🤖 AI Summary
This work addresses the high computational cost of traditional finite element methods in simulating path-dependent constitutive models—such as plasticity—over complex geometries, and the inability of existing generative models to efficiently produce high-resolution stress fields. The authors formulate path-dependent plasticity simulation as a video generation task and propose a Transformer-based flow-matching model operating in the latent space of a variational autoencoder to generate full time-series stress fields in a single forward pass. Innovatively employing a non-Gaussian source distribution to reduce intersecting conditional transport paths, and integrating token-level load embeddings with two auxiliary networks, the method achieves high-fidelity, single-step generation without requiring distillation. Evaluated on limited training data, the approach accurately synthesizes high-resolution stress fields and demonstrates a 6–7× speedup over finite element simulations on CPUs and nearly two orders of magnitude acceleration on consumer-grade GPUs.
📝 Abstract
Physical simulations for intricate geometries with path-dependent constitutive models face difficulties due to the enormous computational cost they require. Recently, the emergence of generative AI models, which succeed in image and video synthesis tasks, has provided a promise to further improve simulations. Although U-Net-based denoising diffusion probabilistic models (DDPMs) have been adopted for elastic stress field generation, they typically require hundreds of sampling steps, and applications of generative models to path-dependent, e.g. plastic, stress fields remain very limited. In this work, we propose a novel flow matching (FM) model based on a transformer backbone for high-resolution path-dependent stress field generation with stochastic loading-unloading paths and geometry. The proposed model operates within the latent space of a variational autoencoder (VAE) and formulates the simulation of plastic fields as a video synthesis task, directly generating the stress fields across all time steps. Meanwhile, we design a non-Gaussian source distribution for flow matching, such that crossings among conditional transport paths are reduced during training. This enables our model to generate satisfactory samples in one step without relying on distillation. In addition, we introduce token-level loading embeddings and two auxiliary networks to further enhance the model performance in path-dependent simulation. The results demonstrate that, even with a limited training dataset, our model can accurately generate high-resolution path-dependent fields. It is much more computationally efficient than finite element analysis, providing a speedup of 6 to 7 times over FEM on CPUs and approximately two orders of magnitude speedup on consumer-grade GPUs.