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Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…

The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based…

Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural network. Therefore,…

Physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs) relevant to multiscale modeling, but they often fail when applied to materials with discontinuous coefficients, such as media with…

Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data. Biologically-informed neural networks (BINNs) are a variant of PINNs that preserve the known differential…

The residual loss in Physics-Informed Neural Networks (PINNs) alters the simple recursive relation of layers in a feed-forward neural network by applying a differential operator, resulting in a loss landscape that is inherently different…

As is well known, differential algebraic equations (DAEs), which are able to describe dynamic changes and underlying constraints, have been widely applied in engineering fields such as fluid dynamics, multi-body dynamics, mechanical systems…

The accurate solution of nonlinear hyperbolic partial differential equations (PDEs) remains challenging due to steep gradients, discontinuities, and multiscale structures that make conventional solvers computationally demanding.…

In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning…

Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…

We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as Physics Informed Neural Networks (PINNs). PINNs are popular machine-learning templates…

A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics.…

Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real…

Our recent intensive study has found that physics-informed neural networks (PINN) tend to be local approximators after training. This observation leads to this novel physics-informed radial basis network (PIRBN), which can maintain the…

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…

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,…

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…

Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…

Physics-informed neural networks (PINNs) have emerged as a new learning paradigm for solving partial differential equations (PDEs) by enforcing the constraints of physical equations, boundary conditions (BCs), and initial conditions (ICs)…

Physics-informed neural networks (PINNs) have attracted attention as an alternative approach to solve partial differential equations using a deep neural network (DNN). Their simplicity and capability allow them to solve inverse problems for…