machine learning
We integrate data, physics, and uncertainties by combining neural networks, physics informed modeling, and Bayesian inference to improve the predictive potential of classical neural networks. Our physics informed neural networks seamlessly integrate data and physics, robustly solve forward and inverse problems, and perform well in both interpolation and extrapolation, even for a small amount of noisy and incomplete data. They can serve as priors in a Bayesian inference, and provide credible intervals for uncertainty quantification. We routinely use these techniques to study the brain, the heart, and the COVID-19 pandemic: We predict the progression of Alzheimer's disease, cardiac activation mappings, and the effect of travel restrictions. We explore combinations of neural networks, physics informed modeling, and Bayesian inference for real-world nonlinear dynamical systems and share our source codes and examples on GitHub.
exploring the potential of bayesian physics informed neural networks
we integrate data, physics, and uncertainties by combining neural networks, physics informed modeling, and Bayesian inference to predict the behavior of nonlinear dynamical systems. our study reveals the inherent advantages and disadvantages of neural networks, Bayesian inference, and a combination of both with a view towards interpolation, extrapolation, end prediction, and provides guidelines for problem-specific model selection
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bayesian inference predicts progression of alzheimer's disease
we use bayesian inference hierarchical priors structure to infer group and personalized tau production and brain shrinking rates of Alzheimer's brains and healthy controls. our model can quantify correlations between amyloid-beta, tau, and brain atrophy and predict the personalized progression of tau, atrophy, and cognitive impairment in single individuals from a sequence of medical images
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physics informed neural networks predict cardiac activation mappings
we establish physics-informed neural networks for cardiac activation mapping that account for the physics of wave propagation dynamics and allow us to quantify the epistemic uncertainty of our predictions. our findings open the door toward physics-based electro-anatomic mapping with the ultimate goals to reduce procedural time and improve diagnostics for patients affected by atrial fibrillation
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bayesian inference explains effects of lockdown in covid-19
we use machine learning to identify correlations between the drop in mobility during lockdown and the reduction in the reproduction covid-19 with a time delay of two weeks. our new dynamic epidemiology model provides the flexibility to simulate various outbreak control and exit strategies to inform political decision making and identify safe solutions in the benefit of global health
learn moreLinka K, Schafer A, Meng X, Zou Z, Karniadakis GE, Kuhl E. Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems. arXiv:2205.08304 (download) (arXiv)
Peng GCY, Alber M, Buganza Tepole A, Cannon W, De S, Dura-Bernal S, Garikipati K, Karniadakis G, Lytton WW, Perdikaris P, Petzold L, Kuhl E. Multiscale modeling meets machine learning: What can we learn? Arch Comp Meth Eng; 2021; 28:1017-1037. (open access) (download)
Schafer A, Chaggar P, Goriely A, Kuhl E. Correlating tau pathology to brain atrophy using a physics-based Bayesian model. Eng Comp. 2022; doi:10/1007/s00366-022-01660-3. (download) (eng comp)
Schafer A, Peirlinck M, Linka K, Kuhl E. Bayesian physics-based modeling of tau propagation in Alzheimer's disease. Front Physiology. 2021; 12:702975. (download) (frontiers)
Sahli Costabal F, Seo K, Ashley E, Kuhl E. Classifying drugs by their arrhythmogenic risk using machine learning. Biophys J. 2020; 118:1-12. (open access) (download)
Linka K, Peirlinck M, Kuhl E. The reproduction number of COVID-19 and its correlation with public heath interventions. Comp Mech. 2020; 66:1035-1050. (download) (computational mechanics) (medRxiv) (medical life sciences) (the conversation)
Alber M, Buganza Tepole A, Cannon W, De S, Dura-Bernal S, Garikipati K, Karniadakis G, Lytton WW, Perdikaris P, Petzold L, Kuhl E. Integrating machine learning and multiscale modeling: Perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences. npj Digital Medicine; 2019; 2:115. (open access) (download)