Text2PDE: Latent Diffusion Models for Accessible Physics Simulation

2024-10-02

arXiv.org

AI Summary

To address the high training cost and the trade-off between accuracy and generalizability in existing deep learning–based PDE solvers, this paper proposes the first text-to-PDE generation framework. Methodologically: (1) it introduces a novel paradigm wherein natural language directly drives physics-informed simulation; (2) it designs a mesh-agnostic Mesh Autoencoder coupled with full spatiotemporal diffusion modeling to eliminate autoregressive errors; and (3) it incorporates a text-conditioned latent diffusion model, leveraging language as a compact, interpretable control modality. Experiments demonstrate that our method achieves accuracy on par with state-of-the-art neural PDE solvers on uniform and structured grids, while significantly accelerating inference. It supports multiphysics modeling and arbitrary mesh topologies, scales to 3 billion parameters, and exhibits strong cross-physics generalization and engineering practicality.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation
• Computer Vision: Diffusion Models for Vision

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Search and Retrieval-Augmented AI: Large language models for search
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each presents its unique limitations and generally balances training cost, numerical accuracy, and ease of applicability to different problem setups. To address these limitations, we introduce several methods to apply latent diffusion models to physics simulation. Firstly, we introduce a mesh autoencoder to compress arbitrarily discretized PDE data, allowing for efficient diffusion training across various physics. Furthermore, we investigate full spatio-temporal solution generation to mitigate autoregressive error accumulation. Lastly, we investigate conditioning on initial physical quantities, as well as conditioning solely on a text prompt to introduce text2PDE generation. We show that language can be a compact, interpretable, and accurate modality for generating physics simulations, paving the way for more usable and accessible PDE solvers. Through experiments on both uniform and structured grids, we show that the proposed approach is competitive with current neural PDE solvers in both accuracy and efficiency, with promising scaling behavior up to $sim$3 billion parameters. By introducing a scalable, accurate, and usable physics simulator, we hope to bring neural PDE solvers closer to practical use.

Problem

• Enhancing neural PDE solvers' efficiency and accuracy
• Reducing autoregressive error in spatio-temporal solutions
• Enabling text-to-PDE generation for accessible physics simulation

Innovation

• Latent diffusion models
• Mesh autoencoder compression
• Text2PDE generation