Related papers: Data-driven forward-inverse problems for Yajima-Oi…

It was recently shown that the loss function used for training physics-informed neural networks (PINNs) exhibits local minima at solutions corresponding to fixed points of dynamical systems. In the forward setting, where the PINN is trained…

In recent years, physics-informed neural networks (PINNs) have gained significant attention for solving differential equations, although they suffer from two fundamental limitations, namely, spectral bias inherent in neural networks and…

Flexoelectricity, the coupling between strain gradients and electric polarization, poses significant computational challenges due to its governing fourth-order partial differential equations that require C1-continuous solutions. To address…

Physics-informed neural networks have attracted significant attention in scientific machine learning for their capability to solve forward and inverse problems governed by partial differential equations. However, the accuracy of PINN…

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…

Direct observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into modeling efforts. Machine learning (ML)…

This paper presents NSGA-PINN, a multi-objective optimization framework for effective training of Physics-Informed Neural Networks (PINNs). The proposed framework uses the Non-dominated Sorting Genetic Algorithm (NSGA-II) to enable…

Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to uncover…

The electromagnetic inverse scattering problem (ISP), due to its inherent strong nonlinearity and severe ill-posedness, has long been a core challenge in microwave imaging. In recent years, physics-informed neural networks (PINNs) have…

This study introduces an accelerated training method for Vanilla Physics-Informed-Neural-Networks (PINN) addressing three factors that imbalance the loss function: initial weight state of a neural network, domain to boundary points ratio,…

Physics-Informed Neural Networks (PINNs) are effective methods for solving inverse problems and discovering governing equations from observational data. However, their performance degrades significantly under complex measurement noise and…

In this paper, we develop a deep learning approach for the accurate solution of challenging problems of near-field microscopy that leverages the powerful framework of physics-informed neural networks (PINNs) for the inversion of the complex…

Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…

Physics-informed neural networks (PINNs) have been proposed to solve two main classes of problems: data-driven solutions and data-driven discovery of partial differential equations. This task becomes prohibitive when such data is highly…

Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…

Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

Physics-informed neural networks (PINNs) have emerged as a promising deep learning method, capable of solving forward and inverse problems governed by differential equations. Despite their recent advance, it is widely acknowledged that…

We demonstrate a deep learning framework capable of recovering physical parameters from the Nonlinear Schrodinger Equation (NLSE) under severe noise conditions. By integrating Physics-Informed Neural Networks (PINNs) with automatic…

In this work, we investigate various approaches that use learning from training data to solve inverse problems, following a bi-level learning approach. We consider a general framework for optimal inversion design, where training data can be…

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian…