Physics-Embedded Feature Learning for AI in Medical Imaging

Abstract

Deep learning (DL) models have achieved strong performance in an intelligence healthcare setting, yet most existing approaches operate as black boxes and ignore the physical processes that govern tumor growth, limiting interpretability, robustness, and clinical trust. To address this limitation, we propose PhysNet, a physics-embedded DL framework that integrates tumor growth dynamics directly into the feature learning process of a convolutional neural network (CNN). Unlike conventional physics-informed methods that impose physical constraints only at the output level, PhysNet embeds a reaction diffusion model of tumor growth within intermediate feature representations of a ResNet backbone. The architecture jointly performs multi-class tumor classification while learning a latent tumor density field, its temporal evolution, and biologically meaningful physical parameters, including tumor diffusion and growth rates, through end-to-end training. This design is necessary because purely data-driven models, even when highly accurate or ensemble-based, cannot guarantee physically consistent predictions or provide insight into tumor behavior. Experimental results on a large brain MRI dataset demonstrate that PhysNet outperforms multiple state-of-the-art DL baselines, including MobileNetV2, VGG16, VGG19, and ensemble models, achieving superior classification accuracy and F1-score. In addition to improved performance, PhysNet produces interpretable latent representations and learned bio-physical parameters that align with established medical knowledge, highlighting physics-embedded representation learning as a practical pathway toward more trustworthy and clinically meaningful medical AI systems.

Figures (5)

• Figure 1: Overview of the proposed PhysNet framework. A ResNet-50 backbone extracts features for tumor classification, while a physics-embedded branch enforces reaction–diffusion tumor growth dynamics at an intermediate feature level, enabling physically consistent and interpretable representation learning.
• Figure 2: Classification performance comparison. PhysNet achieves higher accuracy and F1-score than baseline models, with error bars indicating 95% confidence intervals from 5-fold cross-validation.
• Figure 3: Physics-informed features learned by PhysNet across tumor classes. Shown from left to right are the input MRI, learned tumor concentration $u(x,t)$, temporal derivative $\partial u/\partial t$, Laplacian $\nabla^2 u$, and PDE residual $|R(x)|$. Distinct spatial patterns reflect tumor biology, while low residuals indicate adherence to physical constraints.
• Figure 4: Learned biophysical parameters. Violin plots show distributions of diffusion coefficient $D$ (left), proliferation rate $\rho$ (center-left), and carrying capacity $K$ (center-right) across tumor classes. Scatter plot (right) reveals positive $D$-$\rho$ correlation in glioma, consistent with aggressive phenotype. Parameters align with biological expectations without explicit supervision.
• Figure 5: Training dynamics of multi-objective optimization. Top-left: individual loss components on a log-scale showing differential convergence rates. Top-right: total loss with mean (solid) and standard deviation (shaded) from 5 runs. Bottom-left: training (blue) vs. validation (red) accuracy showing minimal overfitting. Bottom-right: adaptive weight $\lambda_p$ evolution via EMA-based scheduling.