# Spatiotemporal Inference on Matérn-1-2 simulated 2D grid 1.0 (N=1024)

Source: [Spatiotemporal Inference on Matérn-1-2 simulated 2D grid 1.0 (N=1024)](<https://www.sota2.com/research/sota/spatiotemporal-inference-on-mat-rn-1-2-simulated-2d-grid-1-0-n-1024>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-04-01T07:42:19.134Z

Evaluation of Spatiotemporal Inference performance on a synthetic 2D grid dataset generated using a Matérn-1-2 kernel with N=1024 points, measured using MSE and Wasserstein distance.

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 | Spatiotemporal Inference |
| Dataset (including any stated split) | Matérn-1-2 simulated 2D grid 1.0 (N=1024) |
| Metric | MSE (y\_gp vs y\_hat) |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 6 of 6 |
| 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

- [MSE (y\_gp vs y\_hat)](<https://www.sota2.com/research/sota/spatiotemporal-inference-on-mat-rn-1-2-simulated-2d-grid-1-0-n-1024.md?metric=MSE%20(y_gp%20vs%20y_hat)>): Lower is better; unit: SCALAR.

- [Wasserstein Distance (l\_gp vs l)](<https://www.sota2.com/research/sota/spatiotemporal-inference-on-mat-rn-1-2-simulated-2d-grid-1-0-n-1024.md?metric=Wasserstein%20Distance%20(l_gp%20vs%20l)>): Lower is better; unit: SCALAR.

## Recorded results

| Method | MSE (y\_gp vs y\_hat) | Result date | Report paper |
| --- | --- | --- | --- |
| DeepRV-gMLP | 0.009 | Not recorded | 68fa7c3c1e209131cea8d164 |
| INLA | 0.411 | Not recorded | 68fa7c3c1e209131cea8d164 |
| DeepRV-MLP | 4.895 | Not recorded | 68fa7c3c1e209131cea8d164 |
| Inducing Pts | 6.436 | Not recorded | 68fa7c3c1e209131cea8d164 |
| RFF | 9.735 | Not recorded | 68fa7c3c1e209131cea8d164 |
| PriorCVAE | 17.752 | Not recorded | 68fa7c3c1e209131cea8d164 |

### DeepRV-gMLP

MSE (y\_gp vs y\_hat): 0.009. Result ID: 69cccbf047f34ce924b63344.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7c3c1e209131cea8d164.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa7c3c1e209131cea8d164.md>)

Recorded evaluation configuration: {"ESS(l)/sec":"6.47 ± 2.44","Infer Time (s)":"510 ± 177.81","Averaged across lengthscales (10, 30, 50)":"true"}. This record does not assert independent reproduction.

### INLA

MSE (y\_gp vs y\_hat): 0.411. Result ID: 69cccbf047f34ce924b6333f.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7c3c1e209131cea8d164.md>)

Recorded evaluation configuration: {"Infer Time (s)":"7 ± 0.07","Averaged across lengthscales (10, 30, 50)":"true"}. This record does not assert independent reproduction.

### DeepRV-MLP

MSE (y\_gp vs y\_hat): 4.895. Result ID: 69cccbf047f34ce924b63343.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7c3c1e209131cea8d164.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa7c3c1e209131cea8d164.md>)

Recorded evaluation configuration: {"ESS(l)/sec":"0.87 ± 0.36","Infer Time (s)":"309 ± 52.97","Averaged across lengthscales (10, 30, 50)":"true"}. This record does not assert independent reproduction.

### Inducing Pts

MSE (y\_gp vs y\_hat): 6.436. Result ID: 69cccbf047f34ce924b63340.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7c3c1e209131cea8d164.md>)

Recorded evaluation configuration: {"ESS(l)/sec":"8.10 ± 4.68","Infer Time (s)":"566 ± 184.98","Averaged across lengthscales (10, 30, 50)":"true"}. This record does not assert independent reproduction.

### RFF

MSE (y\_gp vs y\_hat): 9.735. Result ID: 69cccbf047f34ce924b63341.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7c3c1e209131cea8d164.md>)

Recorded evaluation configuration: {"ESS(l)/sec":"0.00 ± 0.00","Infer Time (s)":"1,028 ± 175.29","Averaged across lengthscales (10, 30, 50)":"true"}. This record does not assert independent reproduction.

### PriorCVAE

MSE (y\_gp vs y\_hat): 17.752. Result ID: 69cccbf047f34ce924b63342.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7c3c1e209131cea8d164.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa71201e209131cea4f53b.md>)

Recorded evaluation configuration: {"ESS(l)/sec":"11.98 ± 5.13","Infer Time (s)":"231 ± 13.62","Averaged across lengthscales (10, 30, 50)":"true"}. This record does not assert independent reproduction.

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