Efficient Modelisation for Complex Geometries of Tumor Growth via Thermo-Elastic Diffusion Partial Differential Equations and Artificial Neural Networks

The availability of high quality image data urges the development of new conceptual techniques to realise cancer accurate prognostic and treatment. In this study we propose a boundary value problem to model tumor elasticity impacting various types of mechanical stresses on cancer cell properties, assuming isotropic and inhomogeneous condition. We show the solution of this multiscale model expressed by PDE is numerically approximated by means of an Artificial Neural Network Architecture based on generalised Fourier decomposition. The connective key step is the use of the Laplace Neural Operator, which contributes to an efficient algorithm convergence rate. While further research of this model may address critical points on machine learning optimality checks, this framework is a rational development for oncologic medical prognosis and therapy.