Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences

M Alber, A Buganza Tepole, WR Cannon, S De… - NPJ digital …, 2019 - nature.com
Fueled by breakthrough technology developments, the biological, biomedical, and
behavioral sciences are now collecting more data than ever before. There is a critical need …

Machine learning in geo-and environmental sciences: From small to large scale

P Tahmasebi, S Kamrava, T Bai, M Sahimi - Advances in Water Resources, 2020 - Elsevier
In recent years significant breakthroughs in exploring big data, recognition of complex
patterns, and predicting intricate variables have been made. One efficient way of analyzing …

When and why PINNs fail to train: A neural tangent kernel perspective

S Wang, X Yu, P Perdikaris - Journal of Computational Physics, 2022 - Elsevier
Physics-informed neural networks (PINNs) have lately received great attention thanks to
their flexibility in tackling a wide range of forward and inverse problems involving partial …

DeepXDE: A deep learning library for solving differential equations

L Lu, X Meng, Z Mao, GE Karniadakis - SIAM review, 2021 - SIAM
Deep learning has achieved remarkable success in diverse applications; however, its use in
solving partial differential equations (PDEs) has emerged only recently. Here, we present an …

PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain

H Gao, L Sun, JX Wang - Journal of Computational Physics, 2021 - Elsevier
Recently, the advent of deep learning has spurred interest in the development of physics-
informed neural networks (PINN) for efficiently solving partial differential equations (PDEs) …

Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data

L Sun, H Gao, S Pan, JX Wang - Computer Methods in Applied Mechanics …, 2020 - Elsevier
Numerical simulations on fluid dynamics problems primarily rely on spatially or/and
temporally discretization of the governing equation using polynomials into a finite …

A deep collocation method for the bending analysis of Kirchhoff plate

H Guo, X Zhuang, T Rabczuk - ar**
F Sahli Costabal, Y Yang, P Perdikaris… - Frontiers in …, 2020 - frontiersin.org
A critical procedure in diagnosing atrial fibrillation is the creation of electro-anatomic
activation maps. Current methods generate these map**s from interpolation using a few …

Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks

G Kissas, Y Yang, E Hwuang, WR Witschey… - Computer Methods in …, 2020 - Elsevier
Advances in computational science offer a principled pipeline for predictive modeling of
cardiovascular flows and aspire to provide a valuable tool for monitoring, diagnostics and …