data and under 1 min training time, the DeepONet can be fine-tuned to generate accurate predictions on different materials and loadings. The prediction speed is 104\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{4}$$\end{document} times faster than CP simulations. The efficiency and generalizability of DeepONet render it a powerful data-driven surrogate to bridge scale gaps in multi-scale analyses.

The deep operator network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models in the branch of DeepONet to predict final solutions given time-dependent inputs. In the current work, the S-DeepONet architecture is extended by modifying the information combination mechanism between the branch and trunk networks to simultaneously predict vector solutions with multiple components at multiple time steps of the evolution history, which is the first in the literature using DeepONets. Two example problems, one on transient fluid flow and the other on path-dependent plastic loading, were shown to demonstrate the capabilities of the model to handle different physics problems. The use of a trained S-DeepONet model in inverse parameter identification via the genetic algorithm is shown to demonstrate the application of the model. In almost all cases, the trained model achieved an R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2$$\end{document} value of above 0.99 and a relative L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document} error of less than 10% with only 3200 training data points, indicating superior accuracy. The vector S-DeepONet model, having only 0.4% more parameters than a scalar model, can predict two output components simultaneously at an accuracy similar to the two independently trained scalar models with a 20.8% faster training time. The S-DeepONet inference is at least three orders of magnitude faster than direct numerical simulations, and inverse parameter identifications using the trained model are highly efficient and accurate.

The deep energy method (DEM), a type of physics-informed neural network, is evolving as an alternative to finite element analysis. It employs the principle of minimum potential energy to predict an object’s behavior under various boundary conditions. However, the model’s accuracy is contingent upon choosing the appropriate architecture for the model, which can be challenging due to the high interactions between hyperparameters, large search space, difficulty in identifying objective functions, and non-convex relationships with the objective functions. To improve DEM’s accuracy, we first introduce random Fourier feature (RFF) mapping. RFF mapping helps during the model’s training by reducing bias toward high frequencies. The effects of six hyperparameters are then studied under static compression, tension, and bending loads in planar linear elasticity. Based on this study, a systematic automated hyperparameter optimization approach is proposed. Due to the high interaction between hyperparameters and the non-convex nature of the optimization problem, Bayesian optimization algorithms are used. The models trained using optimized hyperparameters and having Fourier feature mapping can accurately predict deflections compared to finite element analysis. Additionally, the deflections obtained for tension and compression load cases are more sensitive to variations in hyperparameters than bending.

A state-of-the-art large eddy simulation code has been developed to solve compressible flows in turbomachinery. The code has been en-gineered with a high degree of scalability, enabling it to effectively leverage the many-core architecture of the new Sunway system. A consistent performance of 115.8 DP-PFLOPs has been achieved on a high-pressure turbine cascade consisting of over 1.69 billion mesh elements and 865 billion Degree of Freedoms (DOFs). By leveraging a high-order unstructured solver and its portability to large hetero-geneous parallel systems, we have progressed towards solving the

This paper introduces Cybershuttle, a new type of user-facing cyberinfrastructure that provides seamless access to a range of resources for researchers, enhancing their productivity. The Cybershuttle Research Environment is built on open source Apache Airavata software and uses a hybrid approach that integrates locally deployed agent programs with centrally hosted middleware. This enables end-to-end integration of computational science and engineering research across a range of resources, including users’ local resources, centralized university computing and data resources, computational clouds, and NSF-funded national-scale computing centers. To ensure a user-centered approach, we have designed the scientific user environments with the best user-centered design practices.

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to solution functions in contrast to classical neural networks that need re-training for every new set of parametric inputs. In this work, we have extended the classical formulation of DeepONets by introducing sequential learning models like the gated recurrent unit (GRU) and long short-term memory (LSTM) in the branch network to allow for accurate predictions of the solution contour plots under parametric and time-dependent loading histories. Two example problems, one on transient heat transfer and the other on path-dependent plastic loading, were shown to demonstrate the capabilities of the new architectures compared to the benchmark DeepONet model with a feed-forward neural network (FNN) in the branch. Despite being more computationally expensive, the GRU- and LSTM-DeepONets lowered the prediction error by half (0.06\% vs. 0.12\%) compared to FNN-DeepONet in the heat transfer problem, and by 2.5 times (0.85\% vs. 3\%) in the plasticity problem. In all cases, the proposed DeepONets achieved a prediction $R^2$ value of above 0.995, indicating superior accuracy. Results show that once trained, the proposed DeepONets can accurately predict the final full-field solution over the entire domain and are at least two orders of magnitude faster than direct finite element simulations, rendering it an accurate and robust surrogate model for rapid preliminary evaluations.

A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk network is devised to predict full-field highly nonlinear elastic-plastic stress response for complex geometries obtained from topology optimization under variable loads. The proposed DeepONet uses a ResUNet in the trunk to encode complex input geometries, and a fully-connected branch network encodes the parametric loads. Additional information fusion is introduced via an element-wise multiplication of the encoded latent space to improve prediction accuracy further. The performance of the proposed DeepONet was compared to two baseline models, a standalone ResUNet and a DeepONet with fully connected networks as the branch and trunk. The results show that ResUNet and the proposed DeepONet share comparable accuracy; both can predict the stress field and accurately identify stress concentration points. However, the novel DeepONet is more memory efficient and allows greater flexibility with framework architecture modifications. The DeepONet with fully connected networks suffers from high prediction error due to its inability to effectively encode the complex, varying geometry. Once trained, all three networks can predict the full stress distribution orders of magnitude faster than finite element simulations. The proposed network can quickly guide preliminary optimization, designs, sensitivity analysis, uncertainty quantification, and many other nonlinear analyses that require extensive forward evaluations with variable geometries, loads, and other parameters. This work marks the first time a ResUNet is used as the trunk network in the DeepONet architecture and the first time that DeepONet solves problems with complex, varying input geometries under parametric loads and elasto-plastic material behavior.

Triply periodic minimal surface (TPMS) metamaterials characterized by mathematically-controlled topologies exhibit better mechanical properties compared to uniform structures. The unit cell topology of such metamaterials can be further optimized to improve a desired mechanical property for a specific application. However, such inverse design involves multiple costly 3D finite element analyses in topology optimization and hence has not been attempted. Data-driven models have recently gained popularity as surrogate models in the geometrical design of metamaterials. Gyroid-like unit cells are designed using a novel voxel algorithm, a homogenization-based topology optimization, and a Heaviside filter to attain optimized densities of 0-1 configuration. Few optimization data are used as input-output for supervised learning of the topology optimization process from a 3D CNN model. These models could then be used to instantaneously predict the optimized unit cell geometry for any topology parameters, thus alleviating the need to run any topology optimization for future design. The high accuracy of the model was demonstrated by a low mean square error metric and a high dice coefficient metric. This accelerated design of 3D metamaterials opens the possibility of designing any computationally costly problems involving complex geometry of metamaterials with multi-objective properties or multi-scale applications.

Abstract The paper explores the possibility of using the novel Deep Operator Networks (DeepONet) for forward analysis of numerically intensive and challenging multiphysics designs and optimizations of advanced materials and processes. As an important step towards that goal, DeepONet networks were devised and trained on GPUs to solve the Poisson equation (heat-conduction equation) with the spatially variable heat source and highly nonlinear stress distributions under plastic deformation with variable loads and material properties. Since DeepONet can learn the parametric solution of various phenomena and processes in science and engineering, it was found that a properly trained DeepONet can instantly and accurately inference thermal and mechanical solutions for new parametric inputs without re-training and transfer learning and several orders of magnitude faster than classical numerical methods.