Performance of a Parallel Time Integrator for Noisy Nonlinear System
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".