ArticleScientific reports2022
Investigating molecular transport in the human brain from MRI with physics-informed neural networks.
Article in Scientific reports, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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Who cites it
14 citing papers in PubMed.
- Physics-informed deep learning for robust trajectory prediction in automated driving.Scientific reports · 2026Article
- MR-AIV reveals in vivo brain-wide fluid flow with physics-informed AI.Science advances · 2026Article
- Robust MR-AIV: A Systematic Study of Robustness Improvement and Sensitivity Analysis of MR-AIV.bioRxiv : the preprint server for biology · 2026Article
- Left atrial flow and thrombosis risk from 4D CT contrast dynamics by physics-informed neural network and indicator dilution theory.bioRxiv : the preprint server for biology · 2026Article
- FMEnets: Flow, material, and energy networks for non-ideal plug flow reactor design.Chemical engineering science · 2026Article
- Learning in PINNs: Phase transition, diffusion equilibrium, and generalization.Neural networks : the official journal of the International Neural Network Society · 2026Article
- MR-AIV revealsbioRxiv : the preprint server for biology · 2025Article
- From PINNs to PIKANs: recent advances in physics-informed machine learning.Machine learning for computational science and engineering · 2025Article
- U-Net-Based Prediction of Cerebrospinal Fluid Distribution and Ventricular Reflux Grading.NMR in biomedicine · 2025Article
- The pulsing brain: state of the art and an interdisciplinary perspective.Interface focus · 2025Review
- ISRSL0: compressed sensing MRI with image smoothness regularized-smoothed [Formula: see text] norm.Scientific reports · 2024Article
- Multi-modal fusion and feature enhancement U-Net coupling with stem cell niches proximity estimation for voxel-wise GBM recurrence predictionPhysics in medicine and biology · 2024Article
- Physics informed contour selection for rapid image segmentation.Scientific reports · 2024Article
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6 authors.
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Abstract
In recent years, a plethora of methods combining neural networks and partial differential equations have been developed. A widely known example are physics-informed neural networks, which solve problems involving partial differential equations by training a neural network. We apply physics-informed neural networks and the finite element method to estimate the diffusion coefficient governing the long term spread of molecules in the human brain from magnetic resonance images. Synthetic testcases are created to demonstrate that the standard formulation of the physics-informed neural network faces challenges with noisy measurements in our application. Our numerical results demonstrate that the residual of the partial differential equation after training needs to be small for accurate parameter recovery. To achieve this, we tune the weights and the norms used in the loss function and use residual based adaptive refinement of training points. We find that the diffusion coefficient estimated from magnetic resonance images with physics-informed neural networks becomes consistent with results from a finite element based approach when the residuum after training becomes small. The observations presented here are an important first step towards solving inverse problems on cohorts of patients in a semi-automated fashion with physics-informed neural networks.
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