Brain tumors such as glioma, meningioma, and pituitary adenoma alter the mechanical behavior of soft brain tissue, yet common diagnostic methods rely on static imaging that cannot capture tumor growth, tissue displacement, or changes in stiffness over time. Deep learning models for this task typically require pooling patient data at one site, which conflicts with privacy rules such as GDPR and HIPAA and limits generalization across institutions, a challenge that is pronounced in neuro oncology given patient diversity. This study presents a federated physics informed neural network combining federated learning with a physics informed loss built on the equations of linear elasticity. Three simulated clinical sites each train a local network on patient specific MRI data using a physics informed loss, and only model weights are shared with a central server through the FedAvg protocol over one hundred rounds, keeping raw data at its site of origin. The federated model reached an overall accuracy of 91.4%, against 90.0% for a non federated baseline trained on pooled data, an average AUC of 0.985 across tumor classes, and a rise in pituitary tumor accuracy from 85.6 to 94.5%. Training produced smooth, divergence free displacement fields consistent with expected tissue deformation, showing that federated training can be paired with physics based constraints without a meaningful loss in performance.

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