Performance of a Parallel Time Integrator for Noisy Nonlinear System
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Bibliographic record
Abstract
The paper demonstrates the performance of a parallel time integration algorithm for simulating the trajectories (sample path) of a noisy non-linear dynamical system described by Ito stochastic differential equation (SDE). In particular the numerical algorithm is an extension of so-called parareal algorithm for ordinary differential equations (ODEs). We adapt the parareal algorithm to Euler-Maruyama scheme to tackle the Ito SDE describing a Duffing system driven by random noise. Note that the presenceof Wiener process in Ito SDEs leads to difficulties in the straightforward extension of numerical techniques of ODEs. This is due to the fact that the Wiener process, although continuous, is not differentiable and possesses unbounded variation in any integration subinterval. In this paper we conduct a numerical investigation to simulate the sample path of a Duffing oscillator driven by combined deterministic and random inputs. It turns out that for low to medium strength of noise, the parallel integrator is capable of computing the sample path of the oscillator reasonably well.
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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 | 0.000 |
| 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)
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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