Source Anchoring for Physical Consistency in Flow Matching Models
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 syst...
| Authors | Giulia Romoli, Filippo Ruffini, Paolo Soda |
|---|---|
| Primary category | cs.LG |
| Published | 27 September 2026 |
| Last updated at source | 27 September 2026 |
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