Acceleration of PDE-based biological simulation through the development of neural network metamodels

PDE models are a major tool used in quantitative modeling of biological and scientific phenomena. Their major shortcoming is the high computational complexity of solving each model. When scaling up to millions of simulations needed to find their optimal parameters we frequently have to wait days or weeks for results to come back. To cope with that we propose a neural network approach that can produce comparable results to a PDE model while being about 1000x faster. We quantitatively and qualitatively show the neural network metamodels are accurate and demonstrate their potential for multi-objective optimization in biology. We hope this approach can speed up scientific research and discovery in biology and beyond.