# LD-weighted PDF reconstruction on Duffing equation Source: [LD-weighted PDF reconstruction on Duffing equation]() Collection index: [llms.txt]() Data updated: 2026-04-02T09:35:02.530Z Evaluation of model performance on reconstructing the probability density function (PDF) for the Duffing equation using LD-weighting, measured by KL divergence. A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. | Scope | Recorded value | | --- | --- | | Task | LD-weighted PDF reconstruction | | Dataset (including any stated split) | Duffing equation | | Metric | KL Divergence | | Unit | SCALAR | | Direction | Lower is better | | Results loaded | 32 of 32 | | Coverage | All results currently returned for this benchmark | Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol. ## Metrics - [KL Divergence](): Lower is better; unit: SCALAR. ## Recorded results | Method | KL Divergence | Result date | Report paper | | --- | --- | --- | --- | | RC | 0.000062 | Not recorded | 69cdf83d0636e5bf4afccc73 | | RC | 0.00011 | Not recorded | 69cdf83d0636e5bf4afccc73 | | GHNN | 0.000128 | Not recorded | 69cdf83d0636e5bf4afccc73 | | GHNN | 0.000174 | Not recorded | 69cdf83d0636e5bf4afccc73 | | GHNN | 0.000271 | Not recorded | 69cdf83d0636e5bf4afccc73 | | SympNet | 0.000324 | Not recorded | 69cdf83d0636e5bf4afccc73 | | HénonNet | 0.000416 | Not recorded | 69cdf83d0636e5bf4afccc73 | | GHNN | 0.00063 | Not recorded | 69cdf83d0636e5bf4afccc73 | | SympNet | 0.000687 | Not recorded | 69cdf83d0636e5bf4afccc73 | | RC | 0.00084 | Not recorded | 69cdf83d0636e5bf4afccc73 | | SympNet | 0.00101 | Not recorded | 69cdf83d0636e5bf4afccc73 | | GHNN | 0.00102 | Not recorded | 69cdf83d0636e5bf4afccc73 | | SympNet | 0.00132 | Not recorded | 69cdf83d0636e5bf4afccc73 | | GHNN | 0.00275 | Not recorded | 69cdf83d0636e5bf4afccc73 | | HénonNet | 0.00464 | Not recorded | 69cdf83d0636e5bf4afccc73 | | GHNN | 0.00711 | Not recorded | 69cdf83d0636e5bf4afccc73 | | HénonNet | 0.00803 | Not recorded | 69cdf83d0636e5bf4afccc73 | | RC | 0.00803 | Not recorded | 69cdf83d0636e5bf4afccc73 | | HénonNet | 0.00804 | Not recorded | 69cdf83d0636e5bf4afccc73 | | HénonNet | 0.0107 | Not recorded | 69cdf83d0636e5bf4afccc73 | | HénonNet | 0.0184 | Not recorded | 69cdf83d0636e5bf4afccc73 | | RC | 0.102 | Not recorded | 69cdf83d0636e5bf4afccc73 | | RC | 0.107 | Not recorded | 69cdf83d0636e5bf4afccc73 | | HénonNet | 0.176 | Not recorded | 69cdf83d0636e5bf4afccc73 | | HénonNet | 0.18 | Not recorded | 69cdf83d0636e5bf4afccc73 | | SympNet | 0.212 | Not recorded | 69cdf83d0636e5bf4afccc73 | | SympNet | 0.213 | Not recorded | 69cdf83d0636e5bf4afccc73 | | SympNet | 0.217 | Not recorded | 69cdf83d0636e5bf4afccc73 | | GHNN | 0.217 | Not recorded | 69cdf83d0636e5bf4afccc73 | | SympNet | 0.219 | Not recorded | 69cdf83d0636e5bf4afccc73 | | RC | 0.359 | Not recorded | 69cdf83d0636e5bf4afccc73 | | RC | 0.616 | Not recorded | 69cdf83d0636e5bf4afccc73 | ### RC KL Divergence: 0.000062. Result ID: 69ce384247f34ce924b7be09. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"200"}. This record does not assert independent reproduction. ### RC KL Divergence: 0.00011. Result ID: 69ce384247f34ce924b7be0a. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"300"}. This record does not assert independent reproduction. ### GHNN KL Divergence: 0.000128. Result ID: 69ce384247f34ce924b7be04. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"500"}. This record does not assert independent reproduction. ### GHNN KL Divergence: 0.000174. Result ID: 69ce384247f34ce924b7be03. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"400"}. This record does not assert independent reproduction. ### GHNN KL Divergence: 0.000271. Result ID: 69ce384247f34ce924b7be02. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"300"}. This record does not assert independent reproduction. ### SympNet KL Divergence: 0.000324. Result ID: 69ce384247f34ce924b7bdf2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"300"}. This record does not assert independent reproduction. ### HénonNet KL Divergence: 0.000416. Result ID: 69ce384247f34ce924b7bdfb. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"400"}. This record does not assert independent reproduction. ### GHNN KL Divergence: 0.00063. Result ID: 69ce384247f34ce924b7bdff. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"50"}. This record does not assert independent reproduction. ### SympNet KL Divergence: 0.000687. Result ID: 69ce384247f34ce924b7bdf4. