Related papers: Physics-agnostic and Physics-infused machine learn…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations. In particular, we seek to leverage the…
In recent years, there have been a surge in applications of neural networks (NNs) in physical sciences. Although various algorithmic advances have been proposed, there are, thus far, limited number of studies that assess the…
We use dynamical systems theory to construct the normal form of the Navier--Stokes equations for the flow of a thin layer of fluid upon a solid substrate. The normal form equations illuminate the fluid dynamics by decoupling the long-term…
Physics-Informed Neural Networks (PINN) has evolved into a powerful tool for solving partial differential equations, which has been applied to various fields such as energy, environment, en-gineering, etc. When utilizing PINN to solve…
In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology,…
The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…
We investigate flow pattern formation and viscosity reduction mechanisms in active fluids by studying a generalized Navier-Stokes model that captures the experimentally observed bulk vortex dynamics in microbial suspensions. We present…
We present our progress on the application of physics informed deep learning to reservoir simulation problems. The model is a neural network that is jointly trained to respect governing physical laws and match boundary conditions. The…
Gas-particle flows are commonly simulated through two-fluid model at industrial-scale. However, these simulations need very fine grid to have accurate flow predictions, which is prohibitively demanding in terms of computational resources.…
The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…
Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws…
Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case of a viscosity that depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general…
We report on the numerical implementation of thin film equations that describe the capillary-driven evolution of viscous films, in two-dimensional configurations. After recalling the general forms and features of these equations, we focus…
We demonstrate the results of the numerical modelling of a plane two-dimensional viscous incompressible flow in a channel with a back-step. As a mathematical model we take equations for a incompressible flow based on the quasi-hydrodynamic…
Physics-informed neural networks (PINNs) provide a mesh-free framework for solving partial differential equations by embedding governing physics into neural-network training. Recent studies have shown that parameterized PINNs can learn…
The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a…
The transformative impact of machine learning, particularly Deep Learning (DL), on scientific and engineering domains is evident. In the context of computational fluid dynamics (CFD), Physics-Informed Neural Networks (PINNs) represent a…
This paper deals with the derivation of compressible two-phase flow models. We use a thin domain approximation of a two-layer configuration governed by the Navier-Stokes equations, following the works [H. B. Stewart and B. Wendroff, J.…
Polydisperse gas-solid flows, which is notoriously difficult to model due to the complex gas-particle and particle-particle interactions, are widely encountered in industry. In this article, a refined kinetic theory for polydisperse flow is…