Orthogonal Discrepancy Kernels for Learning with Partial Physics

2026-06-19

AI Summary

This work addresses the challenge of achieving both interpretability and high accuracy in nonlinear system identification when physical models are incomplete. The authors propose a semi-parametric modeling framework that, for the first time, enables orthogonal decoupling between physics-based white-box components and data-driven bias terms. By employing orthogonal Gaussian process regression, the method jointly optimizes sparse physical parameter selection and black-box bias learning. This approach preserves model interpretability while significantly enhancing predictive accuracy, thereby establishing a high-fidelity, interpretable nonlinear system identification model suitable for scenarios where only partial physical knowledge is available.

Abstract

We introduce a semi-parametric framework for nonlinear system identification, which decouples discrepancy functions from physics-based components. Orthogonal Gaussian process regression balances sparse parameter selection (the white box) with discrepancy learning (the black box) to produce interpretable models from incomplete physics.

Problem

• nonlinear system identification
• incomplete physics
• interpretable models
• discrepancy learning

Innovation

• Orthogonal Discrepancy Kernels
• Semi-parametric Modeling
• Gaussian Process Regression
• Physics-Informed Learning
• Nonlinear System Identification