Physics-Informed Diffusion Models
Jan-Hendrik Bastek WaiChing Sun Dennis Kochmann
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied data distribution are expected to adhere to specific governing equations. We present a framework that unifies generative modeling and partial differential equation fulfillment by introducing a first-principle-based loss term that enforces generated samples to fulfill the underlying physical constraints. Our approach reduces the residual error by up to two orders of magnitudes compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. Our framework is simple to implement and versatile in its applicability for imposing equality and inequality constraints as well as auxiliary optimization objectives. Code is available at https://github.com/jhbastek/PhysicsInformedDiffusionModels.
physics-informed, scientific machine learning, denoising diffusion, inverse problems, generative modeling
We introduce a framework that unifies diffusion models with physics-informed neural networks and significantly improves the adherence of generated samples to physical laws.