mlsanityData to 7 Oct 2026

Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression

arXiv 2307.08107 ↗First posted 16 Jul 2023cs.LG q-bio.QMcited by 25

On the map: Diffusion models → Medical imaging and segmentation

Abstract (arXiv)

Misfolded tau proteins play a critical role in the progression and pathology of Alzheimer's disease. Recent studies suggest that the spatio-temporal pattern of misfolded tau follows a reaction-diffusion type equation. However, the precise mathematical model and parameters that characterize the progression of misfolded protein across the brain remain incompletely understood. Here, we use deep learning and artificial intelligence to discover a mathematical model for the progression of Alzheimer's disease using longitudinal tau positron emission tomography from the Alzheimer's Disease Neuroimaging Initiative database. Specifically, we integrate physics informed neural networks (PINNs) and symbolic regression to discover a reaction-diffusion type partial differential equation for tau protein misfolding and spreading. First, we demonstrate the potential of our model and parameter discovery on synthetic data. Then, we apply our method to discover the best model and parameters to explain tau imaging data from 46 individuals who are likely to develop Alzheimer's disease and 30 healthy controls. Our symbolic regression discovers different misfolding models f(c) for two groups, with a faster misfolding for the Alzheimer's group, f(c) = 0.23c3 - 1.34c2 + 1.11c, than for the healthy control group, f(c) = -c3 +0.62c2 + 0.39c. Our results suggest that PINNs, supplemented by symbolic regression, can discover a reaction-diffusion type model to explain misfolded tau protein concentrations in Alzheimer's disease. We expect our study to be the starting point for a more holistic analysis to provide image-based technologies for early diagnosis, and ideally early treatment of neurodegeneration in Alzheimer's disease and possibly other misfolding-protein based neurodegenerative disorders.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models. Builds on 19 of its 53 references that are in the map. First posted on arXiv 16 Jul 2023.

Builds on

19 of 53 references.

References · 19

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7 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 11; 2025: 8; 2026: 3.

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  1. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  2. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  3. 2024Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modelingcited by 36
  4. 2023Correcting model misspecification in physics-informed neural networks (PINNs)cited by 33
  5. 2023AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identificationcited by 29
  6. 2023Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operatorscited by 28
  7. 2024Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solvingcited by 17
  8. 2025Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemblecited by 13
  9. 2024Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learningcited by 9
  10. 2024BiLO: Bilevel Local Operator Learning for PDE Inverse Problemscited by 8
  11. 2024Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problemcited by 8
  12. 2024Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networkscited by 6
13 more
  1. 2024NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elementscited by 6
  2. 2025Physics-Informed Machine Learning in Biomedical Science and Engineeringcited by 4
  3. 2024Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiologycited by 3
  4. 2025SatelliteFormula: Multi-Modal Symbolic Regression from Remote Sensing Imagery for Physics Discoverycited by 3
  5. 2024Deep learning for model correction of dynamical systems with data scarcitycited by 2
  6. 2025Physics-informed deep learning for infectious disease forecastingcited by 2
  7. 2025Analyzing Generalization in Pre-Trained Symbolic Regressioncited by 2
  8. 2025Discovering Partially Known Ordinary Differential Equations: a Case Study on the Chemical Kinetics of Cellulose Degradationcited by 0
  9. 2025Augmented Physics-Based Li-ion Battery Model via Adaptive Ensemble Sparse Learning and Conformal Predictioncited by 0
  10. 2025GIMLET: Generalizable and Interpretable Model Learning through Embedded Thermodynamicscited by 0
  11. 2026A Comparative Investigation of Thermodynamic Structure-Informed Neural Networkscited by 0
  12. 2026Neural operator-based digital twins for modeling amyloid-β and tau propagation and treatment optimization in Alzheimer's diseasecited by 0
  13. 2026On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancementcited by 0

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  1. 2026Tau-BNO: Brain Neural Operator for Tau Transport Model
  2. 2024Tau Anomaly Detection in PET Imaging via Bilateral-Guided Deterministic Diffusion Model
  3. 2022Pathology Steered Stratification Network for Subtype Identification in Alzheimer's Disease
  4. 2025Understanding Mechanistic Role of Structural and Functional Connectivity in Tau Propagation Through Multi-Layer Modeling
  5. 2026SC-TauPath: A Structural Connectivity Attribution Framework for Mapping Tau Propagation Pathways in Alzheimer's Disease
  6. 2025TauGenNet: Plasma-Driven Tau PET Image Synthesis via Text-Guided 3D Diffusion Models
  7. 2025A Stage-Aware Mixture of Experts Framework for Neurodegenerative Disease Progression Modelling
  8. 2026Structural MRI Synthesis for Alzheimer's Disease via Conditional Diffusion on Anatomical Masks