Analogs on the Lorenz Attractor and Ensemble Spread
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract Intrinsic predictability is defined as the uncertainty in a forecast due to small errors in the initial conditions. In fact, not only the amplitude but also the structure of these initial errors plays a key role in the evolution of the forecast. Several methodologies have been developed to create an ensemble of forecasts from a feasible set of initial conditions, such as bred vectors or singular vectors. However, these methodologies consider only the fastest growth direction globally, which is represented by the Lyapunov vector. In this paper, the simple Lorenz 63 model is used to compare bred vectors, random perturbations, and normal modes against analogs. The concept of analogs is based on the ergodicity theory to select compatible states for a given initial condition. These analogs have a complex structure in the phase space of the Lorenz attractor that is compatible with the properties of the nonlinear chaotic system. It is shown that the initial averaged growth rate of errors of the analogs is similar to the one obtained with bred vectors or normal modes (fastest growth), but they do not share other properties or statistics, such as the spread of these growth rates. An in-depth study of different properties of the analogs and the previous existing perturbation methodologies is carried out to shed light on the consequences of forecasting the choice of the perturbations.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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