An Adaptive Physics-Informed Neural Network by Sampling Alternately from Time and Space for Solving Spatiotemporal PDE
Bibliographic record
Abstract
In the past several years, Physics-Informed Neural Network (PINN) for solving partial differential equations (PDE) has an advance development, however, under the traditional sampling method, it is difficult for the network to accurately capture the changes of the solution in complex areas. For this reason, we propose a spatio-temporal collaborative sampling strategy of PINN for solving PDE, to optimize the layout of omni-directional sampling points. In our method, the time interval is first subdivided into multiple sub-intervals, and local optimization sampling is performed for each sub-interval. The entire procedures of sampling will be pulled out alternatively in two stages in each sub-interval: first, in the aspect of spatial adaptive sampling, we adopt a dynamic resampling strategy based on the dynamical training error of neural network, which can sensitively identify the changing region of the solution and automatically increase the sampling density in the region with dramatic changes to capture more details; Secondly, time dimension sampling was performed similarly. Numerical tests on the Schrödinger and heat-conduction PDE show over 40% faster convergence and a reduction in relative L2 compared to traditional PINN. This work presents a new approach for efficiently solving complex PDE with PINN.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".