PINN Model

Physics-Informed Neural Networks (PINNs) are a class of machine learning models designed to solve partial differential equations (PDEs) by incorporating the governing equations directly into the network's loss function. Current research focuses on improving PINN training efficiency and accuracy, exploring diverse architectures like those leveraging tensor decompositions for high-dimensional problems, Bayesian inference for uncertainty quantification, and adaptive methods for optimized point selection and domain decomposition. These advancements enhance PINNs' ability to tackle complex scientific and engineering problems, offering a powerful alternative to traditional numerical methods for solving and analyzing PDEs across various fields.

Papers

November 13, 2024

Physics-Informed Neural Networks for Electrical Circuit Analysis: Applications in Dielectric Material Modeling
Reyhaneh Taj
Financial Application Physic Informed Neural Network Scientific Machine Learning PINN Model Circuit Model High Dielectric Constant

August 27, 2024

GINN-KAN: Interpretability pipelining with applications in Physics Informed Neural Networks
Nisal Ranasinghe, Yu Xia, Sachith Seneviratne, Saman Halgamuge
Financial Application Inherent Interpretability Physic Informed Neural Network Kolmogorov Arnold Network Interpretable Neural Network PINN Model

August 23, 2024

Functional Tensor Decompositions for Physics-Informed Neural Networks
Sai Karthikeya Vemuri, Tim Büchner, Julia Niebling, Joachim Denzler
Physic Informed Neural Network High Dimensional Partial Differential Equation PINN Model Multivariate Function

August 18, 2024

Improvement of Bayesian PINN Training Convergence in Solving Multi-scale PDEs with Noise
Yilong Hou, Xi'an Li, Jinran Wu
Industrial Disturbing Noise Bayesian Inference Large Relevance Improvement Hamiltonian Monte Carlo PINN Model Bayesian Physic Informed Neural Network

June 21, 2024

On the estimation rate of Bayesian PINN for inverse problems
Yi Sun, Debarghya Mukherjee, Yves Atchade
Physic Informed Neural Network Inverse Problem Partial Differential Equation PINN Model

May 23, 2024

RoPINN: Region Optimized Physics-Informed Neural Networks
Haixu Wu, Huakun Luo, Yuezhou Ma, Jianmin Wang, Mingsheng Long
Physic Informed Neural Network Region Specific PINN Model Reduce SCATTER

April 11, 2024

PINNACLE: PINN Adaptive ColLocation and Experimental points selection
Gregory Kang Ruey Lau, Apivich Hemachandra, See-Kiong Ng, Bryan Kian Hsiang Low
Experimental Design Fidelity Reward PINN Model Collocation Point Training Point PINN Training

February 5, 2024

Architectural Strategies for the optimization of Physics-Informed Neural Networks
Hemanth Saratchandran, Shin-Fang Chng, Simon Lucey
Optimization Purpose Physic Informed Neural Network Neural Architecture Neural Tangent Kernel PINN Model Architectural Design

February 2, 2024

Challenges in Training PINNs: A Loss Landscape Perspective
Pratik Rathore, Weimu Lei, Zachary Frangella, Lu Lu, Madeleine Udell
Technical Challenge Physic Informed Neural Network Second Order Loss Landscape Adam Optimizer PINN Model Differential Operator

February 1, 2024

PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks
Sifan Wang, Bowen Li, Yuhan Chen, Paris Perdikaris
Physic Informed Neural Network Deep Learning Architecture Residual Connection Physic Informed Deep Learning Residual Neural Network PINN Model Residual Physic

November 1, 2023

Domain decomposition-based coupling of physics-informed neural networks via the Schwarz alternating method
Will Snyder, Irina Tezaur, Christopher Wentland
Physic Informed Neural Network Practical Method Internet Service Domain Numerical Method PINN Method PINN Model Optimal Coupling

August 12, 2023

A Domain-adaptive Physics-informed Neural Network for Inverse Problems of Maxwell's Equations in Heterogeneous Media
Shiyuan Piao, Hong Gu, Aina Wang, Pan Qin
Physic Informed Neural Network Inverse Problem Diverse Equation PINN Model Heterogeneous Medium Elliptic Interface Problem

July 12, 2023

Spectral-Bias and Kernel-Task Alignment in Physically Informed Neural Networks
Inbar Seroussi, Asaf Miron, Zohar Ringel
Neural Network Differential Equation Gaussian Process Regression Spectral Bias PINN Model Kernel Target Alignment Informed Neural Network

May 18, 2023

A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data
Elham Kiyani, Khemraj Shukla, George Em Karniadakis, Mikko Karttunen
Physic Informed Neural Network Motion Information Symbolic Regression Diverse Equation Gray Box PINN Method PINN Model Allen Cahn Equation

February 15, 2023

On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it
Andrea Bonfanti, Roberto Santana, Marco Ellero, Babak Gholami
Neural Network Strong Generalization Physic Informed Neural Network Related Hyperparameters Domain Decomposition Training Domain PINN Model Consistent Prediction

December 8, 2022

AutoPINN: When AutoML Meets Physics-Informed Neural Networks
Xinle Wu, Dalin Zhang, Miao Zhang, Chenjuan Guo, Shuai Zhao, Yi Zhang, Huai Wang, Bin Yang
Neural Network Physic Informed Neural Network Neural Architecture Online autoML PINN Model

November 16, 2022

Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology
Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi
Neural Network Physic Informed Neural Network PINN Model Gated Recurrent

September 29, 2022

Scaling transformation of the multimode nonlinear Schr\"odinger equation for physics-informed neural networks
Ivan Chuprov, Dmitry Efremenko, Jiexing Gao, Pavel Anisimov, Viacheslav Zemlyakov
Physic Informed Neural Network PINN Model Light Propagation Nonlinear Schr\"odinger Equation

July 15, 2022

Physics-Aware Neural Networks for Boundary Layer Linear Problems
Antonio Tadeu Azevedo Gomes, Larissa Miguez da Silva, Frederic Valentin
Neural Network Partial Differential Equation PINN Model Linear Partial Differential Equation

May 19, 2022

Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizations
Ramansh Sharma, Varun Shankar
Physic Informed Neural Network Radial Basis Function Faster Training PINN Model

PINN Model

Papers

Physics-Informed Neural Networks for Electrical Circuit Analysis: Applications in Dielectric Material Modeling

GINN-KAN: Interpretability pipelining with applications in Physics Informed Neural Networks

Functional Tensor Decompositions for Physics-Informed Neural Networks

Improvement of Bayesian PINN Training Convergence in Solving Multi-scale PDEs with Noise

On the estimation rate of Bayesian PINN for inverse problems

RoPINN: Region Optimized Physics-Informed Neural Networks

PINNACLE: PINN Adaptive ColLocation and Experimental points selection

Architectural Strategies for the optimization of Physics-Informed Neural Networks

Challenges in Training PINNs: A Loss Landscape Perspective

PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks

Domain decomposition-based coupling of physics-informed neural networks via the Schwarz alternating method

A Domain-adaptive Physics-informed Neural Network for Inverse Problems of Maxwell's Equations in Heterogeneous Media

Spectral-Bias and Kernel-Task Alignment in Physically Informed Neural Networks

A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data

On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it

AutoPINN: When AutoML Meets Physics-Informed Neural Networks

Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology

Scaling transformation of the multimode nonlinear Schr\"odinger equation for physics-informed neural networks

Physics-Aware Neural Networks for Boundary Layer Linear Problems

Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizations