Abstract Machine learning is rapidly becoming a core technology for scientific computing,
with numerous opportunities to advance the field of computational fluid dynamics. Here we …

The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

The rapid increase in both the quantity and complexity of data that are being generated daily
in the field of environmental science and engineering (ESE) demands accompanied …

Machine learning methods have been remarkably successful for a wide range of application
areas in the extraction of essential information from data. An exciting and relatively recent …

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data
from experiments, field measurements, and large-scale simulations at multiple …

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 …

Numerical simulations on fluid dynamics problems primarily rely on spatially or/and
temporally discretization of the governing equation using polynomials into a finite …

Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …

Abstract Machine learning-based modeling of physical systems has experienced increased
interest in recent years. Despite some impressive progress, there is still a lack of …

Abstract Machine learning (ML) has been increasingly used to aid aerodynamic shape
optimization (ASO), thanks to the availability of aerodynamic data and continued …