Minimum-Excess-Work Guidance

2025-05-19

AI Summary

Generative modeling in scientific computing faces significant challenges under data-scarce regimes, particularly in guiding sampling toward physically meaningful configurations. Method: This paper proposes a thermodynamics-driven probabilistic flow generative modeling framework. It innovatively introduces excess work—drawn from statistical mechanics—as a regularization objective and integrates optimal transport theory to design two complementary guidance strategies: Path Guidance (enabling transition-state sampling from sparse data) and Observable Guidance (ensuring alignment with physical observables). Technically, the framework unifies continuous normalizing flows and diffusion models, jointly regularizing path optimization and observable constraints. Contribution/Results: Evaluated on coarse-grained protein folding/unfolding, the method substantially improves sample efficiency and corrects systematic biases, demonstrating its effectiveness and practicality for low-data domains such as molecular simulation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

We propose a regularization framework inspired by thermodynamic work for guiding pre-trained probability flow generative models (e.g., continuous normalizing flows or diffusion models) by minimizing excess work, a concept rooted in statistical mechanics and with strong conceptual connections to optimal transport. Our approach enables efficient guidance in sparse-data regimes common to scientific applications, where only limited target samples or partial density constraints are available. We introduce two strategies: Path Guidance for sampling rare transition states by concentrating probability mass on user-defined subsets, and Observable Guidance for aligning generated distributions with experimental observables while preserving entropy. We demonstrate the framework's versatility on a coarse-grained protein model, guiding it to sample transition configurations between folded/unfolded states and correct systematic biases using experimental data. The method bridges thermodynamic principles with modern generative architectures, offering a principled, efficient, and physics-inspired alternative to standard fine-tuning in data-scarce domains. Empirical results highlight improved sample efficiency and bias reduction, underscoring its applicability to molecular simulations and beyond.

Problem

• Minimize excess work in generative models using thermodynamics
• Guide models with sparse data or partial constraints
• Align generated distributions with experimental observables preserving entropy

Innovation

• Minimizes excess work for generative models
• Uses Path and Observable Guidance strategies
• Bridges thermodynamics with generative architectures