# Autoregressive PDE rollout on CE-RM (test) Source: [Autoregressive PDE rollout on CE-RM (test)]() Collection index: [llms.txt]() Data updated: 2026-02-26T05:45:17.248Z Evaluation of models performing Autoregressive PDE rollout on the test split of the CE-RM dataset, typically measured using Final-time relative L2 error and Gain. 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 | Autoregressive PDE rollout | | Dataset (including any stated split) | CE-RM (test) | | Metric | Final Relative L2 Error | | Unit | SCALAR | | Direction | Lower is better | | Results loaded | 16 of 16 | | 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 - [Final Relative L2 Error](): Lower is better; unit: SCALAR. - [Gain](): Higher is better; unit: PERCENT. ## Recorded results | Method | Final Relative L2 Error | Result date | Report paper | | --- | --- | --- | --- | | Memory-Conditioned Flow-Matching | 0.0069 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memory-Conditioned Flow-Matching | 0.0071 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memory-Conditioned Flow-Matching | 0.0102 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memory-Conditioned Flow-Matching | 0.0104 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memoryless Baseline | 0.011 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memory-Conditioned Flow-Matching | 0.0111 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memoryless Baseline | 0.0112 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memoryless Baseline | 0.0114 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memoryless Baseline | 0.0125 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memory-Conditioned Flow-Matching | 0.0145 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memoryless Baseline | 0.0148 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memoryless Baseline | 0.0158 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memory-Conditioned Flow-Matching | 0.0167 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memoryless Baseline | 0.0168 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memory-Conditioned Flow-Matching | 0.0169 | Not recorded | 698969f5c97a0b3e3b5dc471 | | Memoryless Baseline | 0.0172 | Not recorded | 698969f5c97a0b3e3b5dc471 | ### Memory-Conditioned Flow-Matching Final Relative L2 Error: 0.0069. Result ID: 6998e63a5698665ec44a9242. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Downsampled","Sampling":"D0.05 (20)"}. This record does not assert independent reproduction. ### Memory-Conditioned Flow-Matching Final Relative L2 Error: 0.0071. Result ID: 6998e63a5698665ec44a923a. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Regular","Sampling":"D0.05 (20)"}. This record does not assert independent reproduction. ### Memory-Conditioned Flow-Matching Final Relative L2 Error: 0.0102. Result ID: 6998e63a5698665ec44a9244. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Downsampled","Sampling":"S0.10 (10)"}. This record does not assert independent reproduction. ### Memory-Conditioned Flow-Matching Final Relative L2 Error: 0.0104. Result ID: 6998e63a5698665ec44a923c. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Regular","Sampling":"S0.10 (10)"}. This record does not assert independent reproduction. ### Memoryless Baseline Final Relative L2 Error: 0.011. Result ID: 6998e63a5698665ec44a9243. [Reporting paper]() Recorded evaluation configuration: {"Train":"Downsampled","Sampling":"D0.05 (20)"}. This record does not assert independent reproduction. ### Memory-Conditioned Flow-Matching Final Relative L2 Error: 0.0111. Result ID: 6998e63a5698665ec44a9240. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Downsampled","Sampling":"Inc (10)"}. This record does not assert independent reproduction. ### Memoryless Baseline Final Relative L2 Error: 0.0112. Result ID: 6998e63a5698665ec44a923d. [Reporting paper]() Recorded evaluation configuration: {"Train":"Regular","Sampling":"S0.10 (10)"}. This record does not assert independent reproduction. ### Memoryless Baseline Final Relative L2 Error: 0.0114. Result ID: 6998e63a5698665ec44a9245. [Reporting paper]() Recorded evaluation configuration: {"Train":"Downsampled","Sampling":"S0.10 (10)"}. This record does not assert independent reproduction. ### Memoryless Baseline Final Relative L2 Error: 0.0125. Result ID: 6998e63a5698665ec44a923b. [Reporting paper]() Recorded evaluation configuration: {"Train":"Regular","Sampling":"D0.05 (20)"}. This record does not assert independent reproduction. ### Memory-Conditioned Flow-Matching Final Relative L2 Error: 0.0145. Result ID: 6998e63a5698665ec44a9238. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Regular","Sampling":"Inc (10)"}. This record does not assert independent reproduction. ### Memoryless Baseline Final Relative L2 Error: 0.0148. Result ID: 6998e63a5698665ec44a9241. [Reporting paper]() Recorded evaluation configuration: {"Train":"Downsampled","Sampling":"Inc (10)"}. This record does not assert independent reproduction. ### Memoryless Baseline Final Relative L2 Error: 0.0158. Result ID: 6998e63a5698665ec44a9239. [Reporting paper]() Recorded evaluation configuration: {"Train":"Regular","Sampling":"Inc (10)"}. This record does not assert independent reproduction. ### Memory-Conditioned Flow-Matching Final Relative L2 Error: 0.0167. Result ID: 6998e63a5698665ec44a923e. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Downsampled","Sampling":"U0.05 (10)"}. This record does not assert independent reproduction. ### Memoryless Baseline Final Relative L2 Error: 0.0168. Result ID: 6998e63a5698665ec44a923f. [Reporting paper]() Recorded evaluation configuration: {"Train":"Downsampled","Sampling":"U0.05 (10)"}. This record does not assert independent reproduction. ### Memory-Conditioned Flow-Matching Final Relative L2 Error: 0.0169. Result ID: 6998e63a5698665ec44a9236. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Regular","Sampling":"U0.05 (10)"}. This record does not assert independent reproduction. ### Memoryless Baseline Final Relative L2 Error: 0.0172. Result ID: 6998e63a5698665ec44a9237. [Reporting paper]() Recorded evaluation configuration: {"Train":"Regular","Sampling":"U0.05 (10)"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.