# Off the Normal Path: Learning Spatial Density Models of Node Mobility

arXiv: https://arxiv.org/abs/2411.10997 · HTML: https://mlsanity.com/paper/2411.10997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 17 Nov 2024.

## Builds on (most cited first, 12 of 12)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [Normalizing Flows on Tori and Spheres](https://mlsanity.com/paper/2002.02428/) (2020)
- [Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction](https://mlsanity.com/paper/1906.03631/) (2019)
- [Latent Variable Modelling with Hyperbolic Normalizing Flows](https://mlsanity.com/paper/2002.06336/) (2020)
- [A Comprehensive Review of Digital Twin -- Part 1: Modeling and Twinning Enabling Technologies](https://mlsanity.com/paper/2208.14197/) (2022)
- [Uncertainty-Aware Learning from Demonstration using Mixture Density Networks with Sampling-Free Variance Modeling](https://mlsanity.com/paper/1709.02249/) (2017)
- [How to Distribute Computation in Networks](https://mlsanity.com/paper/1912.03531/) (2019)

## Abstract (arXiv)

We consider the problem of learning models of spatial density functions, representing the steady-state density of mobile nodes moving on a two-dimensional terrain. Deriving such models can assist in network design and optimization problems, e.g., by accelerating the computation of the density function during a parameter sweep. We address the question of applicability of off-the-shelf mixture density network models and of, two varieties of, normalizing flows for the description of mobile node density over a disk. We introduce the use of M"obius distributions to retain symmetric spatial relations. Our results indicate that mixtures of M"obius distributions provide interpretable, parsimonious models for the studied steady state density distributions, that match or outperform the alternatives.