AI-based software toolkit for finite element modeling of aerospace structures based on Convolutional Hierarchical Deep-l Learning Neural Network- Artificial Intelligence (C-HiDeNN-AI)

Finite Element Method (FEM) is more integral to the engineering process than ever before, Ýthough it remains rooted in the Engineering Software 1.0 paradigm, where users manually specify each step of the computational workflow. This concept aligns with "Software 1.0," as described by Andrej Karpathy (Tesla, OpenAI), in which software behavior is explicitly programmed by humans. Karpathy's "Software 2.0" envisions a shift where users define the overall desired outcomes, and machine learning (ML) algorithms generate the underlying logic automatically. This transition gives rise to Engineering Software 2.0 (ES2.0), where artificial intelligence (AI) and ML are used to automate learning, calibration, and solution processes into engineering workflows, including FEM, removing user bias and many other errors. This ES2.0 vision as an integration of AI/ML into approaches like FEM is supported by leading voices in industry. Stephen Wolfram (Mathematica) suggests combining AI with computational methods as the best approach to advance science, and researchers at Google DeepMind write that AI will enhance, rather than replace, traditional numerical modeling approaches.ÝWe propose an AI-based toolkit grounded in the ES2.0 paradigm and Convolutional FEM (C-FEM), an AI/ML technology developed under Wing Kam Liu at Northwestern University and at HIDENN-AI, LLC. C-FEM can provide instantaneous physics-based solutions to a dense spatial, parametric, and temporal space with AI/ML through automated and optimized mesh generation from geometric input lists (e.g., CAD) and by assessing accuracy impact and providing error mitigation advice via cutting-edge supervised and unsupervised learning techniques.ÝKey capabilities of the proposed C-FEM framework include: (1) Automated, adaptive CAD-to-mesh generationÝvia HiDeNN-FEM, which enables CAD-aware automatic rh-adaptivity for mitigating discretization and geometrical approximation errors; (2) Linear meshes capable of arbitrary polynomial reproducing order with high smoothness, alleviating element formulation errors; (3) Interpretable, adaptive neural network structure with trainable element-wise hyperparameters such as patch size, polynomial order, and activation functions that are optimized via unsupervised and reinforcement learning to minimize modeling errors; (4) Built-in post-processing accuracy as C-FEMís interpolation framework preserves solution fidelityÝwhen the node-wise FEM solutions are interpolated for post-processing; (5) Multiscale coupling viaÝSelf-consistent Clustering Analysis (SCA) enhancing computational efficiency and reducing material modeling errors; and (6) Scalable hardware-accelerated approach by combining ML/AI hardware and software.ÝThis project aims to advance FEM simulation tools for aerospace structures by transforming FEM modeling into an automated, efficient, and accurate AI-driven analysis framework suitable for forward and inverse problems and optimization tasks.Ý