N252-088 TITLE: Advanced Artificial Intelligence/Machine Learning-based Intelligent Agent for Finite Element Modeling of Aerospace Structures

OUSD (R&E) CRITICAL TECHNOLOGY AREA(S): Advanced Computing and Software;Sustainment;Trusted AI and Autonomy

OBJECTIVE: Develop an advanced Artificial Intelligence/Machine Learning (AI/ML)-based intelligent agent to automate the generation, prediction, and optimization of finite element models, with the ability to accurately account for model errors, enhance modeling fidelity, and reduce user input bias.

DESCRIPTION: Finite Element Analysis (FEA) is a critical computational tool used across a spectrum of engineering disciplines, including, but not limited to, automotive, aeronautical, civil engineering, and biomedical engineering. FEA enables the prediction of the behavior of materials and systems in response to various physical effects such as mechanical stress, strain, heat transfer, fluid flow, and electrostatics. This computational method has empowered engineers with the ability to develop safer and more efficient designs, optimize systems, and predict failure points, significantly reducing the need for physical prototypes and expensive testing procedures. However, the process of building a Finite Element Model (FEM) is subject to multiple sources of errors, including discretization error, errors from geometrical approximation, errors due to assumptions in material modeling, element formulation selection, and errors from inaccurately represented boundary conditions. The iterative process related to model development helps to better understand the physics and mechanical behavior in the actual assembled system, and better understanding is the purpose of FEM and FEA. The intelligence gained through the iterative modeling process often reveals complexities and system effects that can and should be added into the model to achieve accurate physical behavior or acceptable calibration to the physical system. While conventional error mitigation strategies such as mesh refinement techniques, manual error checking, and model validation against experimental data do exist, these methods can be time-intensive, require extensive human intervention, and may still result in biased results due to user subjectivity. In recent years, AI/ML methods such as Generative Adversarial Networks (GANs), Deep Reinforcement Learning, Machine Vision, and Artificial Neural Networks (ANNs) have demonstrated significant potential to revolutionize the FEM/FEA fields. These advanced computational methods offer the ability to automate model generation, accurately predict and mitigate modeling errors, and streamline the process, thereby significantly reducing human intervention and the associated subjectivity. However, a comprehensive, integrated framework utilizing these AI/ML methods for finite element modeling, accuracy modeling impact assessment, and model optimization is lacking.

The Navy seeks to develop a comprehensive AI/ML software toolkit that can transform an input geometry list to generate the finite elements and nodes used in the FEM input deck automatically. The toolkit will estimate the accuracy impact, optimize the model parameters for enhanced fidelity, ensure the meshing process matches the problem, be efficient, and be free from user input bias. The Navy seeks a software toolkit that can refine the ML models based on the outcomes of these tests. The goal is to improve the system's predictive accuracy and error mitigation advice. With constant learning and adjustment, the system will progressively improve and adapt to handle more complex and varied finite element models. The successful completion of Phase II will provide an advanced prototype system capable of automatically generating FEM input decks from input geometry lists, assessing accuracy impact, and providing strategies for error mitigation, thus enhancing the fidelity of finite element modeling processes.

The envisioned AI/ML software toolkit will be capable of handling complex geometries and boundary conditions, accurately representing material behaviors, and robustly accounting for various physical phenomena. Furthermore, the toolkit will provide a user-friendly interface, streamline the workflow of finite element modeling, and effectively communicate results to the user, enabling them to make informed decisions. The toolkit will encapsulate modern AI/ML techniques such as GANs, Deep Reinforcement Learning, Machine Vision, and ANNs.

The system's capabilities will include detecting and analyzing the source of errors in the FEMs, assessing these errors, and offering insights into how to mitigate them. A comprehensive series of tests will be conducted to assess the performance of the prototype system. These will include various scenarios and geometries to ensure the system can handle a broad spectrum of FEM tasks.

To validate the designed system, a basic prototype is needed to demonstrate the core functionalities. This prototype will facilitate the automation of simple finite models' generation from existing CAD data and demonstrate the potential of AI/ML techniques in predicting and mitigating modeling errors. An example of this would be the impact of element size, type, and transition on accuracy.

Additionally, the small business awardee will develop a detailed verification and validation (V & V) test plan, which will define clear, measurable metrics and benchmarks that can be used to quantitatively assess the toolkit's performance and effectiveness. The plan will also aid in identifying areas for potential improvements and modifications in the following phases.

