# Learning Discrepancy Models From Experimental Data

arXiv: https://arxiv.org/abs/1909.08574 · HTML: https://mlsanity.com/paper/1909.08574/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2019.

## Built on by (most cited first, 15 of 15)

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- [A toolkit for data-driven discovery of governing equations in high-noise regimes](https://mlsanity.com/paper/2111.04870/) (2021)
- [Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects](https://mlsanity.com/paper/2203.05164/) (2022)
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- [Physics-guided weak-form discovery of reduced-order models for trapped ultracold hydrodynamics](https://mlsanity.com/paper/2406.07519/) (2024)
- [Ensemble WSINDy for Data Driven Discovery of Governing Equations from Laser-based Full-field Measurements](https://mlsanity.com/paper/2409.20510/) (2024)
- [Structural Constraints for Physics-augmented Learning](https://mlsanity.com/paper/2410.05507/) (2024)
- [A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series](https://mlsanity.com/paper/2511.06609/) (2025)
- [Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization](https://mlsanity.com/paper/2602.13513/) (2026)
- [Stacked Generative Machine Learning Models for Fast Approximations of Steady-State Navier-Stokes Equations](https://mlsanity.com/paper/2112.06419/) (2021)
- [The impact of AI on engineering design procedures for dynamical systems](https://mlsanity.com/paper/2412.12230/) (2024)
- [Convergence of physics-informed neural networks modeling time-harmonic wave fields](https://mlsanity.com/paper/2506.11395/) (2025)

## Abstract (arXiv)

First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured behavior. Even in mechanical systems, where the equations are assumed to be well-known, there are often model discrepancies corresponding to nonlinear friction, wind resistance, etc. Discovering models for these discrepancies remains an open challenge for many complex systems. In this work, we use the sparse identification of nonlinear dynamics (SINDy) algorithm to discover a model for the discrepancy between a simplified model and measurement data. In particular, we assume that the model mismatch can be sparsely represented in a library of candidate model terms. We demonstrate the efficacy of our approach on several examples including experimental data from a double pendulum on a cart. We further design and implement a feed-forward controller in simulations, showing improvement with a discrepancy model.