Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …

Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …

We propose a conservative physics-informed neural network (cPINN) on discrete domains
for nonlinear conservation laws. Here, the term discrete domain represents the discrete sub …

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward
and inverse nonlinear problems described by partial differential equations (PDEs) and noisy …

A physics informed neural network (PINN) incorporates the physics of a system by satisfying
its boundary value problem through a neural network's loss function. The PINN approach …

Data assimilation (DA) and uncertainty quantification (UQ) are extensively used in analysing
and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical …

We employ adaptive activation functions for regression in deep and physics-informed neural
networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of …

We introduce physics-informed neural networks–neural networks that are trained to solve
supervised learning tasks while respecting any given laws of physics described by general …

Fueled by breakthrough technology developments, the biological, biomedical, and
behavioral sciences are now collecting more data than ever before. There is a critical need …

We introduce physics informed neural networks--neural networks that are trained to solve
supervised learning tasks while respecting any given law of physics described by general …