PINNOCHIO: Physics-Informed Neural Network for Coupled Hyperelastic Interface-Volume Simulation in Orthognathic Surgery

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.

Physics-informed neural operators (PINOs) have recently gained attention as fast numerical simulators with potential for solving inverse problems. This study proposes the first PINO-based method for speech production analysis. The model learns the governing one-dimensional wave equations directly without requiring pre-computed supervised training data. Using vocal tract shape data as input features, we compare the proposed model's predicted f0, glottal volume velocity and sound pressure at the lip for five static vowels to a conventional Runge Kutta/Finite difference approach. With errors of 0.8% for glottal volume flow and 3.2% for speech waveforms, the proposed model enables efficient GPU-parallelized simulation without iterative calculations. We conclude that PINO is a promising approach for fast analysis of speech.

Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE). However, PINNs have been shown to perform poorly, sometimes even converging to trivial solutions, in challenging PDE domains, or when generalizing to unseen but related PDE domains. Previously proposed solutions detail hyperparameter tuning to reduce loss imbalance between data-driven and physics guided losses, curriculum learning based training strategies, or dynamic re-sampling of hard collocation points. These methods face certain pitfalls: hyperparameter tuning is expensive, designing a training curriculum is ambiguous in multi-parameter PDE settings, and dynamic resampling still fails in complex PDE settings. Complementary to this line of thinking, we believe the initial PINN network weights also play a crucial role in the emergence of catastrophic failures during training, yet the effect of PINN weight initialization has been surprisingly under-investigated. To this end, we propose a framework for Learned Initialization via Gated Layerwise Optimization (LIGO-PINN) to overcome PINN convergence failures. Through rigorous evaluation on 1D and 2D PDE domains, including a challenging 2D fluid dynamics setting, we demonstrate that our methodology outperforms state-of-the-art methods designed to alleviate PINN failures, achieving a 91.5% average performance improvement across six baselines and 81% over the strongest baseline. We also verify that LIGO-PINN generalizes to 3D unstructured domains. Finally, we analyze training dynamics across all three PDE domains to explain both LIGO-PINN's improvement and the convergence failure of traditional PINNs. Code: https://github.com/scailab/ligo-pinn Keywords: Machine Learning, Physics-Informed Neural Networks, Deep Learning, PDE Modeling