Related papers: Physics-informed machine learning of the correlati…
The closure problem in fluid modeling is a well-known challenge to modelers aiming to accurately describe their system of interest. Over many years, analytic formulations in a wide range of regimes have been presented but a practical,…
The carbon pump of the world's ocean plays a vital role in the biosphere and climate of the earth, urging improved understanding of the functions and influences of the ocean for climate change analyses. State-of-the-art techniques are…
A modified physics-informed neural network is used to predict the dynamics of optical pulses including one-soliton, two-soliton, and rogue wave based on the coupled nonlinear Schr\"odinger equation in birefringent fibers. At the same time,…
Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical…
The structure of an aqueous solution of sodium chloride at a planar electrode is investigated by integral equation techniques. With the central force water model the aqueous electrolyte is modelled as a mixture of sodium and chloride ions…
Physics Informed Neural Networks (PINNs) are shown to be a promising method for the approximation of Partial Differential Equations (PDEs). PINNs approximate the PDE solution by minimizing physics-based loss functions over a given domain.…
We present a new hybrid physics-based machine-learning approach to reservoir modeling. The methodology relies on a series of deep adversarial neural network architecture with physics-based regularization. The network is used to simulate the…
Predicting the outcome of liquid droplet collisions is an extensively studied phenomenon but the current physics based models for predicting the outcomes are poor (accuracy $\approx 43\%$). The key weakness of these models is their limited…
The lattice Boltzmann equation (LBE), rooted in kinetic theory, provides a powerful framework for capturing complex flow behaviour by describing the evolution of single-particle distribution functions (PDFs). Despite its success, solving…
Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…
Solving partial differential equations (PDEs) is essential in scientific forecasting and fluid dynamics. Traditional approaches often incur expensive computational costs and trade-offs in efficiency and accuracy. Recent deep neural networks…
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…
Eigenvalue problems are critical to several fields of science and engineering. We expand on the method of using unsupervised neural networks for discovering eigenfunctions and eigenvalues for differential eigenvalue problems. The obtained…
Physics-Informed Neural Networks (PINNs) have gained much attention in various fields of engineering thanks to their capability of incorporating physical laws into the models. However, the assessment of PINNs in industrial applications…
Reynolds-averaged Navier-Stokes (RANS) equations are widely used in engineering turbulent flow simulations. However, RANS predictions may have large discrepancies due to the uncertainties in modeled Reynolds stresses. Recently, Wang et al.…
Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…
We use supervised machine learning together with the concepts of classical density functional theory to investigate the effects of interparticle attraction on the pair structure, thermodynamics, bulk liquid-gas coexistence, and associated…
We apply a physics-informed deep-learning approach the PINN approach to the Black-Scholes equation for pricing American and European options. We test our approach on both simulated as well as real market data, compare it to…
In this research, the application of the Physics-Informed Neural Network (PINN) model is explored to solve transport equation-based Partial Differential Equations (PDEs). The primary objective is to analyze the impact of different…
Our understanding of supercooled liquids and glasses has lagged significantly behind that of simple liquids and crystalline solids. This is in part due to the many possibly relevant degrees of freedom that are present due to the disorder…