# Neuro-physical dynamic load modeling using differentiable parametric optimization

arXiv: https://arxiv.org/abs/2203.10582 · HTML: https://mlsanity.com/paper/2203.10582/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 20 Mar 2022.

## Builds on (most cited first, 14 of 14)

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- [Constrained Convolutional Neural Networks for Weakly Supervised Segmentation](https://mlsanity.com/paper/1506.03648/) (2015)
- [Constrained Deep Weak Supervision for Histopathology Image Segmentation](https://mlsanity.com/paper/1701.00794/) (2017)
- [Imposing Hard Constraints on Deep Networks: Promises and Limitations](https://mlsanity.com/paper/1706.02025/) (2017)
- [Constrained Deep Networks: Lagrangian Optimization via Log-Barrier Extensions](https://mlsanity.com/paper/1904.04205/) (2019)
- [Linearly Constrained Neural Networks](https://mlsanity.com/paper/2002.01600/) (2020)
- [Deep Learning Explicit Differentiable Predictive Control Laws for Buildings](https://mlsanity.com/paper/2107.11843/) (2021)
- [Constrained Deep Learning using Conditional Gradient and Applications in Computer Vision](https://mlsanity.com/paper/1803.06453/) (2018)
- [Task-based End-to-end Model Learning in Stochastic Optimization](https://mlsanity.com/paper/1703.04529/) (2017)
- [Adaptive Nonlinear Model Reduction for Fast Power System Simulation](https://mlsanity.com/paper/1711.03583/) (2017)

## Abstract (arXiv)

In this work, we investigate a data-driven approach for obtaining a reduced equivalent load model of distribution systems for electromechanical transient stability analysis. The proposed reduced equivalent is a neuro-physical model comprising of a traditional ZIP load model augmented with a neural network. This neuro-physical model is trained through differentiable programming. We discuss the formulation, modeling details, and training of the proposed model set up as a differential parametric program. The performance and accuracy of this neurophysical ZIP load model is presented on a medium-scale 350-bus transmission-distribution network.