Conditional Denoising Model as a Physical Surrogate Model

2026-01-28

AI Summary

This work addresses the longstanding challenge in surrogate modeling of physical systems, where achieving high data-fitting accuracy while preserving strict physical consistency remains difficult, as existing methods often fail to rigorously satisfy governing equations. The authors propose a Conditional Denoising Model (CDM), which, for the first time, leverages denoising generative models to learn the geometric structure of physical manifolds. By employing a time-independent deterministic fixed-point iteration, CDM projects predicted solutions onto the physically feasible space without explicitly incorporating physical equations, thereby implicitly enforcing physical constraints and overcoming limitations of conventional soft-constraint or post-processing approaches. Evaluated on benchmark problems in low-temperature plasma physicochemical modeling, CDM demonstrates superior parameter and data efficiency compared to physics-consistent baselines, while adhering more strictly to underlying physical constraints.

Technology Category

• Machine Learning: Learning with Manifolds
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

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.

Problem

• surrogate modeling
• physical consistency
• physics-informed learning
• denoising model
• manifold learning

Innovation

• Conditional Denoising Model
• physical surrogate modeling
• manifold learning
• physics-informed machine learning
• fixed-point iteration