Institut für Kontinuums- und Werkstoffmechanik

Physics-Informed Neural Networks for Nonlocal Peridynamic
Diffusion Models in Bio-Corrosion

Fig.: Simulation of the bio-degradation of Mg-based bone implant screws and an artificial neural network.

This master’s thesis involves the development and implementation of a Physics-Informed Neural Network (PINN)
to investigate nonlocal, peridynamic diffusion models, with an emphasis on the bio-corrosion processes of
magnesium-based implant materials. The student will focus on formulating the peridynamic diffusion equation
as a high-order Partial Differential Equation (PDE) using a Taylor series expansion. This equation will then be
employed within the smooth solution sections of the domains using PINNs.

A significant part of the project is dedicated to implementing a novel coupling scheme. This involves integrating
the PINN with a mesh-free one-point Gaussian integration scheme, particularly around the corrosive interface
where material discontinuity occurs. The aim is to capture the spatial variability of diffusion coefficients,
highlighting the phase transition as metallic materials undergo corrosion and diffuse into the surrounding liquid
electrolyte.

The overarching goal of this thesis is to synergize the benefits of PINNs in solving complex, high-order PDEs
efficiently with the advantages of the mesh-free Gaussian integration method for material separation and
discontinuity at the corrosion interface. Through this approach, the project seeks not only to address prevalent
computational challenges but also to enhance the efficiency and accuracy of bio-corrosion modeling in
biomedical applications.

Requirements:

Strong foundation in numerical methods and machine learning, proficiency in programming languages such as
Python or MATLAB, interest in multidisciplinary research and a proactive approach to problem-solving.