Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning

2024-04-04

Journal of Computational Physics

AI Summary

Scientific machine learning faces a fundamental verification challenge: statistical methods rely on strong assumptions, while classical interpolation—though possessing rigorous error bounds—is computationally intractable. This work introduces the first verifiable modeling framework that integrates adaptive interpolation with tight, computationally feasible error upper bounds, enabling pointwise mathematically provable falsifiability of predictions. Our approach innovatively couples radial basis function interpolation, interval analysis, Lipschitz constant estimation, and uncertainty propagation modeling to formulate an error-aware training paradigm, augmented by a constraint-aware loss function. Evaluated on partial differential equation surrogate modeling tasks, the framework achieves a 99.2% error-bound coverage rate and reduces verification latency by three orders of magnitude. These advances significantly enhance trustworthiness and enable reliable closed-loop decision-making in scientific simulation workflows.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Problem

• Develop verifiable scientific machine learning techniques
• Compute efficient error bounds for interpolation models
• Enhance interpretability of black-box deep learning models

Innovation

• Interpolation models for error bounds
• Deep learning latent space interpretability
• Efficient error bound computation methods