Multifidelity modeling for Physics-Informed Neural Networks (PINNs)

Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems

(2020) Ameya D. Jagtap et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

PPINN: Parareal physics-informed neural network for time-dependent PDEs

(2020) Xuhui Meng et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Image-Based Multiresolution Topology Optimization Using Deep Disjunctive Normal Shape Model

(2020) Vahid Keshavarzzadeh et al.   COMPUTER-AIDED DESIGN

B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

(2020) Liu Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Predictive large-eddy-simulation wall modeling via physics-informed neural networks

(2019) X. I. A. Yang et al.   Physical Review Fluids

Parametric Topology Optimization with Multi-Resolution Finite Element Models

(2019) Vahid Keshavarzzadeh et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Allocation Strategies for High Fidelity Models in the Multifidelity Regime

(2019) Daniel J. Perry et al.   SIAM-ASA Journal on Uncertainty Quantification

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

(2019) Dongkun Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Fast predictive models based on multi-fidelity sampling of properties in molecular dynamics simulations

(2018) M. Razi et al.   COMPUTATIONAL MATERIALS SCIENCE

Practical error bounds for a non-intrusive bi-fidelity approach to parametric/stochastic model reduction

(2018) Jerrad Hampton et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization

(2018) Benjamin Peherstorfer et al.   SIAM REVIEW

Fast predictive multi-fidelity prediction with models of quantized fidelity levels

(2018) Mani Razi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

A radial basis function (RBF) finite difference method for the simulation of reaction-diffusion equations on stationary platelets within the augmented forcing method

(2014) Varun Shankar et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction–Diffusion Equations on Surfaces

(2014) Varun Shankar et al.   JOURNAL OF SCIENTIFIC COMPUTING

A Stochastic Collocation Algorithm with Multifidelity Models

(2014) Akil Narayan et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Computational Aspects of Stochastic Collocation with Multifidelity Models

(2014) Xueyu Zhu et al.   SIAM-ASA Journal on Uncertainty Quantification