# Obey validity limits of data-driven models

arXiv: https://arxiv.org/abs/2010.03405 · HTML: https://mlsanity.com/paper/2010.03405/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [When Deep Learning Meets Polyhedral Theory: A Survey](https://mlsanity.com/paper/2305.00241/) (2023)
- [ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projection](https://mlsanity.com/paper/2502.06774/) (2025)
- [Graph Machine Learning for Design of High-Octane Fuels](https://mlsanity.com/paper/2206.00619/) (2022)
- [Data-driven decision-focused surrogate modeling](https://mlsanity.com/paper/2308.12161/) (2023)
- [Picard-KKT-hPINN: Enforcing Nonlinear Enthalpy Balances for Physically Consistent Neural Networks](https://mlsanity.com/paper/2501.17782/) (2025)
- [Constraint Learning to Define Trust Regions in Predictive-Model Embedded Optimization](https://mlsanity.com/paper/2201.04429/) (2022)
- [Semi-supervised Variational Autoencoder for Regression: Application on Soft Sensors](https://mlsanity.com/paper/2211.05979/) (2022)
- [Two-stage Residual Learning for Modelling Strength-Informed Optimisation of Thermal Systems](https://mlsanity.com/paper/2610.19539/) (2026)

## Abstract (arXiv)

Data-driven models are becoming increasingly popular in engineering, on their own or in combination with mechanistic models. Commonly, the trained models are subsequently used in model-based optimization of design and/or operation of processes. Thus, it is critical to ensure that data-driven models are not evaluated outside their validity domain during process optimization. We propose a method to learn this validity domain and encode it as constraints in process optimization. We first perform a topological data analysis using persistent homology identifying potential holes or separated clusters in the training data. In case clusters or holes are identified, we train a one-class classifier, i.e., a one-class support vector machine, on the training data domain and encode it as constraints in the subsequent process optimization. Otherwise, we construct the convex hull of the data and encode it as constraints. We finally perform deterministic global process optimization with the data-driven models subject to their respective validity constraints. To ensure computational tractability, we develop a reduced-space formulation for trained one-class support vector machines and show that our formulation outperforms common full-space formulations by a factor of over 3,000, making it a viable tool for engineering applications. The method is ready-to-use and available open-source as part of our MeLOn toolbox (https://git.rwth-aachen.de/avt.svt/public/MeLOn).