Biologically-informed neural networks guide mechanistic modeling from sparse experimental data

Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks [1], are introduced and used to discover the underlying dynamics of biological systems from sparse experimental data. In the present work, BINNs are trained in a supervised learning framework to approximate in vitro cell biology assay experiments while respecting a generalized form of the governing reaction-diffusion partial differential equation (PDE). By allowing the diffusion and reaction terms to be multilayer perceptrons (MLPs), the nonlinear forms of these terms can be learned while simultaneously converging to the solution of the governing PDE. Further, the trained MLPs are used to guide the selection of biologically interpretable mechanistic forms of the PDE terms which provides new insights into the biological and physical mechanisms that govern the dynamics of the observed system. The method is evaluated on sparse real-world data from wound healing assays with varying initial cell densities [2].Author summary: In this work we extend equation learning methods to be feasible for biological applications with nonlinear dynamics and where data are often sparse and noisy. Physics-informed neural networks have recently been shown to approximate solutions of PDEs from simulated noisy data while simultaneously optimizing the PDE parameters. However, the success of this method requires the correct specification of the governing PDE, which may not be known in practice. Here, we present an extension of the algorithm that allows neural networks to learn the nonlinear terms of the governing system without the need to specify the mechanistic form of the PDE. Our method is demonstrated on real-world biological data from scratch assay experiments and used to discover a previously unconsidered biological mechanism that describes delayed population response to the scratch.