Table 2 Performance of different prediction models on two datasets (\(\alpha =3, 5, 10\)).

From: Interpretable spatial identity neural network-based epidemic prediction

\(\mathrm{\alpha }\)

Models

Japan-Prefectures

US-Regions

Time↓

MAE↓

RMSE↓

PCC↑

MASE↓

Time↓

MAE↓

RMSE↓

PCC↑

MASE↓

3

AR

–

901.092

2301.890

0.408

17,307.353

–

687.998

1202.913

0.726

11,331.757

ARMA

–

893.264

2307.123

0.407

17,157.001

–

537.870

967.471

0.815

8859.046

VAR

–

907.815

2134.757

0.528

17,436.482

–

668.485

1068.316

0.752

11,010.370

GAR

–

849.242

2213.338

0.480

16,311.478

–

551.869

990.890

0.846

9089.628

RNN

–

781.750

2132.552

0.530

15,015.145

–

441.041

865.624

0.869

7264.217

ATTRNN

40.355

933.302

2411.137

0.500

17,926.013

36.136

1004.317

1645.351

0.480

16,541.732

DCRNN

200.051

895.577

2335.206

0.402

17,201.437

272.441

766.220

1323.303

0.751

12,620.119

LSTNet

8.701

662.767

1751.503

0.724

12,729.834

9.352

427.473

834.037

0.871

7040.749

STGCN

17.288

723.386

1835.250

0.727

13,894.146

16.296

717.316

1282.217

0.720

11,814.639

Cola-GNN

36.980

626.126

1640.435

0.768

12,026.058

13.835

555.772

1061.352

0.769

9153.913

ISID

8.104

577.497

1622.780

0.765

11,092.046

5.987

486.672

947.311

0.862

8015.791

ISID-w/o

7.569

579.743

1653.814

0.758

11,135.177

6.636

416.454

840.721

0.887

6859.255

5

AR

–

1016.062

2511.999

0.230

19,803.269

–

772.012

1290.221

0.696

12,696.277

ARMA

–

1006.623

2498.430

0.244

19,619.301

–

745.912

1264.931

0.698

12,267.039

VAR

–

1086.820

2489.193

0.241

21,182.367

–

740.790

1189.132

0.693

12,182.811

GAR

–

1046.382

2527.615

0.205

20,394.219

–

766.383

1332.400

0.729

12,603.710

RNN

–

935.576

2460.424

0.285

18,234.579

–

613.253

1138.828

0.770

10,085.375

ATTRNN

39.867

944.414

2439.369

0.499

18,406.849

35.844

1111.614

1783.450

0.406

18,281.268

DCRNN

159.379

989.724

2543.968

0.179

19,289.936

266.518

978.696

1542.252

0.702

16,095.335

LSTNet

4.704

946.996

2384.207

0.323

18,457.165

8.627

654.376

1189.986

0.716

10,761.663

STGCN

9.176

778.483

1916.113

0.650

15,172.816

16.765

975.935

1622.866

0.608

16,049.926

Cola-GNN

17.099

791.589

1956.292

0.667

15,428.257

18.298

639.610

1185.155

0.800

10,518.829

ISID

4.014

721.849

1893.874

0.639

14,068.998

7.330

672.278

1220.182

0.781

11,056.081

ISID-w/o

4.083

738.649

1954.047

0.632

14,396.427

7.166

559.990

1063.651

0.821

9209.433

10

AR

–

1046.727

2541.373

0.307

21,559.834

–

1122.422

1760.956

0.446

18,319.391

ARMA

–

1030.423

2532.513

0.329

21,224.012

–

1132.658

1781.562

0.441

18,486.455

VAR

–

1055.402

2506.778

0.298

21,738.525

–

1012.296

1582.399

0.435

16,521.980

GAR

–

1125.465

2648.507

0.151

23,181.629

–

1062.144

1711.561

0.505

17,335.567

RNN

–

947.394

2419.028

0.306

19,513.847

–

905.899

1552.777

0.601

14,785.453

ATTRNN

21.100

984.865

2476.640

0.271

20,285.636

35.535

1092.366

1781.418

0.428

17,828.839

DCRNN

122.919

1005.184

2554.305

0.352

20,704.160

256.761

1042.101

1652.853

0.669

17,008.447

LSTNet

4.573

1068.836

2559.348

0.186

22,015.237

7.492

777.090

1355.054

0.677

12,683.112

STGCN

9.024

869.911

2239.212

0.572

17,917.891

14.377

1033.251

1622.881

0.568

16,864.000

Cola-GNN

17.097

882.353

2149.467

0.563

18,174.159

16.470

889.286

1448.841

0.748

14,514.302

ISID

4.137

819.764

2137.616

0.560

16,884.989

5.940

955.910

1575.630

0.562

15,601.694

ISID-w/o

4.628

863.925

2190.761

0.552

17,794.594

5.719

888.376

1522.490

0.609

14,499.446

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