Fig 3. Biologically-informed neural networks for reaction-diffusion models.

(A) BINNs are deep neural networks that approximate the solution of a governing dynamical system. (B) By allowing the terms of the dynamical system (e.g. diffusivity function $\mathcal{D}$ and growth function $\mathcal{G}$) to be function-approximating deep neural networks, the nonlinear forms of these terms can be learned without the need to specify a mechanistic model or library of candidate terms. (C) Automatic differentiation is used on compositions of the different neural network models (e.g. u, D, and G) to construct the PDE that describes the governing dynamical system. (D) The governing system is used in the neural network objective function to jointly learn and satisfy the governing PDE while minimizing the error between the network outputs and noisy observations.