Stochastic Projection Based Gradient Free PINN for Reliability Analysis of System using PDEM
Bibliographic record
Abstract
In this paper, a reliability analysis of stochastic systems is presented using probability density evolution method (PDEM).In PDEM, generalized density evolution equations (GDEEs) are completely decoupled between physical and probability space, which is developed based on the idea of probability conservation.Using the GF-discrepancy technique, a collection of representative points of random variables are constructed in order to provide an accurate estimate of the probability density function.Sufficient precision requires a large number of sample points, which becomes computationally costly.Physics-informed neural network (PINN)-based PDEM is one of promising methods which reduce the computational cost.Beside the advantages of PINN for solving GDEEs in PDEM, PINN may suffer from gradient estimation using Automatic Differentiation.In this study, stochastic projection based PINN, a gradient free method, is a coupled framework of stochastic projection theory and traditional PINN, for solving GDEEs.To illustrate the efficiency of the method, two numerical examples are investigated for estimating probability density function which is utilized for reliability analysis of stochastic systems.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".