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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…

Numerical Analysis · Mathematics 2022-07-27 Ameya D. Jagtap , Zhiping Mao , Nikolaus Adams , George Em Karniadakis

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

Computational Engineering, Finance, and Science · Computer Science 2023-11-14 Ali Harandi , Ahmad Moeineddin , Michael Kaliske , Stefanie Reese , Shahed Rezaei

Physics-Informed Neural Networks (PINNs) have gained much attention in various fields of engineering thanks to their capability of incorporating physical laws into the models. However, the assessment of PINNs in industrial applications…

Machine Learning · Computer Science 2022-07-19 Thi Nguyen Khoa Nguyen , Thibault Dairay , Raphaël Meunier , Mathilde Mougeot

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…

Machine Learning · Computer Science 2022-12-09 Rambod Mojgani , Maciej Balajewicz , Pedram Hassanzadeh

Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform…

Numerical Analysis · Mathematics 2023-12-05 Leon Herrmann , Tim Bürchner , Felix Dietrich , Stefan Kollmannsberger

The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many…

Numerical Analysis · Mathematics 2024-09-10 Hao Zhang , Longxiang Jiang , Xinkun Chu , Yong Wen , Luxiong Li , Yonghao Xiao , Liyuan Wang

In this article, we employ Chien-Physics Informed Neural Networks (C-PINNs) to obtain solutions for singularly perturbed convection-diffusion equations, reaction-diffusion equations, and their coupled forms in both one and two-dimensional…

Numerical Analysis · Mathematics 2025-09-16 Gautam Singh , Sofia Haider

Scientific machine learning (SciML) represents a significant advancement in integrating machine learning (ML) with scientific methodologies. At the forefront of this development are Physics-Informed Neural Networks (PINNs), which offer a…

Machine Learning · Computer Science 2024-11-19 Reyhaneh Taj

Achieving clean combustion systems is crucial in terms of solving environmental impacts, decarbonization needs and sustainability matters. Traditional combustion modeling techniques via computational fluid dynamics with accurate chemical…

Fluid Dynamics · Physics 2025-09-11 Mahmood Mousavi , Caleb Caldwell , Jacob Baltes , Muteb Aljasem , Bok Jik Lee

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for integrating physics-based constraints and data to address forward and inverse problems in machine learning. Despite their potential, the implementation of PINNs…

Optimization and Control · Mathematics 2024-12-19 Alan Williams , Christopher Leon , Alexander Scheinker

In this work, a physics-informed neural networks (PINNs) based algorithm is used for simulation of nonlinear 1D and 2D Burgers' type models. This scheme relies on a neural network built to approximate the problem solution and use a trial…

Machine Learning · Computer Science 2025-06-17 Ajeet Singh , Ram Jiwari , Vikram , Ujjwal Saini

Physics-Informed Neural Networks (PINNs) have advanced the data-driven solution of differential equations (DEs) in dynamic physical systems, yet challenges remain in explainability, scalability, and architectural complexity. This paper…

Signal Processing · Electrical Eng. & Systems 2025-12-03 Ibrahim Shahbaz , Mohammad J. Abdel-Rahman , Eman Hammad

We present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of interface problems with discontinuous coefficients and/or interfacial jumps. This framework…

Machine Learning · Computer Science 2025-04-30 Sumanta Roy , Chandrasekhar Annavarapu , Pratanu Roy , Antareep Kumar Sarma

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…

Numerical Analysis · Mathematics 2024-04-25 Pasquale Ambrosio , Salvatore Cuomo , Mariapia De Rosa

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…

Computational Engineering, Finance, and Science · Computer Science 2022-01-26 Han Gao , Matthew J. Zahr , Jian-Xun Wang

This paper addresses the challenge of transient stability in power systems with missing parameters and uncertainty propagation in swing equations. We introduce a novel application of Physics-Informed Neural Networks (PINNs), specifically an…

Artificial Intelligence · Computer Science 2023-11-23 Ren Wang , Ming Zhong , Kaidi Xu , Lola Giráldez Sánchez-Cortés , Ignacio de Cominges Guerra

Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier-Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms,…

Fluid Dynamics · Physics 2021-05-21 Shengze Cai , Zhiping Mao , Zhicheng Wang , Minglang Yin , George Em Karniadakis

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…

Machine Learning · Computer Science 2026-04-21 William Lavery , Jodie A. Cochrane , Christian Olesen , Dagim S. Tadele , John T. Nardini , Sara Hamis

The emergence of neural networks constrained by physical governing equations has sparked a new trend in deep learning research, which is known as Physics-Informed Neural Networks (PINNs). However, solving high-dimensional problems with…

Machine Learning · Computer Science 2025-09-26 Biao Yuan , Ana Heitor , He Wang , Xiaohui Chen

Differential equations are involved in modeling many engineering problems. Many efforts have been devoted to solving differential equations. Due to the flexibility of neural networks, Physics Informed Neural Networks (PINNs) have recently…

Computational Engineering, Finance, and Science · Computer Science 2025-09-22 Siyuan Yang , Cheng Song , Zhilu Lai , Wenjia Wang