# Orthogonal Discrepancy Kernels for Learning with Partial Physics

arXiv: https://arxiv.org/abs/2606.21199 · HTML: https://mlsanity.com/paper/2606.21199/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 9 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Builds on (most cited first, 5 of 5)

- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression](https://mlsanity.com/paper/2012.01937/) (2020)
- [Sparse Identification of Nonlinear Dynamical Systems via Reweighted ℓ1-regularized Least Squares](https://mlsanity.com/paper/2005.13232/) (2020)
- [A spectrum of physics-informed Gaussian processes for regression in engineering](https://mlsanity.com/paper/2309.10656/) (2023)
- [Orthogonal Gaussian process models](https://mlsanity.com/paper/1611.00203/) (2016)

## Abstract (arXiv)

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.