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Recently, Physics-Informed Neural Networks (PINNs) have gained significant attention for their versatile interpolation capabilities in solving partial differential equations (PDEs). Despite their potential, the training can be…
Solutions to differential equations are of significant scientific and engineering relevance. Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving differential equations, but they lack a theoretical…
Physics-informed neural networks (PINNs) have been widely applied in different fields due to their effectiveness in solving partial differential equations (PDEs). However, the accuracy and efficiency of PINNs need to be considerably…
Accurate vessel trajectory prediction is crucial for navigational safety, route optimization, traffic management, search and rescue operations, and autonomous navigation. Traditional data-driven models lack real-world physical constraints,…
Neural networks are universal approximators and are studied for their use in solving differential equations. However, a major criticism is the lack of error bounds for obtained solutions. This paper proposes a technique to rigorously…
We leverage Physics-Informed Neural Networks (PINNs) to learn solution functions of parametric Navier-Stokes Equations (NSE). Our proposed approach results in a feasible optimization problem setup that bypasses PINNs' limitations in…
Network embedding algorithms are able to learn latent feature representations of nodes, transforming networks into lower dimensional vector representations. Typical key applications, which have effectively been addressed using network…
Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…
Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation,…
A novel framework is proposed for cellular offloading with the aid of multiple unmanned aerial vehicles (UAVs), while the non-orthogonal multiple access (NOMA) technique is employed at each UAV to further improve the spectrum efficiency of…
This paper introduces a novel methodology for simulating the dynamics of beams on elastic foundations. Specifically, Euler-Bernoulli and Timoshenko beam models on the Winkler foundation are simulated using a transfer learning approach…
This work proposes a Physics-informed Neural Network framework with Graph Embedding (GPINN) to perform PINN in graph, i.e. topological space instead of traditional Euclidean space, for improved problem-solving efficiency. The method…
This work introduces the Nirenberg Neural Network: a numerical approach to the Nirenberg problem of prescribing Gaussian curvature on $S^2$ for metrics that are pointwise conformal to the round metric. Our mesh-free physics-informed neural…
During training, the weights of a Deep Neural Network (DNN) are optimized from a random initialization towards a nearly optimum value minimizing a loss function. Only this final state of the weights is typically kept for testing, while the…
Neural Networks (NNs) can be used to solve Ordinary and Partial Differential Equations (ODEs and PDEs) by redefining the question as an optimization problem. The objective function to be optimized is the sum of the squares of the PDE to be…
System-level condition monitoring methods estimate the electrical parameters of multiple components in a converter to assess their health status. The estimation accuracy and variation can differ significantly across parameters. For…
Neural networks have been proposed as efficient numerical wavefunction ansatze which can be used to variationally search a wide range of functional forms for ground state solutions. These neural network methods are also advantageous in that…
Feedforward neural networks with random hidden nodes suffer from a problem with the generation of random weights and biases as these are difficult to set optimally to obtain a good projection space. Typically, random parameters are drawn…
In this paper, we effectively solve the inverse source problem of the fractional Poisson equation using MC-fPINNs. We construct two neural networks $ u_{NN}(x;\theta )$ and $f_{NN}(x;\psi)$ to approximate the solution $u^{*}(x)$ and the…
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…