# Jacobian-Enhanced Neural Networks

arXiv: https://arxiv.org/abs/2406.09132 · HTML: https://mlsanity.com/paper/2406.09132/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 13 Jun 2024.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Robust Learning with Jacobian Regularization](https://mlsanity.com/paper/1908.02729/) (2019)
- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [Real-time optimal control via Deep Neural Networks: study on landing problems](https://mlsanity.com/paper/1610.08668/) (2016)

## Abstract (arXiv)

Jacobian-Enhanced Neural Networks (JENN) are densely connected multi-layer perceptrons, whose training process is modified to predict partial derivatives accurately. Their main benefit is better accuracy with fewer training points compared to standard neural networks. These attributes are particularly desirable in the field of computer-aided design, where there is often the need to replace computationally expensive, physics-based models with fast running approximations, known as surrogate models or meta-models. Since a surrogate emulates the original model accurately in near-real time, it yields a speed benefit that can be used to carry out orders of magnitude more function calls quickly. However, in the special case of gradient-enhanced methods, there is the additional value proposition that partial derivatives are accurate, which is a critical property for one important use-case: surrogate-based optimization. This work derives the complete theory and exemplifies its superiority over standard neural nets for surrogate-based optimization.