  Resolving the diffusion coefficient is a key element in many biological and
engineering systems, including pharmacological drug transport and fluid
mechanics analyses. Additionally, these systems often have spatial variation in
the diffusion coefficient which must be determined, such as for injectable
drug-eluting implants into heterogeneous tissues. Unfortunately, obtaining the
diffusion coefficient from images in such cases is an inverse problem with only
discrete data points. The development of a robust method that can work with
such noisy and ill-posed datasets to accurately determine spatially-varying
diffusion coefficients is of great value across a large range of disciplines.
Here, we developed an inverse solver that uses physics informed neural networks
(PINNs) to calculate spatially-varying diffusion coefficients from numerical
and experimental image data in varying biological and engineering applications.
The residual of the transient diffusion equation for a concentration field is
minimized to find the diffusion coefficient. The robustness of the method as an
inverse solver was tested using both numerical and experimental datasets. The
predictions show good agreement with both the numerical and experimental
benchmarks; an error of less than 6.31% was obtained against all numerical
benchmarks, while the diffusion coefficient calculated in experimental datasets
matches the appropriate ranges of other reported literature values. Our work
demonstrates the potential of using PINNs to resolve spatially-varying
diffusion coefficients, which may aid a wide-range of applications, such as
enabling better-designed drug-eluting implants for regenerative medicine or
oncology fields.
