Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulations

This paper proposes a novel framework for simulating the dynamics of beams on elastic foundations. Specifically, partial differential equations modeling Euler–Bernoulli and Timoshenko beams on the Winkler foundation are simulated using a causal physics-informed neural network (PINN) coupled with transfer learning. Conventional PINNs encounter...

Physics-Informed Machine Learning for Solder Joint Qualification Tests

The ability to accurately predict the reliability and lifetime of electronics is of great importance to the industry. The failure of the solder joint is of particular interest for these predictions, because of their susceptibility to failure under thermo-mechanical stress. However, the experimental or even conventional simulation techniques...

Modelling of coupled reservoir and wellbore for energy transition

Borehole operations play a crucial role in managing various subsurface activities related to energy, including energy storage, geothermal energy production, CO2 sequestration, oil and gas extraction, wastewater disposal, and thermal recovery processes. In recent times, intelligent well technologies, such as long deviated multi-lateral wells...

Physics-Informed Neural Networks for Solving Forward and Inverse Problems in Complex Beam Systems

This article proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler–Bernoulli and Timoshenko theories, where the double beams are connected with a Winkler foundation. In particular, forward and inverse problems for the Euler–Bernoulli...

Physics-informed Neural Networks Based On Sequential Training For CO2 Utilization And Storage In Subsurface Reservoir

CO2 utilization and storage (CCUS) simulation in subsurface reservoirs with complex heterogeneous structures necessitates a model that can capture multiphase compositional flow and transport. The governing equations are highly nonlinear due to the complex thermodynamic behavior, which involves the appearance and disappearance of multiple phases....

PINNs for parametrized problems

Physics Informed Neural Networks are a relatively new subject of study in the area of numerical mathematics. In this thesis, we take a look at part of the work that has been done in this area up until now, with the ultimate goal to develop a new type of PINN that improves upon the old concept. We introduce the concept of parameterized PINNs,...

Solving Partial Differential Equations using Physics-Informed Neural Networks

In an attempt to find alternatives for solving partial differential equations (PDEs)<br/>with traditional numerical methods, a new field has emerged which incorporates<br/>the residual of a PDE into the loss function of an Artificial Neural Network. This<br/>method is called Physics-Informed Neural Network (PINN). In this thesis, we study dense...

Physics-Informed Neural Networks for Fluid Mechanics

Physics-informed machine learning is a novel approach to solving flow problems with physics-informed neural networks (PINNs), that combines physical knowledge and machine learning.<br/>This study aims to investigate the potential of the application of PINNs in fluid mechanics problems by solving two practical flow problems.<br/><br/>The first...

DeepONet Generated Optimal Test Functions for the Finite Element Method

The finite element method (FEM) is a numerical method that is used to approximate the solutions to partial differential equations when solutions in the classical sense do not exist or are very hard to find. The method is used to solve problems that are relevant for industries like the automotive industry, the petroleum industry, and the aviation...

PINN inspired Freeform Design: Using Fraunhofer Diffraction to find Freeforms described by B-spline Surfaces

This project aims to recreate intensity patterns using Fraunhofer diffraction as a means of simulation. These intensity patterns are created by phase shifting specific parts of an incoming field of light. These phase shifts are determined by a B-spline surface, which is in turn controlled by so-called control points. Only a handful of control...

Using a Physics-Informed Neural Network to solve the Ideal Magnetohydrodynamic Equations

In this work we investigate neural networks and subsequently physics-informed neural networks. Physicsinformed neural networks are away to solve physical models that are based on differential equations by using a neural network. The wave equation, Burgers’ equation, Euler’s equation, and the ideal magnetohydrodynamic equations are introduced and...