In scientific computing, physical phenomena are often described using a strong mathematical form consisting of governing differential equations as well as initial and boundary conditions. PiML is a widely-used approach that integrates physical laws into ML models (for example, designing loss functions or regularization), facilitates the accurate capture of dynamic patterns and concomitantly diminishes the search space for model parameters. This approach is sometimes referred to as imposing differentiable constraints in loss functions. It integrates (noisy) data and mathematical models, and implements them through neural networks (physics-informed neural networks) or kernel-based neural operators (physics-informed neural operators).
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