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"500"}. This record does not assert independent reproduction. ### RC KL Divergence: 0.00084. Result ID: 69ce384247f34ce924b7be0c. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"500"}. This record does not assert independent reproduction. ### SympNet KL Divergence: 0.00101. Result ID: 69ce384247f34ce924b7bdf3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"400"}. This record does not assert independent reproduction. ### GHNN KL Divergence: 0.00102. Result ID: 69ce384247f34ce924b7be00. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"100"}. This record does not assert independent reproduction. ### SympNet KL Divergence: 0.00132. Result ID: 69ce384247f34ce924b7bdf1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"200"}. This record does not assert independent reproduction. ### GHNN KL Divergence: 0.00275. Result ID: 69ce384247f34ce924b7be01. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"200"}. This record does not assert independent reproduction. ### HénonNet KL Divergence: 0.00464. Result ID: 69ce384247f34ce924b7bdfa. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"300"}. This record does not assert independent reproduction. ### GHNN KL Divergence: 0.00711. Result ID: 69ce384247f34ce924b7bdfe. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"20"}. This record does not assert independent reproduction. ### HénonNet KL Divergence: 0.00803. Result ID: 69ce384247f34ce924b7bdf9. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"200"}. This record does not assert independent reproduction. ### RC KL Divergence: 0.00803. Result ID: 69ce384247f34ce924b7be0b. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"400"}. This record does not assert independent reproduction. ### HénonNet KL Divergence: 0.00804. Result ID: 69ce384247f34ce924b7bdfc. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"500"}. This record does not assert independent reproduction. ### HénonNet KL Divergence: 0.0107. Result ID: 69ce384247f34ce924b7bdf8. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"100"}. This record does not assert independent reproduction. ### HénonNet KL Divergence: 0.0184. Result ID: 69ce384247f34ce924b7bdf7. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"50"}. This record does not assert independent reproduction. ### RC KL Divergence: 0.102. Result ID: 69ce384247f34ce924b7be08. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"100"}. This record does not assert independent reproduction. ### RC KL Divergence: 0.107. Result ID: 69ce384247f34ce924b7be05. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"10"}. This record does not assert independent reproduction. ### HénonNet KL Divergence: 0.176. Result ID: 69ce384247f34ce924b7bdf5. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"10"}. This record does not assert independent reproduction. ### HénonNet KL Divergence: 0.18. Result ID: 69ce384247f34ce924b7bdf6. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"20"}. This record does not assert independent reproduction. ### SympNet KL Divergence: 0.212. Result ID: 69ce384247f34ce924b7bdee. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"20"}. This record does not assert independent reproduction. ### SympNet KL Divergence: 0.213. Result ID: 69ce384247f34ce924b7bdf0. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"100"}. This record does not assert independent reproduction. ### SympNet KL Divergence: 0.217. Result ID: 69ce384247f34ce924b7bded. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"10"}. This record does not assert independent reproduction. ### GHNN KL Divergence: 0.217. Result ID: 69ce384247f34ce924b7bdfd. [Reporting paper]() Recorded evaluation configuration: {"Number of training trajectories N":"10"}. This record does not assert independent reproduction. ### SympNet KL Divergence: 0.219. Result ID: 69ce384247f34ce924b7bdef. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"50"}. This record does not assert independent reproduction. ### RC KL Divergence: 0.359. Result ID: 69ce384247f34ce924b7be07. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"50"}. This record does not assert independent reproduction. ### RC KL Divergence: 0.616. Result ID: 69ce384247f34ce924b7be06. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training trajectories N":"20"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.