Neural networks tend to learn low-frequency functions first. This means PINNs often struggle to capture high-frequency details or sharp discontinuities in the solution (like shock waves in fluid dynamics) without specialized architecture modifications (like Fourier Feature Embeddings).
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Sensors are expensive. You can’t put a thousand sensors inside a human artery or a jet engine.
In 3D printing, PINNs predict how heat will warp metal parts, allowing engineers to fix designs before they even start the machine.