Core Concepts
物理情報を取り入れた拡散モデルは、生成されたサンプルが特定の制約条件に従うようにモデルをトレーニングする新しいアプローチであり、標準的な拡散モデルと比較して生成されたサンプルの残差エラーを大幅に削減します。
Abstract
Abstract:
Generative models like denoising diffusion models are advancing in approximating complex data distributions.
A framework is presented to inform denoising diffusion models on underlying constraints during training.
Incorporating constraints during training improves sample alignment and provides regularization against overfitting.
1. Introduction:
Denoising diffusion models learn intricate data distributions across various modalities.
Diffusion models have been used for upscaling low-fidelity data and designing new molecules or materials.
Traditional diffusion models do not strictly enforce intrinsic constraints, leading to potential issues in scientific applications.
2. Background:
Denoising diffusion models convert samples from a simple prior to a sample from an unknown data distribution.
Physical laws are formulated as PDEs over a domain, with boundary conditions and solution fields satisfying the PDEs.
3. Physics-informed diffusion models:
The model must learn a distribution whose samples comply with governing equations like PDEs.
Virtual observables are introduced to enforce residual minimization during training.
Inequality constraints can also be incorporated into the loss function.
4. Experiments:
Toy problem: Demonstrates implications of physics-informed loss on learning a distribution that adheres to an algebraic constraint.
Darcy flow: Evaluates performance of physics-informed model in reducing residual error compared to standard diffusion models.