# Forward PDE solving on Klein-Gordon 10K-epoch Source: [Forward PDE solving on Klein-Gordon 10K-epoch]() Collection index: [llms.txt]() Data updated: 2026-05-12T14:45:14.476Z Evaluation of models performing Forward Partial Differential Equation (PDE) solving on the Klein-Gordon 10K-epoch dataset, measured by Relative L2 error and average rank. 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 | Forward PDE solving | | Dataset (including any stated split) | Klein-Gordon 10K-epoch | | Metric | 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 - [Relative L2 Error](): Lower is better; unit: SCALAR. - [Average Rank](): Lower is better; unit: SCALAR. ## Recorded results | Method | Relative L2 Error | Result date | Report paper | | --- | --- | --- | --- | | GradNorm | 1.13 | Not recorded | 6a02b498dbc836b87d824dd5 | | AlignedMTL | 1.14 | Not recorded | 6a02b498dbc836b87d824dd5 | | FAMO+UAM | 1.6 | Not recorded | 6a02b498dbc836b87d824dd5 | | FAMO+LCAM | 1.6 | Not recorded | 6a02b498dbc836b87d824dd5 | | ConFIG | 2.39 | Not recorded | 6a02b498dbc836b87d824dd5 | | FAMO | 2.5 | Not recorded | 6a02b498dbc836b87d824dd5 | | NashMTL | 3.6 | Not recorded | 6a02b498dbc836b87d824dd5 | | SelfAdapt | 3.8 | Not recorded | 6a02b498dbc836b87d824dd5 | | UAM | 4.3 | Not recorded | 6a02b498dbc836b87d824dd5 | | Vanilla | 4.6 | Not recorded | 6a02b498dbc836b87d824dd5 | | CAGrad | 4.7 | Not recorded | 6a02b498dbc836b87d824dd5 | | GN+UAM | 4.8 | Not recorded | 6a02b498dbc836b87d824dd5 | | Uncertainty | 4.89 | Not recorded | 6a02b498dbc836b87d824dd5 | | GN+LCAM | 6.2 | Not recorded | 6a02b498dbc836b87d824dd5 | | PCGrad | 9 | Not recorded | 6a02b498dbc836b87d824dd5 | | Causal | 9.8 | Not recorded | 6a02b498dbc836b87d824dd5 | ### GradNorm Relative L2 Error: 1.13. Result ID: 6a033cef47f34ce924e822b0. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### AlignedMTL Relative L2 Error: 1.14. Result ID: 6a033cef47f34ce924e822b8. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### FAMO+UAM Relative L2 Error: 1.6. Result ID: 6a033cef47f34ce924e822ba. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### FAMO+LCAM Relative L2 Error: 1.6. Result ID: 6a033cef47f34ce924e822bc. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### ConFIG Relative L2 Error: 2.39. Result ID: 6a033cef47f34ce924e822b4. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### FAMO Relative L2 Error: 2.5. Result ID: 6a033cef47f34ce924e822af. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### NashMTL Relative L2 Error: 3.6. Result ID: 6a033cef47f34ce924e822b7. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### SelfAdapt Relative L2 Error: 3.8. Result ID: 6a033cef47f34ce924e822b2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### UAM Relative L2 Error: 4.3. Result ID: 6a033cef47f34ce924e822b9. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### Vanilla Relative L2 Error: 4.6. Result ID: 6a033cef47f34ce924e822ae. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### CAGrad Relative L2 Error: 4.7. Result ID: 6a033cef47f34ce924e822b6. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### GN+UAM Relative L2 Error: 4.8. Result ID: 6a033cef47f34ce924e822bb. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### Uncertainty Relative L2 Error: 4.89. Result ID: 6a033cef47f34ce924e822b3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### GN+LCAM Relative L2 Error: 6.2. Result ID: 6a033cef47f34ce924e822bd. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### PCGrad Relative L2 Error: 9. Result ID: 6a033cef47f34ce924e822b5. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. ### Causal Relative L2 Error: 9.8. Result ID: 6a033cef47f34ce924e822b1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"dh":"128","Seeds":"5","Epochs":"10K"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.