Accelerated solving of coupled, non-linear ODEs through LSTM-AI

TL;DR

This paper demonstrates that LSTM neural networks can effectively learn coupled non-linear ODE trajectories, significantly reducing computation time while maintaining accuracy, with potential applications in biological modeling and agent-based simulations.

Contribution

The study introduces a neural network surrogate model for coupled non-linear ODEs, achieving substantial speed-ups in solution computation compared to traditional numerical methods.

Findings

Speed-ups of up to 197 times in ODE solution predictions

Neural networks achieved 3% accuracy on test data

Networks predicted beyond input time series by 0.25 to 6.25 minutes

Abstract

The present project aims to use machine learning, specifically neural networks (NN), to learn the trajectories of a set of coupled ordinary differential equations (ODEs) and decrease compute times for obtaining ODE solutions by using this surragate model. As an example system of proven biological significance, we use an ODE model of a gene regulatory circuit of cyanobacteria related to photosynthesis \cite{original_biology_Kehoe, Sundus_math_model}. Using data generated by a numeric solution to the exemplar system, we train several long-short-term memory neural networks. We stopping training when the networks achieve an accuracy of of 3\% on testing data resulting in networks able to predict values in the ODE time series ranging from 0.25 minutes to 6.25 minutes beyond input values. We observed computational speed ups ranging from 9.75 to 197 times when comparing prediction compute time with compute time for obtaining the numeric solution. Given the success of this proof of concept, we plan on continuing this project in the future and will attempt to realize the same computational speed-ups in the context of an agent-based modeling platfom.