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We simulate the response of acoustic seismic waves in horizontally layered media using a deep neural network. In contrast to traditional finite-difference modelling techniques our network is able to directly approximate the recorded seismic…
Ultrafast optics is driven by a myriad of complex nonlinear dynamics. The ubiquitous presence of governing equations in the form of partial integro-differential equations (PIDE) necessitates the need for advanced computational tools to…
Full Waveform Inversion (FWI) is a powerful technique for estimating high-resolution subsurface velocity models by minimizing the discrepancy between modeled and observed seismic data. However, the oscillatory nature of seismic waveforms…
As artificial intelligence emerges as a transformative enabler for fusion energy commercialization, fast and accurate solvers become increasingly critical. In magnetic confinement nuclear fusion, rapid and accurate solution of the…
Accurate modeling of personalized cardiovascular dynamics is crucial for non-invasive monitoring and therapy planning. State-of-the-art physics-informed neural network (PINN) approaches employ deep, multi-branch architectures with…
In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first…
Accurate interpolation of seismic data is crucial for improving the quality of imaging and interpretation. In recent years, deep learning models such as U-Net and generative adversarial networks have been widely applied to seismic data…
Physics-informed neural networks (PINNs) integrate physical laws with data-driven models to improve generalization and sample efficiency. This work introduces an open-source implementation of the Physics-Informed Neural Network with Control…
Neural networks offer powerful tools to solve partial differential equations (PDEs). We present a Variational Physics-Informed Neural Network (VPINN) designed for parabolic problems. Our approach combines a classical time discretization…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
Accurate prediction of nonlinear structural responses is essential for earthquake risk assessment and management. While high-fidelity nonlinear time history analysis provides the most comprehensive and accurate representation of the…
Acquisition of large datasets for three-dimensional (3D) partial differential equations (PDE) is usually very expensive. Physics-informed neural operator (PINO) eliminates the high costs associated with generation of training datasets, and…
In this article we develop a Physics Informed Neural Network (PINN) approach to simulate ice sheet dynamics governed by the Shallow Ice Approximation. This problem takes the form of a time-dependent parabolic obstacle problem. Prior work…
Physics-Informed Neural Networks (PINNs) frequently encounter difficulties in accurately resolving shock waves within high-speed compressible flows, a failure largely attributed to the "gradient pathology" arising from extreme stiffness at…
Physics-informed neural networks (PINNs) are a class of deep learning models that utilize physics in the form of differential equations to address complex problems, including those with limited data availability. However, solving…
Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the…
Deep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by PDEs, even in presence of integral terms. In this paper, we…
We propose a method utilizing physics-informed neural networks (PINNs) to solve Poisson equations that serve as control variates in the computation of transport coefficients via fluctuation formulas, such as the Green--Kubo and generalized…
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…
A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…