Related papers: Error Bound Analysis of Physics-Informed Neural Ne…
Magnetic resonance imaging (MRI) is an important non-invasive imaging method in clinical diagnosis. Beyond the common image structures, parametric imaging can provide the intrinsic tissue property thus could be used in quantitative…
Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…
Tracer-kinetic models allow for the quantification of kinetic parameters such as blood flow from dynamic contrast-enhanced magnetic resonance (MR) images. Fitting the observed data with multi-compartment exchange models is desirable, as…
Physics-Informed Neural Networks (PINNs) are fast becoming an important tool to solve differential equations rapidly and accurately, and to identify the systems parameters that best agree with a given set of measurements. PINNs have been…
Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust for smaller training sets, derive better generalization…
We consider the approximation of a class of dynamic partial differential equations (PDE) of second order in time by the physics-informed neural network (PINN) approach, and provide an error analysis of PINN for the wave equation, the…
Quantum state tomography (QST) faces exponential measurement requirements and noise sensitivity in multi-qubit systems, bottlenecking practical quantum technologies. We present a physics-informed neural network (PINN) framework integrating…
We propose a deep learning-based approach that integrates MRI sequence parameters to improve the accuracy and generalizability of quantitative image synthesis from clinical weighted MRI. Our physics-driven neural network embeds MRI sequence…
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)…
Accurate reconstruction of magnetic fields in inaccessible regions is vital for many high-precision experiments in physics. Traditional methods, such as spherical harmonic expansion, often suffer from truncation errors that limit their…
Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of…
Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for…
Physics informed neural networks approximate solutions of PDEs by minimizing pointwise residuals. We derive rigorous bounds on the error, incurred by PINNs in approximating the solutions of a large class of linear parabolic PDEs, namely…
We prove a priori and a posteriori error estimates for physics-informed neural networks (PINNs) for linear PDEs. We analyze elliptic equations in primal and mixed form, elasticity, parabolic, hyperbolic and Stokes equations; and a PDE…
Magnetic resonance imaging (MRI) is a cornerstone of clinical neuroimaging, yet conventional MRIs provide qualitative information heavily dependent on scanner hardware and acquisition settings. While quantitative MRI (qMRI) offers intrinsic…
Estimating $T_2$ relaxation time distributions from multi-echo $T_2$-weighted MRI ($T_2W$) data can provide valuable biomarkers for assessing inflammation, demyelination, edema, and cartilage composition in various pathologies, including…
In this paper, the physics-informed neural networks (PINN) is applied to high-dimensional system to solve the (N+1)-dimensional initial boundary value problem with 2N+1 hyperplane boundaries. This method is used to solve the most classic…
The Physics-Informed Neural Network (PINN) approach is a new and promising way to solve partial differential equations using deep learning. The $L^2$ Physics-Informed Loss is the de-facto standard in training Physics-Informed Neural…
Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We…
In this paper, we study physics-informed neural networks (PINN) to approximate solutions to one-dimensional boundary value problems for linear elliptic equations and establish robust error estimates of PINN regardless of the quantities of…