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This study investigates the benefits of frequency decomposition for Physics-Informed Neural Networks (PINNs) by proposing a dual-branch, spectrally-gated architecture (DBSG-PINN). Ablation experiments on 1D PDE benchmarks indicate that frequency decomposition is most effective on spectrally complex problems, reducing error by up to 59.2%.
This paper proposes learnable wavelet activations to combat plasticity loss in continual learning, decomposing activations into low- and high-frequency components with dynamic injection and regularization, achieving state-of-the-art results on benchmarks.
This paper proposes FALM-PINN, an alternating Levenberg-Marquardt training framework for physics-informed neural networks that uses Fourier-enhanced features to address spectral bias and representation-coefficient coupling, achieving up to two orders of magnitude lower errors on high-frequency and nonlinear PDEs.
This paper introduces a differentiable training objective based on the Rice level-crossing density from random-field theory, which acts as a mesh-free high-frequency auxiliary loss for implicit neural representations. It requires no grid or FFT, and improves performance on non-uniform samples.
This paper proposes a Frequency Shift Physics-Informed Extreme Learning Machine (FS-PIELM) that uses an additive weight initialization mechanism to overcome spectral bias in solving high-frequency PDEs. The method achieves up to five orders of magnitude improvement over existing PIELM variants on benchmark problems.
This paper studies transfer specificity in implicit neural representations across SIREN, ReLU MLPs, and Fourier-feature MLPs, finding that transfer magnitude and specificity depend on architecture, with ReLU being more selective and SIREN reusing weights broadly. Results suggest architecture selection should consider explicit control conditions, not just transfer magnitude.
Introduces Colored Noise Sampling (CNS), a training-free stochastic solver for diffusion models that dynamically allocates energy based on frequency-dependent schedules, improving image quality metrics like FID significantly on ImageNet-256.
This paper identifies and explains a spectral bias in reconstruction-based EEG foundation models, where embeddings over-represent aperiodic and low-frequency components while under-representing oscillatory components, especially at higher frequencies, leading to poor performance in low-resource settings.
This paper introduces the Iterative Refinement Neural Operator (IRNO), which augments pretrained neural operators with a learned refinement module applied via fixed-point iteration to mitigate spectral bias. IRNO progressively corrects high-frequency errors, achieving up to 56% improvement on turbulent flow and showing stable extrapolation beyond the trained iteration count.
This paper introduces the Spectral Energy Centroid (SEC) metric to analyze and improve spectral bias in implicit neural representations, demonstrating its utility for hyperparameter selection, signal complexity measurement, and cross-architecture alignment.