# Robust Hybrid Learning With Expert Augmentation

arXiv: https://arxiv.org/abs/2202.03881 · HTML: https://mlsanity.com/paper/2202.03881/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 55 references that are in the map.
- First posted on arXiv 8 Feb 2022.

## Builds on (most cited first, 28 of 28)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [Learning from Simulated and Unsupervised Images through Adversarial Training](https://mlsanity.com/paper/1612.07828/) (2016)
- [Fairness without Demographics through Adversarially Reweighted Learning](https://mlsanity.com/paper/2006.13114/) (2020)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Disentangling Physical Dynamics from Unknown Factors for Unsupervised Video Prediction](https://mlsanity.com/paper/2003.01460/) (2020)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [On Calibration and Out-of-domain Generalization](https://mlsanity.com/paper/2102.10395/) (2021)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Sim2real transfer learning for 3D human pose estimation: motion to the rescue](https://mlsanity.com/paper/1907.02499/) (2019)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression](https://mlsanity.com/paper/2106.02875/) (2021)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Skillful Twelve Hour Precipitation Forecasts using Large Context Neural Networks](https://mlsanity.com/paper/2111.07470/) (2021)
- [Sim2Real View Invariant Visual Servoing by Recurrent Control](https://mlsanity.com/paper/1712.07642/) (2017)
- [Neural Dynamical Systems: Balancing Structure and Flexibility in Physical Prediction](https://mlsanity.com/paper/2006.12682/) (2020)
- [Aspect-augmented Adversarial Networks for Domain Adaptation](https://mlsanity.com/paper/1701.00188/) (2017)
- [Physics-Incorporated Convolutional Recurrent Neural Networks for Source Identification and Forecasting of Dynamical Systems](https://mlsanity.com/paper/2004.06243/) (2020)

## Built on by (most cited first, 17 of 17)

- [Addressing Misspecification in Simulation-based Inference through Data-driven Calibration](https://mlsanity.com/paper/2405.08719/) (2024)
- [Mixture of Experts (MoE): A Big Data Perspective](https://mlsanity.com/paper/2501.16352/) (2025)
- [Automatically Learning Hybrid Digital Twins of Dynamical Systems](https://mlsanity.com/paper/2410.23691/) (2024)
- [The Causal Chambers: Real Physical Systems as a Testbed for AI Methodology](https://mlsanity.com/paper/2404.11341/) (2024)
- [Deep Grey-Box Modeling With Adaptive Data-Driven Models Toward Trustworthy Estimation of Theory-Driven Models](https://mlsanity.com/paper/2210.13103/) (2022)
- [AI for Science: An Emerging Agenda](https://mlsanity.com/paper/2303.04217/) (2023)
- [Inductive Domain Transfer In Misspecified Simulation-Based Inference](https://mlsanity.com/paper/2508.15593/) (2025)
- [A Generalizable Physics-Enhanced State Space Model for Long-Term Dynamics Forecasting in Complex Environments](https://mlsanity.com/paper/2507.10792/) (2025)
- [Variational Grey-Box Dynamics Matching](https://mlsanity.com/paper/2602.17477/) (2026)
- [Learning Hybrid Dynamics Models With Simulator-Informed Latent States](https://mlsanity.com/paper/2309.02873/) (2023)
- [PILA: Physics-Informed Low Rank Augmentation for Interpretable Earth Observation](https://mlsanity.com/paper/2405.18953/) (2024)
- [Hybrid Generative Modeling for Incomplete Physics: Deep Grey-Box Meets Optimal Transport](https://mlsanity.com/paper/2506.22204/) (2025)
- [Interpretable Mechanistic Representations for Meal-level Glycemic Control in the Wild](https://mlsanity.com/paper/2312.03344/) (2023)
- [Sharpness-Aware Hybrid Model Learning for Architecture-Agnostic Parameter Estimation](https://mlsanity.com/paper/2602.06837/) (2026)
- [HAPI-EP: Towards Hybrid, Adaptive, and Predictive Digital Twins of Cardiac Electrophysiology](https://mlsanity.com/paper/2606.15637/) (2026)
- [Learning Cardiac Electrophysiology Digital Twins Through Agentic Discovery of Hybrid Structure](https://mlsanity.com/paper/2606.18154/) (2026)
- [Climate Physics Dynamic Matching](https://mlsanity.com/paper/2608.26907/) (2026)

## Abstract (arXiv)

Hybrid modelling reduces the misspecification of expert models by combining them with machine learning (ML) components learned from data. Similarly to many ML algorithms, hybrid model performance guarantees are limited to the training distribution. Leveraging the insight that the expert model is usually valid even outside the training domain, we overcome this limitation by introducing a hybrid data augmentation strategy termed textitexpert augmentation. Based on a probabilistic formalization of hybrid modelling, we demonstrate that expert augmentation, which can be incorporated into existing hybrid systems, improves generalization. We empirically validate the expert augmentation on three controlled experiments modelling dynamical systems with ordinary and partial differential equations. Finally, we assess the potential real-world applicability of expert augmentation on a dataset of a real double pendulum.