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Research map / Probabilistic and scientific modeling / Differential equations and PDEs

Implicit Neural Representations with Periodic Activation Functions

NeurIPS 2020 · Probabilistic and scientific modeling › Differential equations and PDEs · approach: Neural operators for general geometries · 262 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
sine activations instead of ReLUMLP implicit representation · video fittingPSNR: about 5~dBHelped
sine activations instead of ReLU/tanh/RBFneural Helmholtz solver · Helmholtz equationsolution fidelityHelped
sine activations instead of ReLUneural SDF · shape representationdetailHelped
sine activations vs ReLU with positional encodingMLP image fit · image derivativesderivative fidelityHelped
SIREN hypernetwork with set encoder vs CNPfunction-space prior · CelebA inpainting 100 ctxMSE: 0.016 -> 0.013Helped
CNN encoder instead of set encoder (ablation)SIREN hypernetwork · CelebA inpainting 100 ctxMSE: 0.013 -> 0.009Helped
CNN encoder instead of set encoder (ablation)SIREN hypernetwork · CelebA inpainting 1000 ctxMSE: 0.009 -> 0.008No clear effect
use principled uniform init instead of arbitrary uniform weights (ablation)SIREN · fittingaccuracy and convergenceHelped
SIREN vs principled ADMM FWI solverfull-waveform inversion · FWI single frequencyvelocity MSEHelped

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