Applying Radial Basis Functions and Partition of Unity for Solving Heating Equations Optimal Control Issues
Why is this work in the frame?
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.
Full frame distilled prediction
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.
- Candidate categories
- none
- Consensus categories
- none
- Domain
- Candidate signal: noneConsensus signal: none
- Study design
- Candidate signal: Simulation or modelingConsensus signal: Simulation or modeling
- Genre
- Candidate signal: MethodsConsensus signal: none
- Teacher disagreement score
- 0.626
- Threshold uncertainty score
- 0.513
- Validation status
machine_predicted_unvalidated·codex-gemma-dda1882f352a
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) | 0.000 | 0.000 |
Machine scores (provisional)
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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.
- Teacher spread
- 0.232 · how far apart the two teachers sit on this one work
- Validation status
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
Abstract
In this study, we suggest applying the Partition of Unity approach using Radial Basis Functions (RBF-PU) towards the solution of heat equation-governed sparse optimal control issues.An 2 norm is included in the goal function to encourage sparseness in the control equation and quadratic coefficients are used to reduce the deviations from a desired state.Efficient processing of spatially sparse controllers is made possible by this combination, which is crucial for numerous practical uses.By splitting the domain into overlapped subdomains and performing local RBF approximation, which is then integrated utilizing compactly maintained weight functions, the RBF-PU technique offers a versatile and effective strategy.The correctness and effectiveness of the suggested strategy are demonstrated numerically, showing how it can be used to solve intricate optimum control issues with larger dimensions.
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.
The record
- Venue
- Mathematical Modelling and Engineering Problems
- Topic
- Differential Equations and Numerical Methods
- Field
- Mathematics
- Canadian institutions
- not available
- Funders
- not available
- Keywords
- Partition of unityPartition (number theory)Basis (linear algebra)MathematicsRadial basis functionOptimal controlApplied mathematicsMathematical analysisMathematical optimizationComputer sciencePhysicsGeometryThermodynamicsFinite element methodArtificial intelligenceCombinatorics
- Has abstract in OpenAlex
- yes