Multi-physics Simulation Guided Generative Diffusion Models with Applications in Fluid and Heat Dynamics

2024-07-25

AI Summary

Calibrating multi-fidelity physics simulations against real-world observations remains challenging—particularly when high-fidelity simulations are unavailable or suffer from simplification-induced distortions. To address this, we propose the Multi-fidelity Physics-guided Diffusion Model (MPDM), the first framework enabling real-time injection of low-cost simulation context while dynamically integrating guidance from high-cost simulation outputs. MPDM adopts a decoupled conditional diffusion training paradigm, theoretically guaranteeing an upper bound on approximation error under the Wasserstein metric and enabling natural uncertainty quantification. The method synergistically combines Bayesian conditional modeling, multi-fidelity simulation ensembling, and guided denoising sampling. Evaluated on fluid dynamics and laser powder bed fusion thermal evolution tasks, MPDM achieves significant improvements in predictive accuracy and generalization—demonstrating robust performance even under imperfect simulations or sparse observational data.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Diffusion Models for Vision

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

In this paper, we present a generic physics-informed generative model called MPDM that integrates multi-fidelity physics simulations with diffusion models. MPDM categorizes multi-fidelity physics simulations into inexpensive and expensive simulations, depending on computational costs. The inexpensive simulations, which can be obtained with low latency, directly inject contextual information into DDMs. Furthermore, when results from expensive simulations are available, MPDM refines the quality of generated samples via a guided diffusion process. This design separates the training of a denoising diffusion model from physics-informed conditional probability models, thus lending flexibility to practitioners. MPDM builds on Bayesian probabilistic models and is equipped with a theoretical guarantee that provides upper bounds on the Wasserstein distance between the sample and underlying true distribution. The probabilistic nature of MPDM also provides a convenient approach for uncertainty quantification in prediction. Our models excel in cases where physics simulations are imperfect and sometimes inaccessible. We use a numerical simulation in fluid dynamics and a case study in heat dynamics within laser-based metal powder deposition additive manufacturing to demonstrate how MPDM seamlessly integrates multi-idelity physics simulations and observations to obtain surrogates with superior predictive performance.

Problem

• Calibrating multi-fidelity physics simulations with diffusion models
• Reducing reliance on expensive simulations for training
• Improving predictive accuracy with uncertainty quantification

Innovation

• Diffusion-based surrogate for multi-fidelity calibration
• Guided diffusion refines samples from expensive simulations
• Bayesian models with theoretical guarantees on distribution