PMosFM: Preconditioned Manifold Matching for One-Step Physics-Constrained Generation
PMosFM learns one-step physics-constrained generation by matching flows on a constraint manifold.
PMosFM is a preconditioned manifold flow-matching method for generating physical fields that match a target distribution while satisfying constraints. Constraints live in a manifold decoder, so the model learns transport in intrinsic coordinates without separate residual losses or terminal residual unrolling. A geometric preconditioner and regularized covariance transform address conditioning, and a finite-interval objective ties velocity supervision to decoded physical endpoints. Experiments report lower training and sampling time than multi-step baselines at comparable physical and distributional fidelity, with one network evaluation at inference.
- Constraints are encoded in a manifold decoder rather than residual losses.
- A geometric preconditioner and covariance transform improve local conditioning.
- Inference is one neural transport step plus physical decoding.
- Training and sampling are faster than multi-step baselines at similar fidelity.
- Code and datasets are planned for public release.
From the original article
1 min read at arxiv.orgPhysics-constrained generative models aim to generate physical fields that match a target distribution and satisfy prescribed constraints. However, enforcing these constraints often increases sampling costs through iterative corrections or training costs through residual optimization and trajectory unrolling.
By Zhangyong Liang · arxiv.org
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