Physical consistency improved by anchoring source noise in flow matching
Source Anchoring for Physical Consistency in Flow Matching Models
Machine LearningArtificial Intelligence
Summary
Generating realistic simulations of physical systems is hard because the results must obey the laws of physics. The researchers studied a new trick: instead of fixing problems after making noisy guesses, they adjust the initial guesses so they naturally follow physical rules. This method, called Source Anchoring for Physical Consistency, makes the simulations more accurate and physically realistic. They tested it on several challenging systems and found it worked better than other methods.
What this means in practice
- •For simulation engineers: Create more accurate physical system simulations that better obey governing laws from the start of the modeling process.
- •For computational fluid dynamics teams: Improve the generation of fluid flow simulations ensuring outputs consistently satisfy physical constraints without extra corrections.
Authors
Giulia Romoli, Filippo Ruffini, Paolo Soda
Abstract
Deep generative models are used to solve partial differential equations and model distributions of physical system states, but ensuring that the generated samples satisfy the governing laws remains challenging. Projection-based flow-matching methods enforce physics by correcting the flow from an unconstrained noise distribution. These corrections shift the generated samples away from the distribution of target solutions, especially in high noise regions. To address this limitation, we propose Source Anchoring for Physical Consistency (SAPC), a Functional Flow Matching method that encodes the physical constraints into the source noise before generation begins. We evaluate SAPC on five systems governed by partial differential equations, covering six tasks with linear and non-linear dynamics, and compare results against five baselines and the unconstrained backbone. Anchoring the source reduces the need for large corrections that drive samples onto admissible but off-distribution states, and SAPC reproduces the target distributions most accurately on every evaluated task, while matching the constraint precision of the best projection-based baselines. Ablation experiments show that this gain arises from pairing source projection with a matched training objective that regresses toward the projected source. These results identify the source distribution as a key design choice for physically consistent generative modelling.