Temel Kavramlar
Informing diffusion models with physics constraints improves accuracy and generalization.
Özet
The content discusses the application of denoising diffusion models in scientific machine learning, focusing on incorporating physics constraints during model training. The framework presented significantly reduces residual errors and enhances model robustness against overfitting. Different approaches are compared, highlighting the effectiveness of the proposed physics-informed diffusion model.
Abstract:
- Generative models like denoising diffusion models are advancing rapidly.
- A framework is introduced to inform these models about underlying constraints during training.
- Results show improved alignment with constraints and reduced overfitting.
Introduction:
- Denoising diffusion models excel in learning complex data distributions.
- Applications extend to various domains like image generation and material design.
- Traditional training methods lack strict enforcement of intrinsic constraints.
Contributions:
- Novel approach informs denoising diffusion models on PDE constraints during training.
- Demonstrated reduction in PDE residual compared to state-of-the-art methods.
- Additional training objective acts as effective regularization against overfitting.
Background:
- Denoising diffusion models convert samples from a simple prior to unknown data distribution.
- Physical laws formulated as PDEs are considered as equality constraints for generated samples.
Physics-informed Diffusion Models:
- Scenario explored where generative diffusion model must learn a distribution adhering to governing equations.
- Proposed method significantly reduces residual error compared to standard setup and earlier frameworks.
Related Work:
- Comparison with recent contributions by Shu et al. [12] and Jacobsen et al. [22].
- Highlighting the effectiveness of embedding physical consistency within the training process.
Alıntılar
"We present a novel, theoretically motivated approach that informs denoising diffusion models on PDE constraints of generated samples during model training."
"Our approach significantly reduces the residual error of generated samples compared to the standard setup."