Computed Tomography (CT)-derived Cardiovascular Flow Estimation Using Physics-Informed Neural Networks Improves with Sinogram-based Training: A Simulation Study

The Poisson-Conditioned Generative Model (PoCGM) has been proposed to enhance sparse-view computed tomography (CT) reconstruction. This model aims to mitigate the challenges of aliasing artifacts and loss of structural details that arise from reducing projection views, which is crucial for minimizing radiation exposure and improving temporal resolution. By reformulating the Poisson Flow Generative Model (PFGM++) into a conditional framework, PoCGM integrates sparse-view data during training and sampling, improving the quality of reconstructed images.

The study presents the first application of physics-informed neural networks (PINNs) for predicting hydrogen crossover in polymer electrolyte membrane (PEM) electrolyzers. This innovation addresses safety and efficiency concerns in green hydrogen production, as hydrogen crossover can lead to explosive limits and reduce Faradaic efficiency. The PINN model integrates mass conservation, Fick's diffusion law, and Henry's solubility law, achieving validation across six membranes under various industrial conditions.

A new framework for solving nonlinear partial differential equations (PDEs) has been proposed, integrating perturbation theory with one-shot transfer learning in Physics-Informed Neural Networks (PINNs). This method decomposes nonlinear PDEs into linear subproblems, which are solved using a Multi-Head PINN. The approach allows for quick adaptation to new PDE instances with varying conditions, achieving errors around 1e-3 and adaptation times under 0.2 seconds, demonstrating comparable accuracy to classical solvers.

Neuro-Spectral Architectures (NeuSA) have been introduced as a new class of Physics-Informed Neural Networks (PINNs) aimed at solving complex partial differential equations (PDEs). Traditional MLP-based PINNs often struggle with convergence in intricate initial value problems, leading to solutions that can violate causality. NeuSA addresses these challenges by learning a projection of the underlying PDE onto a spectral basis, thus improving convergence and enforcing causality through its integration with Neural ODEs.

This study introduces a data augmentation strategy designed to enhance the training of neural networks, thereby improving prediction accuracy. By generating synthetic data using a compartmental model and incorporating uncertainty, the model is calibrated with available data and integrated with deep learning techniques. The findings indicate that neural networks trained on these augmented datasets demonstrate significantly better predictive performance, particularly with Physics-Informed Neural Networks (PINNs) and Nonlinear Autoregressive (NAR) models.