# Physics-based machine learning for modeling stochastic IP3-dependent calcium dynamics

arXiv: https://arxiv.org/abs/2109.05053 · HTML: https://mlsanity.com/paper/2109.05053/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 10 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Bird Species Categorization Using Pose Normalized Deep Convolutional Nets](https://mlsanity.com/paper/1406.2952/) (2014)
- [Deep Learning Moment Closure Approximations using Dynamic Boltzmann Distributions](https://mlsanity.com/paper/1905.12122/) (2019)

## Abstract (arXiv)

We present a machine learning method for model reduction which incorporates domain-specific physics through candidate functions. Our method estimates an effective probability distribution and differential equation model from stochastic simulations of a reaction network. The close connection between reduced and fine scale descriptions allows approximations derived from the master equation to be introduced into the learning problem. This representation is shown to improve generalization and allows a large reduction in network size for a classic model of inositol trisphosphate (IP3) dependent calcium oscillations in non-excitable cells.