Conformal Prediction for Neural Operators: Distribution-Free Uncertainty Quantification in Physics Simulation

Researchers propose the first application of split conformal prediction to neural operators for physics simulation, enabling distribution-free uncertainty quantification with formal coverage guarantees. The method achieves 89.1% empirical coverage on heat conduction benchmarks while providing spatially adaptive prediction intervals, addressing a critical gap in deploying AI models for safety-critical engineering applications.

This research addresses a fundamental limitation in deploying neural operators—AI models trained to solve complex physics problems—in real-world engineering systems. While neural operators like FNO have proven computationally efficient compared to traditional numerical solvers, their adoption in safety-critical domains has been constrained by the lack of rigorous uncertainty estimates. Existing approaches provide only relative confidence measures without formal mathematical guarantees, creating liability and safety concerns for applications like thermal management in electronics and battery systems.

The conformal prediction framework represents a paradigm shift in neural operator validation. By providing distribution-free prediction intervals with finite-sample coverage guarantees, the approach eliminates assumptions about underlying data distributions—a critical advantage when dealing with complex physical systems. The innovation of normalized conformal prediction, which leverages MC Dropout uncertainty to create adaptive-width intervals, demonstrates sophisticated engineering: regions where the model operates with high confidence yield tighter intervals, while uncertain areas produce appropriately widened bounds that reflect genuine knowledge gaps.

For the broader AI and scientific computing landscape, this work bridges the gap between academic rigor and practical deployment. The decomposition of epistemic uncertainty (68%) from aleatoric uncertainty (32%) provides practitioners actionable guidance—epistemic uncertainty can be reduced through better data or model architecture, while aleatoric uncertainty reflects inherent physical randomness. The open-source implementation with REST API endpoints and visualization tools democratizes access to these methods.

The significance extends beyond neural operators to any surrogate model in safety-critical domains. As industries increasingly adopt machine learning for engineering simulations, formal uncertainty quantification becomes non-negotiable for regulatory compliance and risk management.

• →Split conformal prediction enables rigorous, distribution-free uncertainty quantification for neural operators with formal coverage guarantees.
• →Adaptive-width prediction intervals achieve 89.1% empirical coverage while remaining tighter in low-uncertainty regions.
• →Uncertainty decomposition separates epistemic (reducible) from aleatoric (inherent) uncertainty, guiding data collection strategies.
• →Open-source implementation with REST API and 3D visualization accelerates adoption in safety-critical engineering applications.
• →Method addresses critical deployment barriers for AI physics surrogates in thermal management, battery systems, and similar domains.