Gradient-Free Generation for Hard-Constrained Systems
Chaoran Cheng, Boran Han, Danielle C. Maddix, Abdul Fatir Ansari,, Andrew Stuart, Michael W. Mahoney, Yuyang Wang
TL;DR
This paper introduces ECI sampling, a zero-shot, gradient-free method for generating data that strictly satisfies complex physical constraints, especially PDEs, by adapting pre-trained models without fine-tuning.
Contribution
The paper presents a novel zero-shot framework, ECI sampling, that enforces hard constraints in generative models without gradient computations or fine-tuning.
Findings
ECI sampling strictly enforces physical constraints in PDE systems.
The method outperforms baseline approaches in zero-shot constrained generation.
It achieves competitive results in regression tasks without additional training.
Abstract
Generative models that satisfy hard constraints are critical in many scientific and engineering applications, where physical laws or system requirements must be strictly respected. Many existing constrained generative models, especially those developed for computer vision, rely heavily on gradient information, which is often sparse or computationally expensive in some fields, e.g., partial differential equations (PDEs). In this work, we introduce a novel framework for adapting pre-trained, unconstrained flow-matching models to satisfy constraints exactly in a zero-shot manner without requiring expensive gradient computations or fine-tuning. Our framework, ECI sampling, alternates between extrapolation (E), correction (C), and interpolation (I) stages during each iterative sampling step of flow matching sampling to ensure accurate integration of constraint information while preserving…
Peer Reviews
Decision·ICLR 2025 Poster
1. The work is well-motivated, it's important in scientific applications to have constraint generation 2. The proposed method is effective and does have constrained generation. Also, the method is zero-shot which is a big benefit for constraint sampling method. Although it's based on functional FM not FM in general 3. The experimental results show advantages over other baseline models.
1. The writing is also a bit confusing. Actually comments from reviewer KM5e help me better understand the algorithm 2. 2. The authors are recommended to better formulate the contribution of this work. In particular, the model works in functional space and applies projection to constraint spaces to guarantee hard-constraint met. 3. The authors mention supply chain optimization in abstract and introduction as a hard-constrained system. However, it lacks experiments on such problems. It would be
1. The paper is easy to follow with high readability. The problem setting is well motivated and important. 2. The paper provides quite comphrenseive numerical results with comparison to relevant benchmarks. The extension to regression setting is also quite impressive. 3. The paper also provides a quite detailed ablation study on the choice of algorithm hyperparameters.
*1. Clarification of Problem Setup* The problem setup is not sufficiently explained, which may lead to confusion. Although the authors repeatedly emphasize that ECI is intended for the generative modeling of constrained PDE solutions, it remains unclear what distribution of constrained solutions ECI aims to recover. Specifically, is it targeting a uniform distribution over the space of constrained solutions $\mathcal{U}_{|\mathcal{G}}$? The authors should invest more effort in formally clarifyi
* The method does seem to operate as advertised. The generated results have 0 constraint error, compared to > 0 constraint error of other soft-constrained methods. At the very least, the claim that ECI guarantees hard-constraint satisfaction is well supported * The ablation study that shows the effect of the resampling intervals and the mixing iterations is quite good. * Reporting both generation quality as well as runtime for various experiments helps objectively evaluate the proposed methodolo
__Theoretical Concerns__ * While the authors do a great job of citing the existing context for SciML applications and flow-matching models, they do not cite the large existing bodies of work related to constraint satisfaction/constrained optimization. In particular, many methods share many similarities with ECI in that they perform unconditional update steps, and then project back into the feasibility region. As such, the method lacks theoretical motivation and context of existing works. __Expe
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Taxonomy
TopicsIterative Learning Control Systems · Advanced Control Systems Optimization · Reservoir Engineering and Simulation Methods