Dealiased convolutions for pseudospectral simulations
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Bibliographic record
Abstract
Summary Efficient algorithms have recently been developed for calculating dealiased linear convolution sums without the expense of conventional zero-padding or phase-shift techniques. For one-dimensional in-place convolutions, the memory requirements are identical with the zero-padding technique, with the important distinction that the additional work memory need not be contiguous with the input data. This decoupling of data and work arrays dramatically reduces the memory and computation time required to evaluate higher-dimensional in-place convolutions. The memory savings is achieved by computing the in-place Fourier transform of the data in blocks, rather than all at once. The technique also allows one to dealias the n-ary convolutions that arise on Fourier transforming cubic and higher powers. Implicitly dealiased convolutions can be built on top of state-of-the-art adaptive fast Fourier transform libraries like FFTW. Vectorized multidimensional implementations for the complex and centered Hermitian (pseudospectral) cases have already been implemented in the open-source software FFTW++. With the advent of this library, writing a high-performance dealiased pseudospectral code for solving nonlinear partial differential equations has now become a relatively straightforward exercise. New theoretical estimates of computational complexity and memory use are provided, including corrected timing results for 3D pruned convolutions and further consideration of higher-order convolutions. ONE-DIMENSIONAL CONVOLUTIONS A discrete non-centered convolution is a binary operation on two sequences Fk and Gk, k = 0,...,m − 1, and is defined as
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it