# Parameter Estimation for the SEIR Model Using Recurrent Nets

arXiv: https://arxiv.org/abs/2105.14524 · HTML: https://mlsanity.com/paper/2105.14524/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 30 May 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Simple Recurrent Units for Highly Parallelizable Recurrence](https://mlsanity.com/paper/1709.02755/) (2017)
- [Residual LSTM: Design of a Deep Recurrent Architecture for Distant Speech Recognition](https://mlsanity.com/paper/1701.03360/) (2017)
- [ABC random forests for Bayesian parameter inference](https://mlsanity.com/paper/1605.05537/) (2016)

## Abstract (arXiv)

The standard way to estimate the parameters ThetaSEIR (e.g., the transmission rate β) of an SEIR model is to use grid search, where simulations are performed on each set of parameters, and the parameter set leading to the least L2 distance between predicted number of infections and observed infections is selected. This brute-force strategy is not only time consuming, as simulations are slow when the population is large, but also inaccurate, since it is impossible to enumerate all parameter combinations. To address these issues, in this paper, we propose to transform the non-differentiable problem of finding optimal ThetaSEIR to a differentiable one, where we first train a recurrent net to fit a small number of simulation data. Next, based on this recurrent net that is able to generalize SEIR simulations, we are able to transform the objective to a differentiable one with respect to ThetaSEIR, and straightforwardly obtain its optimal value. The proposed strategy is both time efficient as it only relies on a small number of SEIR simulations, and accurate as we are able to find the optimal ThetaSEIR based on the differentiable objective. On two COVID-19 datasets, we observe that the proposed strategy leads to significantly better parameter estimations with a smaller number of simulations.