用去噪模型隐式学习物理系统解空间,提升精度与物理一致性。
Conditional Denoising Model as a Physical Surrogate Model
- 通过去噪训练让模型学习物理解的几何结构,自动对齐约束。
- 在等离子体基准上参数效率更高,且无需显式物理损失仍更守恒。
- 适合需要高物理保真度的科学建模场景,如气候、材料模拟。
复杂物理系统的代理建模常面临数据拟合精度与物理一致性之间的权衡。现有物理一致方法通常将物理定律作为损失函数中的软约束,难以严格满足控制方程,或依赖后处理修正,无法内在学习解空间几何。为此,我们提出条件去噪模型(Conditional Denoising Model, CDM),一种旨在学习物理流形几何的生成模型。通过训练网络从噪声状态中恢复清洁状态,模型学习到一个指向有效解子空间的连续向量场。我们引入时间无关的公式,将推理转化为确定性的定点迭代,实现对噪声近似值的投影。在低温等离子体物理与化学基准测试中,CDM在参数和数据效率上均优于物理一致基线。关键发现是:去噪目标起到了强大隐式正则化作用——即使训练中未接触控制方程,其遵守物理约束的能力仍强于显式加入物理损失的基线。
原文摘要 · Abstract (English)
Surrogate modeling for complex physical systems typically faces a trade-off between data-fitting accuracy and physical consistency. Physics-consistent approaches typically treat physical laws as soft constraints within the loss function, a strategy that frequently fails to guarantee strict adherence to the governing equations, or rely on post-processing corrections that do not intrinsically learn the underlying solution geometry. To address these limitations, we introduce the {Conditional Denoising Model (CDM)}, a generative model designed to learn the geometry of the physical manifold itself. By training the network to restore clean states from noisy ones, the model learns a vector field that points continuously towards the valid solution subspace. We introduce a time-independent formulation that transforms inference into a deterministic fixed-point iteration, effectively projecting noisy approximations onto the equilibrium manifold. Validated on a low-temperature plasma physics and chemistry benchmark, the CDM achieves higher parameter and data efficiency than physics-consistent baselines. Crucially, we demonstrate that the denoising objective acts as a powerful implicit regularizer: despite never seeing the governing equations during training, the model adheres to physical constraints more strictly than baselines trained with explicit physics losses.
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