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Article
Computer Science, Interdisciplinary Applications
Xuhui Meng et al.
Summary: We propose a new Bayesian framework based on deep neural networks to extrapolate in space-time using historical data and quantify uncertainties. The framework consists of two stages: prior learning and posterior estimation, where a physics-informed Generative Adversarial Network is used for prior learning and Hamiltonian Monte Carlo method is used for posterior estimation. Experimental results demonstrate the accuracy and uncertainty quantification capability of the proposed method using limited scattered and noisy data.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Review
Computer Science, Interdisciplinary Applications
Grace C. Y. Peng et al.
Summary: Machine learning excels in image recognition in fields like biomedicine, but struggles with sparse data. Integrating machine learning with multiscale modeling can create more efficient biological system models, benefiting both approaches.
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING
(2021)
Article
Biophysics
Kevin Linka et al.
Summary: The study shows a correlation between driving mobility and COVID-19 dynamics, which can be used to forecast outbreak and adjust control strategies in real time.
BIOMECHANICS AND MODELING IN MECHANOBIOLOGY
(2021)
Article
Computer Science, Interdisciplinary Applications
Liu Yang et al.
Summary: The paper introduces a Bayesian physics-informed neural network (B-PINN) for solving nonlinear problems, and conducts experimental comparisons on posterior estimation methods and uncertainty quantification. The KL model is as accurate and faster than BNN, but cannot be applied to high-dimensional problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Mohamed Aziz Bhouri et al.
Summary: This paper introduces a deep learning framework for identifying epidemiological systems from noisy and sparse observations with quantified uncertainty. The approach utilizes deep neural networks to accurately predict future trends in COVID-19 spread, aiding in policy and decision making.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Xuhui Meng et al.
Summary: A novel class of Bayesian neural networks is proposed for training with noisy data of variable fidelity, applied to function approximations and solving inverse problems based on partial differential equations (PDEs). The multi-fidelity BNNs consist of three neural networks, effectively modeling the correlation and uncertainty between different fidelity data and accurately estimating posterior distributions of hyperparameters. The method demonstrates adaptively capturing linear and nonlinear correlation, identifying unknown parameters in PDEs, and quantifying uncertainties in predictions, ultimately enhancing prediction accuracy through active learning.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Biochemical Research Methods
Sheng Zhang et al.
Summary: This study presents a general framework for building a reliable data-driven epidemiological model, which successfully projects the transmission dynamics of COVID-19 in New York City. By integrating data acquisition, model development, analysis, and calibration, the model parameters are accurately estimated, providing scientific support for controlling and responding to the pandemic.
PLOS COMPUTATIONAL BIOLOGY
(2021)
Article
Computer Science, Interdisciplinary Applications
Ehsan Kharazmi et al.
Summary: This study employs physics-informed neural networks to analyze various epidemiological models, identifying time-dependent parameters and data-driven fractional differential operators, while inferring the spread of COVID-19 in different regions. The results show that identifying time-dependent parameters using neural networks is suitable for integer-order and time-delay models, while determining different time-dependent derivative orders using neural networks is suitable for fractional differential models.
NATURE COMPUTATIONAL SCIENCE
(2021)
Review
Physics, Applied
George Em Karniadakis et al.
Summary: Physics-informed learning seamlessly integrates data and mathematical models through neural networks or kernel-based regression networks for accurate inference of realistic and high-dimensional multiphysics problems. Challenges remain in incorporating noisy data seamlessly, complex mesh generation, and addressing high-dimensional problems.
NATURE REVIEWS PHYSICS
(2021)
Article
Biophysics
Mathias Peirlinck et al.
BIOMECHANICS AND MODELING IN MECHANOBIOLOGY
(2020)
Article
Computer Science, Interdisciplinary Applications
Kevin Linka et al.
COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING
(2020)
Editorial Material
Medicine, General & Internal
Inga Holmdahl et al.
NEW ENGLAND JOURNAL OF MEDICINE
(2020)
Article
Mathematics, Interdisciplinary Applications
Kevin Linka et al.
COMPUTATIONAL MECHANICS
(2020)
Article
Mathematics, Interdisciplinary Applications
Prashant K. Jha et al.
COMPUTATIONAL MECHANICS
(2020)
Article
Computer Science, Interdisciplinary Applications
M. Raissi et al.
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Article
Computer Science, Interdisciplinary Applications
Yibo Yang et al.
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Review
Health Care Sciences & Services
Mark Alber et al.
NPJ DIGITAL MEDICINE
(2019)
Article
Mathematics
J. Tinsley Oden
Article
Computer Science, Artificial Intelligence
John Salvatier et al.
PEERJ COMPUTER SCIENCE
(2016)
