Table 4 Performance metrics of ablation experiment prediction results.

From: Novel hybrid data-driven modeling based on feature space reconstruction and multihead self-attention gated recurrent unit: applied to PM2.5 concentrations prediction

Dataset

Model

RMSE

/(µg/m3)

MAE

/(µg/m3)

SMAPE

/(%)

PCC

DA

MBE

Lanzhou

GRU

11.6285

6.6551

18.80%

0.7148

0.4094

-0.1408

STL-GRU

5.3648

3.0980

9.24%

0.9460

0.7464

0.1726

MSAGRU

11.2284

6.5533

18.94%

0.7309

0.4275

0.0151

STL-MSAGRU

5.2494

3.2411

9.97%

0.9475

0.6957

-0.1645

FSR-GRU

0.6086

0.3268

1.13%

0.9993

0.9855

-0.0499

FSR-MSAGRU

0.5246

0.1875

0.63%

0.9995

0.9928

-0.0936

Xi’an

GRU

17.9032

12.3766

31.24%

0.8202

0.5181

-0.8399

STL-GRU

8.8417

5.7235

15.03%

0.9597

0.7935

-0.6880

MSAGRU

17.6251

12.3692

31.47%

0.8282

0.4891

0.9421

STL-MSAGRU

8.6651

5.8252

15.41%

0.9614

0.7862

-0.0458

FSR-GRU

0.5656

0.4236

1.71%

0.9998

0.9783

-0.0035

FSR-MSAGRU

0.3301

0.2259

0.75%

0.9999

0.9964

0.0344

Beijing

GRU

21.1930

14.4576

51.84%

0.5503

0.5882

2.6320

STL-GRU

14.7382

10.1124

41.86%

0.8031

0.6360

1.2777

MSAGRU

20.9408

14.4503

51.84%

0.5489

0.5662

1.1008

STL-MSAGRU

14.8991

10.2026

42.63%

0.7972

0.6691

-0.7834

FSR-GRU

4.2872

3.0766

17.06%

0.9850

0.9191

-0.4729

FSR-MSAGRU

4.0701

2.9749

16.33%

0.9863

0.9081

-0.0455

Shijiazhuang

GRU

17.1549

12.8019

32.49%

0.7490

0.5507

2.0505

STL-GRU

7.6280

5.7090

16.21%

0.9561

0.7971

-0.1310

MSAGRU

17.0979

12.9560

33.24%

0.7493

0.5543

1.8308

STL-MSAGRU

8.0901

6.1116

17.22%

0.9493

0.8080

-0.5207

FSR-GRU

1.0322

0.8166

2.53%

0.9993

0.9928

-0.2723

FSR-MSAGRU

0.1681

0.1257

0.45%

0.9999

0.9999

0.0111

Chengdu

GRU

11.6151

8.4413

26.39%

0.7878

0.5181

1.3740

STL-GRU

5.1486

3.9717

14.09%

0.9647

0.7754

0.8519

MSAGRU

11.4977

8.6241

27.27%

0.7944

0.5109

-0.0929

STL-MSAGRU

5.3238

4.0010

13.99%

0.9596

0.7935

0.0596

FSR-GRU

0.4492

0.3514

1.31%

0.9997

0.9783

0.0970

FSR-MSAGRU

0.1854

0.1195

0.53%

1.0000

0.9855

0.0272

Lhasa

GRU

2.1926

1.6367

22.06%

0.8314

0.3824

0.3797

STL-GRU

1.4493

1.0628

13.52%

0.9256

0.6029

0.0198

MSAGRU

2.1333

1.5813

21.12%

0.8367

0.3676

0.3406

STL-MSAGRU

1.8817

1.2830

16.28%

0.8722

0.5809

-0.1272

FSR-GRU

0.8170

0.6331

10.19%

0.9776

0.8125

0.1131

FSR-MSAGRU

0.5615

0.4099

6.61%

0.9897

0.8493

-0.1322

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