Physics-Informed Neural Networks and Neural Operators for Parametric PDEs: A Human-AI Collaborative Analysis

arXiv — stat.ML•Friday, November 7, 2025 at 5:00:00 AM

Recent advancements in machine learning, particularly physics-informed neural networks (PINNs) and neural operators, are transforming how we solve parametric partial differential equations (PDEs). These equations are crucial in various scientific and engineering fields, but traditional methods can be costly and time-consuming. By leveraging AI, researchers can now explore parameter spaces more efficiently, making it easier to find solutions that depend on different physical properties and conditions. This shift not only saves time but also opens up new possibilities for innovation in complex systems.

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