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[2506.08604] Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints
Summary
This article presents a novel method, Physics-Based Flow Matching (PBFM), which integrates physical constraints into generative modeling, achieving a Pareto-optimal trade-off between physical and distributional accuracy.
Why It Matters
The integration of physical constraints in generative modeling is crucial for applications in scientific machine learning. This research addresses the common challenge of balancing conflicting optimization objectives, offering a practical solution that enhances inference performance without compromising fidelity.
Key Takeaways
- PBFM allows for simultaneous optimization of generative and physical objectives.
- The method mitigates the trade-off between physical accuracy and generative fidelity.
- PBFM achieves competitive inference speed across various benchmarks.
- This approach eliminates the need for manual loss balancing.
- The findings provide a valuable tool for scientific applications in machine learning.
Computer Science > Machine Learning arXiv:2506.08604 (cs) [Submitted on 10 Jun 2025 (v1), last revised 23 Feb 2026 (this version, v4)] Title:Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints Authors:Giacomo Baldan, Qiang Liu, Alberto Guardone, Nils Thuerey View a PDF of the paper titled Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints, by Giacomo Baldan and 3 other authors View PDF HTML (experimental) Abstract:Physics-constrained generative modeling aims to produce high-dimensional samples that are both physically consistent and distributionally accurate, a task that remains challenging due to often conflicting optimization objectives. Recent advances in flow matching and diffusion models have enabled efficient generative modeling, but integrating physical constraints often degrades generative fidelity or requires costly inference-time corrections. Our work is the first to recognize the trade-off between distributional and physical accuracy. Based on the insight of inherently conflicting objectives, we introduce Physics-Based Flow Matching (PBFM) a method that enforces physical constraints at training time using conflict-free gradient updates and unrolling to mitigate Jensen's gap. Our approach avoids manual loss balancing and enables simultaneous optimization of generative and physical objectives. As a consequence, physics constraints do not impede inference performance. We benchmark our method across three repr...
