On the eigenvector bias of Fourier feature networks: From regression to solvingmulti-scale PDEs with physics-informed neural net

Why physics-aware AI misses tiny waves — a simple fix

AI that knows physics is helping fill gaps in messy data, but it often miss sharp, fast patterns or things happening at many sizes.
Researchers found these networks prefer easy, smooth patterns first, so tiny waves or fast ripples can be overlooked.
By looking inside the learning process they saw this bias and tried a fix: feed the model extra, random wave signals so it can notice details at different scales.
The new layer used simple sine-like inputs — called random Fourier features — and it help the network learn much faster on hard cases.
Tests with moving waves and chemical-like spreads show the approach works where common models fail, giving more stable and accurate answers.
That means physics-aware AI can tackle tricky multi-scale puzzles and do both forward predictions and find hidden causes.
The idea is small, practical change that bring better predictions for real world problems like wave faults, material behavior, or disease patterns.

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On the eigenvector bias of Fourier feature networks: From regression to solvingmulti-scale PDEs with physics-informed neural networks

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