Advancements in Physics-Informed Neural Networks

The field of physics-informed neural networks (PINNs) is rapidly advancing, with a focus on developing innovative methods for solving complex problems in various domains. Recent research has explored the application of PINNs to optimal control problems, phase-field models, and inverse problems, demonstrating their potential for improving accuracy and efficiency. Notably, the integration of physical laws and constraints into neural network architectures has enabled the development of more robust and interpretable models. Furthermore, the use of PINNs has been extended to areas such as speech production, ultrasound-derived flow fields, and principal-agent problems, showcasing their versatility and broad applicability.

Some noteworthy papers in this area include: The paper Solving Infinite-Horizon Optimal Control Problems using the Extreme Theory of Functional Connections, which presents a novel approach for synthesizing optimal feedback control policies using PINNs. The paper A DeepONet joint Neural Tangent Kernel Hybrid Framework for Physics-Informed Inverse Source Problems and Robust Image Reconstruction, which introduces a hybrid framework for solving inverse problems using DeepONets and Neural Tangent Kernels. The paper Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation, which proposes a structure-preserving PINN framework for solving the KdV equation, ensuring physically consistent and energy-stable evolution throughout training and prediction.

Sources

Solving Infinite-Horizon Optimal Control Problems using the Extreme Theory of Functional Connections

Gamma convergence for a phase-field cohesive energy

Physics-Informed Neural Network Frameworks for the Analysis of Engineering and Biological Dynamical Systems Governed by Ordinary Differential Equations

Automated Discovery of Conservation Laws via Hybrid Neural ODE-Transformers

Deep recurrent-convolutional neural network learning and physics Kalman filtering comparison in dynamic load identification

A DeepONet joint Neural Tangent Kernel Hybrid Framework for Physics-Informed Inverse Source Problems and Robust Image Reconstruction

Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation

Physics-Informed Neural Networks for Speech Production

Fast PINN Eigensolvers via Biconvex Reformulation

Orthogonal-by-construction augmentation of physics-based input-output models

Defining Energy Indicators for Impact Identification on Aerospace Composites: A Physics-Informed Machine Learning Perspective

Dynamic Reconstruction of Ultrasound-Derived Flow Fields With Physics-Informed Neural Fields

A convolutional neural network deep learning method for model class selection

DeepPAAC: A New Deep Galerkin Method for Principal-Agent Problems

A Two-stage Adaptive Lifting PINN Framework for Solving Viscous Approximations to Hyperbolic Conservation Laws