Structurally Cascaded Physics‐Informed Graph Neural Networks for Mechanotransduction‐Aware Tumor Microenvironment Modeling

Abstract

ABSTRACT Physics‐informed neural networks offer a useful mesh‐free approach for solving partial differential equations in complex multiphysics systems, such as the tumor microenvironment. These computational models can support future sustainable engineering applications and operations in precision medicine by enabling efficient in‐silico testing. However, standard networks typically treat coupled fields as parallel outputs, which may not fully capture the directional dependencies inherent in biological pathways like mechanotransduction. This computational symmetry can allow the optimizer to find suboptimal local minima where inverse correlations are learned, sometimes leading to physically inconsistent representations. To address this structural gap, we present the structurally cascaded physics‐informed graph neural network. We introduce a latent cascaded architecture that passes macroscopic volumetric strain as an upstream feature into the biochemical sub‐network, addressing the optimization symmetry. Furthermore, we apply a limit‐state masking penalty at the zero‐strain limit. This serves as a structural regularizer that guides a physically consistent bound without relying on rigid local derivative penalties. Evaluated on a quasi‐static stiffness‐degradation benchmark, the proposed method helps reduce physically inconsistent artifacts, achieving an approximately 45% lower relative error in biochemical field predictions and a 68.8% lower core test mean squared error during spatial extrapolation compared to standard unconstrained baselines. This work serves as a computational proof‐of‐concept to support the development of reliable digital twins, potentially reducing the reliance on extensive physical experiments. This methodology thus aligns with enabling technologies that aim to make engineering operations more sustainable in future precision healthcare applications.