Bridging the Physics-Data Gap with FNO-Guided Conditional Flow Matching: Designing Inductive Bias through Hierarchical Physical Constraints

2025-10-09

AI Summary

To address the decoupling of physical consistency and statistical validity in time-series generation, this paper proposes a hierarchical physics-constrained generative framework. It integrates multi-level physical priors—including conservation laws, dynamical equations, boundary conditions, and empirical relationships—into a conditional flow matching (CFM) generative process via a Fourier neural operator (FNO) that learns the underlying physical evolution operator. A time-dependent constraint mechanism and an FNO-guided correction strategy are introduced to enable differentiable and scalable physics-informed integration. Evaluated on three diverse tasks—harmonic oscillator modeling, human activity recognition, and lithium-ion battery aging prediction—the framework achieves a 16.3% improvement in generation quality, a 46% reduction in physics constraint violations, and an 18.5% gain in predictive accuracy, significantly outperforming state-of-the-art methods.

Technology Category

• Natural Language Processing: Generation
• Computer Vision: Low Level & Physics-based Vision
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Conventional time-series generation often ignores domain-specific physical constraints, limiting statistical and physical consistency. We propose a hierarchical framework that embeds the inherent hierarchy of physical laws-conservation, dynamics, boundary, and empirical relations-directly into deep generative models, introducing a new paradigm of physics-informed inductive bias. Our method combines Fourier Neural Operators (FNOs) for learning physical operators with Conditional Flow Matching (CFM) for probabilistic generation, integrated via time-dependent hierarchical constraints and FNO-guided corrections. Experiments on harmonic oscillators, human activity recognition, and lithium-ion battery degradation show 16.3% higher generation quality, 46% fewer physics violations, and 18.5% improved predictive accuracy over baselines.

Problem

• Bridging physics-data gap with hierarchical physical constraints
• Embedding physical laws into deep generative models
• Improving generation quality while reducing physics violations

Innovation

• Hierarchical framework embeds physical laws into generative models
• Combines Fourier Neural Operators with Conditional Flow Matching
• Integrates time-dependent constraints and FNO-guided corrections