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Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at…
In chemical engineering, process data are expensive to acquire, and complex phenomena are difficult to fully model. We explore the use of physics-informed neural networks (PINNs) for modeling dynamic processes with incomplete mechanistic…
Physics-Informed Neural Networks (PINNs) provide a framework for integrating physical laws with data. However, their application to Prognostics and Health Management (PHM) remains constrained by the limited uncertainty quantification (UQ)…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
The assimilation and prediction of phase-resolved surface gravity waves are critical challenges in ocean science and engineering. Potential flow theory (PFT) has been widely employed to develop wave models and numerical techniques for wave…
Despite the remarkable progress of physics-informed neural networks (PINNs) in scientific computing, they continue to face challenges when solving hydrodynamic problems with multiple discontinuities. In this work, we propose…
Recent works have explored the potential of machine learning as data-driven turbulence closures for RANS and LES techniques. Beyond these advances, the high expressivity and agility of physics-informed neural networks (PINNs) make them…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
Physics-informed neural networks (PINNs) have great potential for flexibility and effectiveness in forward modeling and inversion of seismic waves. However, coordinate-based neural networks (NNs) commonly suffer from the "spectral bias"…
How to solve inverse problems is the challenge of many engineering and industrial applications. Recently, physics-informed neural networks (PINNs) have emerged as a powerful approach to solve inverse problems efficiently. However, it is…
The recent surge of interest in physics-informed neural network (PINN) methods has led to a wave of studies that attest to their potential for solving partial differential equations (PDEs) and predicting the dynamics of physical systems.…
We predict steady-state Stokes flow of fluids within porous media at pore scales using sparse point observations and a novel class of physics-informed neural networks, called "physics-informed PointNet" (PIPN). Taking the advantages of PIPN…
Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren…
Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…
Physics-informed neural networks (PINNs) have emerged as a flexible framework for solving partial differential equations, but their performance on interface problems remains challenging because continuity and flux conditions are typically…
The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and…
Accurately and stably solving the incompressible Navier--Stokes equations with physics-informed neural networks (PINNs) remains challenging, particularly for sparse or noisy observations and for flow regimes in which the local balance among…
We report a new approach to flow field tomography that uses the Navier-Stokes and advection-diffusion equations to regularize reconstructions. Tomography is increasingly employed to infer 2D or 3D fluid flow and combustion structures from a…
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving PDEs, yet existing uncertainty quantification (UQ) approaches for PINNs generally lack rigorous statistical guarantees. In this work, we bridge this…
The goal of this paper is to provide a simple approach to perform local sensitivity analysis using Physics-informed neural networks (PINN). The main idea lies in adding a new term in the loss function that regularizes the solution in a…