Accelerated solving of coupled, non-linear ODEs through LSTM-AI
This provides a proof-of-concept for accelerating ODE solving in computational biology, specifically for gene regulatory circuits in cyanobacteria, though it is incremental as it applies existing LSTM methods to a new biological dataset.
The researchers tackled the problem of slow computation times for solving coupled non-linear ordinary differential equations (ODEs) by training LSTM neural networks as surrogate models, achieving computational speed-ups of 9.75 to 197 times compared to numerical solutions while maintaining 3% accuracy on test data.
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.