Wavelet Neural Operator for solving parametric partial differential equations in computational mechanics problems

A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data

(2022) Lu Lu et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials

(2022) Somdatta Goswami et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Koopman operator for time-dependent reliability analysis

(2022) Navaneeth N. et al.   PROBABILISTIC ENGINEERING MECHANICS

A seamless multiscale operator neural network for inferring bubble dynamics

(2021) Chensen Lin et al.   JOURNAL OF FLUID MECHANICS

An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications

(2020) E. Samaniego et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Data-driven deep learning of partial differential equations in modal space

(2020) Kailiang Wu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A higher order nonlocal operator method for solving partial differential equations

(2020) Huilong Ren et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Transfer learning based multi-fidelity physics informed deep neural network

(2020) Souvik Chakraborty   JOURNAL OF COMPUTATIONAL PHYSICS

A deep energy method for finite deformation hyperelasticity

(2019) Vien Minh Nguyen-Thanh et al.   EUROPEAN JOURNAL OF MECHANICS A-SOLIDS

A nonlocal operator method for solving partial differential equations

(2019) Huilong Ren et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks

(2019) Sharmila Karumuri et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Transfer learning enhanced physics informed neural network for phase-field modeling of fracture

(2019) Somdatta Goswami et al.   THEORETICAL AND APPLIED FRACTURE MECHANICS

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Data-driven discovery of partial differential equations

(2017) Samuel H. Rudy et al.   Science Advances

Wavelet neural networks: A practical guide

(2013) Antonios K. Alexandridis et al.   NEURAL NETWORKS

Shannon wavelet spectrum analysis on truncated vibration signals for machine incipient fault detection

(2012) Jie Liu   MEASUREMENT SCIENCE and TECHNOLOGY