PHASE I: Develop a concept for an AI/ML-driven software toolkit. Demonstrate technical feasibility of the proposed concept for automating finite element meshing, creating nodes and elements, predicting potential accuracy impact, and optimizing models for improved accuracy and fidelity. Prove feasibility of the proposed concept by first performing in-depth study of the current state of finite element modeling processes and the inherent error sources, including those not addressed by meshing alone (i.e., post-processing methodology, boundary condition errors, misrepresentation of the structural behavior, etc.). This study would guide the design and development of the AI/ML-driven toolkit, ensuring that the toolkit robustly accounts for the most significant error sources. This toolkit will encapsulate modern AI/ML techniques such as GANs, Deep Reinforcement Learning, Machine Vision, and ANNs. The focus would be on creating a road map for how these AI/ML techniques can be integrated and utilized to automate the model generation process, predict potential modeling accuracy impact, and optimize the model parameters.

The Phase I effort will include prototype plans to be developed under Phase II.

PHASE II: Devise an AI/ML software toolkit. Design and develop a prototype intelligent support system utilizing the AI/ML software toolkit. Focus on effectively integrating these methods into an automated software system that can handle geometric transformations for FEM input deck generation and offer a standardized process without user input bias. Ensure that the toolkit will address the problem of model uncertainty prediction in mixed fidelity FEMs.

PHASE III DUAL USE APPLICATIONS: Transition validated AI/ML modeling toolkit to integrate with existing FE engineering analysis tools.

FEA is widely used in aerospace, automotive, trucking, heavy equipment companies, medical reconstruction in a vast plethora of private sectors. The benefits to the private sector would be confidence in FEA solutions in a variety of domains including structural mechanics, fluid flow analysis, heat conduction, additive manufacturing, electrical and electronics field, bio-engineering, and so forth. The reduction in cost in these fields makes this topic highly beneficial to the private sector. Dropping the costs and turn-around time for analyses will allow additional opportunities for analysis arising from the decreased cost threshold. This toolkit will improve analysis availability across the entire domain of manufacturing.

REFERENCES:

1. Bathe, K.-J. "Finite element procedures." Klaus-Jurgen Bathe, 2006. https://www.worldcat.org/title/963526772
2. Goodfellow, I.; Bengio, Y. and Courville, A. "Deep learning." MIT press, 2016. https://www.amazon.com/Deep-Learning-Adaptive-Computation-Machine/dp/0262035618/ref=sr_1_1?keywords=9780262337373&linkCode=qs&qid=1694019496&s=books&sr=1-1
3. Lipton, Z. C.; Berkowitz, J. and Elkan, C. "A critical review of recurrent neural networks for sequence learning." arXiv preprint arXiv:1506.00019, 2015. https://arxiv.org/abs/1506.00019
4. Lu, L.; Jin, P. and Karniadakis, G. E. "Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators." arXiv preprint arXiv:1910.03193, 2019. https://arxiv.org/abs/1910.03193
5. Zhu, Y.; Zabaras, N.; Koutsourelakis, P. S. and Perdikaris, P. "Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data." Journal of Computational Physics, 394, 2019, pp. 56-81. https://doi.org/10.1016/j.jcp.2019.05.024
6. Hughes, T. J. "The finite element method: linear static and dynamic finite element analysis." Courier Corporation, 2012. https://www.amazon.com/s?k=9780486135021&i=stripbooks&linkCode=qs
7. Zhu, Y. and Zabaras, N. "Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification." Journal of Computational Physics, 366, 2018, pp. 415-447.https://doi.org/10.1016/j.jcp.2018.04.018
8. Chollet, F. "Deep learning with Python." Manning, 2021. https://www.amazon.com/Learning-Python-Second-Fran%C3%A7ois-Chollet/dp/1617296864/ref=sr_1_3?keywords=9781617296864&linkCode=qs&qid=1694020165&s=books&sr=1-3
9. Long, J., Shelhamer, E., & Darrell, T. "Fully convolutional networks for semantic segmentation". Proceedings of the IEEE conference on computer vision and pattern recognition, 2015, pp. 3431-3440. https://openaccess.thecvf.com/content_cvpr_2015/html/Long_Fully_Convolutional_Networks_2015_CVPR_paper.html
10. Goodfellow, I.; Pouget-Abadie, J.;, Mirza, M.; Xu, B.; Warde-Farley, D.; Ozair, S.;, Courville, A. and Bengio, Y. "Generative adversarial nets." Advances in neural information processing systems, 27, 2014. https://proceedings.neurips.cc/paper_files/paper/2014/hash/5ca3e9b122f61f8f06494c97b1afccf3-Abstract.html
11. Kohar, C. P.; Greve, L.; Eller, T. K.; Connolly, D. S. and Inal, K. "A machine learning framework for accelerating the design process using CAE simulations: An application to finite element analysis in structural crashworthiness." Computer Methods in Applied Mechanics and Engineering, 385, 1 November 2021, 114008. https://doi.org/10.1016/j.cma.2021.114008

KEYWORDS: Finite Element Analysis; Artificial Intelligence / Machine Learning; Solid Structural Mechanics Stress; Preprocessing and Post Processing; Manual Effort and Manual Review; Shape Function and Numerical Integration Points; Particular Stress Regions

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