Advances in Physics-Informed Neural Networks

The field of physics-informed neural networks (PINNs) is rapidly advancing, with a focus on improving the accuracy and efficiency of inverse analysis and uncertainty quantification. Researchers are exploring new methods to enforce boundary conditions, such as using distance functions and adaptive weight tuning, which have shown to be more effective than traditional penalty-based methods. Additionally, domain decomposition techniques are being developed to enable the solution of large-scale problems and to quantify epistemic and aleatoric uncertainties. The use of physics-informed residual neural networks (PIRNNs) is also being investigated, which has demonstrated superior performance in solving inverse problems. Furthermore, researchers are applying PINNs to a wide range of applications, including vessel length estimation, computer-generated holography, and solving high-frequency partial differential equations. Noteworthy papers include: The paper Reliable and Efficient Inverse Analysis using Physics-Informed Neural Networks with Distance Functions and Adaptive Weight Tuning, which introduces a new method for enforcing boundary conditions using distance functions. The paper Vessel Length Estimation from Magnetic Wake Signature: A Physics-Informed Residual Neural Network Approach, which proposes a novel approach for vessel length estimation using magnetic wake signatures and PIRNNs.

Sources

Reliable and Efficient Inverse Analysis using Physics-Informed Neural Networks with Distance Functions and Adaptive Weight Tuning

\$PINN -- a Domain Decomposition Method for Bayesian Physics-Informed Neural Networks

Vessel Length Estimation from Magnetic Wake Signature: A Physics-Informed Residual Neural Network Approach

Learning Brenier Potentials with Convex Generative Adversarial Neural Networks

Multi-level datasets training method in Physics-Informed Neural Networks

Towards Robust and Generalizable Gerchberg Saxton based Physics Inspired Neural Networks for Computer Generated Holography: A Sensitivity Analysis Framework

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