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2025

Overcoming Challenges in Physics-Informed Neural Networks (PINNs): Gradient Optimization for Inverse Problems

Physics-Informed Neural Networks (PINNs) represent a promising approach for solving complex Partial Differential Equations (PDEs) and inverse problems, such as determining hidden parameters of a physical system – for instance, viscosity (nu) in a 2D Burgers equation. However, the application of PINNs presents inherent challenges. A recent study by Wang et al. (2020) delves into these limitations and proposes innovative solutions that can significantly enhance PINN performance.

Marimo

Interesting alternative to Jupyter Notebook, but with other goals and features. The idea is to embed everything inside a single .py file, instead of an .ipynb file. The .py file is used both for the graphical interface (interactive web app) and for command line execution. It tries to eliminate some of Jupyter's reproducibility issues. It has features such as integration with package and project managers, such as uv. It's worth checking out.

https://marimo.io/