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Article
Engineering, Multidisciplinary
Kevin Linka et al.
Summary: Choosing the best constitutive model and parameters in continuum mechanics has traditionally relied on user experience and preference. This paper proposes a new method that autonomously discovers the best model and parameters to explain experimental data using a neural network. The method is robust and satisfies physical constraints, and has the potential to revolutionize the field of constitutive modeling. Evaluation: 8 points
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Apostolos F. Psaros et al.
Summary: Neural networks have revolutionized computational methods by effectively solving challenging problems that cannot be solved using traditional methods. However, quantifying errors and uncertainties in neural network-based inference is more complex than in traditional methods. This study presents a comprehensive framework for effectively and efficiently quantifying total uncertainty in neural networks, including uncertainty modeling, solution methods, and evaluation metrics. Furthermore, an open-source Python library called NeuralUQ is developed to facilitate the deployment of uncertainty quantification in scientific machine learning research and practice.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Ying H. Huang et al.
Summary: The physics-informed neural network (PINN) is used to solve various systems, including fluid dynamics problems. However, the original PINN method has issues with the gradients of the residuals, leading to poor results. By applying existing techniques that incorporate both boundary and initial conditions in the governing equations, the bif-PINN approach shows improved convergence, lower memory usage, and faster training. Tests on different fluid dynamics problems demonstrate the advantages of bif-PINN over PINN in terms of performance and accuracy.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Biomedical
Kevin Linka et al.
Summary: The brain is an extremely soft and vulnerable organ, and understanding its physics is crucial but challenging. This study proposes a new strategy that combines thermodynamics and machine learning to build an artificial neural network for automated model discovery. The results demonstrate the potential of this method to shift from user-defined model selection to automated model discovery.
ACTA BIOMATERIALIA
(2023)
Article
Engineering, Multidisciplinary
Kevin Linka et al.
Summary: For over a century, scientists from various fields have proposed different models to characterize the behavior of materials under mechanical loading. However, classical neural networks fail to consider previous research in constitutive modeling and have limitations in predicting behavior beyond the training data. In this study, a new family of Constitutive Artificial Neural Networks (CANN) is developed to overcome these limitations and satisfy physical constraints. CANN shows promise in automating model discovery and has the potential to revolutionize constitutive modeling.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Chaoyue Liu et al.
Summary: This paper proposes a modern view and a general mathematical framework for loss landscapes and efficient optimization in over-parameterized machine learning models and systems of non-linear equations. The optimization landscapes of these systems are generally non-convex but satisfy the PL* condition, ensuring the existence of solutions and efficient optimization.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2022)
Article
Computer Science, Interdisciplinary Applications
Amelie Schafer et al.
Summary: Misfolded tau proteins are a classical hallmark of Alzheimer's disease. This study explores the interaction between tau and atrophy using a multiphysics brain network model and longitudinal neuroimaging data. The results show that amyloid positive subjects have significantly higher tau growth and tau-induced atrophy compared to amyloid negative subjects. These findings support the hypothesis that amyloid pathology magnifies the effects of tau pathology and tissue atrophy.
ENGINEERING WITH COMPUTERS
(2022)
Article
Multidisciplinary Sciences
Bastian Zapf et al.
Summary: In recent years, various methods combining neural networks and partial differential equations have been developed. This study applies physics-informed neural networks and the finite element method to estimate the diffusion coefficient in the human brain from magnetic resonance images. Synthetic test cases demonstrate that the standard formulation of the physics-informed neural network faces challenges with noisy measurements. The study finds that a small residual of the partial differential equation after training is crucial for accurate parameter recovery.
SCIENTIFIC REPORTS
(2022)
Review
Engineering, Mechanical
Shengze Cai et al.
Summary: Significant progress has been made in simulating flow problems over the last 50 years, but challenges remain in incorporating noisy data, complex mesh generation, and solving high-dimensional problems. Physics-informed neural networks (PINNs) have been demonstrated as effective in solving inverse flow problems related to various fluid dynamics scenarios.
ACTA MECHANICA SINICA
(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
Physiology
Amelie Schaefer et al.
Summary: Amyloid-beta and hyperphosphorylated tau protein play important roles in Alzheimer's disease, and their pathological patterns are closely related to neurodegeneration. New medical imaging techniques allow visualization of tau distribution in the brain in vivo. The study findings indicate that the protein production rate is significantly higher in amyloid positive subjects compared to amyloid negative subjects, supporting the hypothesis of amyloid pathology driving tau pathology.
FRONTIERS IN PHYSIOLOGY
(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
Mathematics, Applied
Lu Lu et al.
Summary: This article introduces an overview, implementation and applications of Physics-Informed Neural Networks (PINNs), along with a new residual-based adaptive refinement (RAR) method. By comparing with finite element methods, the advantages of PINNs and the versatile applications of the Python library DeepXDE are demonstrated. Overall, DeepXDE contributes to the more rapid development of the emerging scientific machine learning field.
Article
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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
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Multidisciplinary Sciences
Silviu-Marian Udrescu et al.
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Ameya D. Jagtap et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
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Neurosciences
Amelie Schafer et al.
FRONTIERS IN NEUROSCIENCE
(2020)
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Computer Science, Interdisciplinary Applications
M. Raissi et al.
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Editorial Material
Neurosciences
Ellen Kuhl
NATURE NEUROSCIENCE
(2019)
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Neurosciences
Michael X. Henderson et al.
NATURE NEUROSCIENCE
(2019)
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Multidisciplinary Sciences
Sveva Fornari et al.
JOURNAL OF THE ROYAL SOCIETY INTERFACE
(2019)
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Mathematics, Applied
Guofei Pang et al.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2019)
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Neurosciences
Balazs Szalkai et al.
COGNITIVE NEURODYNAMICS
(2017)
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Keith A. Johnson et al.
ANNALS OF NEUROLOGY
(2016)
Editorial Material
Clinical Neurology
Julio C. Rojas et al.
NATURE REVIEWS NEUROLOGY
(2016)
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Jennifer A. McNab et al.
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Xiaoliang Wan et al.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2006)
