Journal of Computer Applications ›› 2025, Vol. 45 ›› Issue (9): 2806-2816.DOI: 10.11772/j.issn.1001-9081.2024091267
• Data science and technology • Previous Articles
Xiang WANG1,2(), Zhixiang CHEN1, Guojun MAO1,2
Received:
2024-09-06
Revised:
2024-10-30
Accepted:
2024-10-31
Online:
2024-11-05
Published:
2025-09-10
Contact:
Xiang WANG
About author:
CHEN Zhixiang, born in 1998, M. S. candidate. His research interests include deep learning, time series analysis.Supported by:
通讯作者:
王翔
作者简介:
陈志祥(1998—),男,福建厦门人,硕士研究生,主要研究方向:深度学习、时间序列分析基金资助:
CLC Number:
Xiang WANG, Zhixiang CHEN, Guojun MAO. Multivariate time series prediction method combining local and global correlation[J]. Journal of Computer Applications, 2025, 45(9): 2806-2816.
王翔, 陈志祥, 毛国君. 融合局部和全局相关性的多变量时间序列预测方法[J]. 《计算机应用》唯一官方网站, 2025, 45(9): 2806-2816.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2024091267
模型 | 时间 复杂度 | 空间 复杂度 | 模型 | 时间 复杂度 | 空间 复杂度 |
---|---|---|---|---|---|
PatchLG | O(L2) | O(L2) | TimesNet | O(L) | O(L) |
PatchTST | O(L2) | O(L2) | BasisFormer | O(L) | O(L) |
DLinear | O(L) | O(L) | ETSformer | O(L2) | O(L2) |
MICN | O(L) | O(L) | FEDformer | O(L) | O(L) |
Tab. 1 Comparison of time and space complexity of different models
模型 | 时间 复杂度 | 空间 复杂度 | 模型 | 时间 复杂度 | 空间 复杂度 |
---|---|---|---|---|---|
PatchLG | O(L2) | O(L2) | TimesNet | O(L) | O(L) |
PatchTST | O(L2) | O(L2) | BasisFormer | O(L) | O(L) |
DLinear | O(L) | O(L) | ETSformer | O(L2) | O(L2) |
MICN | O(L) | O(L) | FEDformer | O(L) | O(L) |
数据集 | 变量数 | 时间长度 | 时间步长 |
---|---|---|---|
Weather | 21 | 52 696 | 10 min |
Electricity | 321 | 26 304 | 1 h |
ETTm1 | 7 | 69 680 | 15 min |
ETTm2 | 7 | 69 680 | 15 min |
ETTh1 | 7 | 17 420 | 1 h |
ETTh2 | 7 | 17 420 | 1 h |
ILI | 7 | 966 | 7 d |
Tab. 2 Detailed information of datasets
数据集 | 变量数 | 时间长度 | 时间步长 |
---|---|---|---|
Weather | 21 | 52 696 | 10 min |
Electricity | 321 | 26 304 | 1 h |
ETTm1 | 7 | 69 680 | 15 min |
ETTm2 | 7 | 69 680 | 15 min |
ETTh1 | 7 | 17 420 | 1 h |
ETTh2 | 7 | 17 420 | 1 h |
ILI | 7 | 966 | 7 d |
数据集 | 预测长度 | PatchLG | PatchTST | DLinear | MICN | TimesNet | BasisFormer | ETSformer | FEDformer | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | ||
Weather | 96 | 0.145 | 0.187 | 0.175 | 0.236 | 0.166 | 0.236 | 0.170 | 0.220 | 0.172 | 0.213 | 0.215 | 0.311 | 0.251 | 0.339 | ||
192 | 0.188 | 0.229 | 0.220 | 0.281 | 0.224 | 0.287 | 0.226 | 0.266 | 0.221 | 0.257 | 0.402 | 0.462 | 0.302 | 0.360 | |||
336 | 0.240 | 0.271 | 0.264 | 0.318 | 0.275 | 0.335 | 0.281 | 0.304 | 0.276 | 0.296 | 0.397 | 0.459 | 0.347 | 0.385 | |||
720 | 0.319 | 0.326 | 0.319 | 0.324 | 0.363 | 0.337 | 0.380 | 0.359 | 0.354 | 0.354 | 0.347 | 0.575 | 0.562 | 0.406 | 0.417 | ||
Electricity | 96 | 0.130 | 0.222 | 0.130 | 0.222 | 0.140 | 0.237 | 0.161 | 0.168 | 0.168 | 0.271 | 0.168 | 0.263 | 0.204 | 0.324 | 0.188 | 0.303 |
192 | 0.147 | 0.237 | 0.153 | 0.250 | 0.183 | 0.290 | 0.191 | 0.293 | 0.180 | 0.272 | 0.226 | 0.342 | 0.197 | 0.311 | |||
336 | 0.162 | 0.253 | 0.169 | 0.267 | 0.189 | 0.300 | 0.199 | 0.301 | 0.194 | 0.287 | 0.240 | 0.356 | 0.214 | 0.329 | |||
720 | 0.199 | 0.287 | 0.203 | 0.300 | 0.215 | 0.326 | 0.227 | 0.323 | 0.234 | 0.318 | 0.261 | 0.371 | 0.244 | 0.353 | |||
ETTm1 | 96 | 0.286 | 0.336 | 0.303 | 0.346 | 0.314 | 0.363 | 0.335 | 0.377 | 0.353 | 0.382 | 0.393 | 0.418 | 0.364 | 0.413 | ||
192 | 0.328 | 0.363 | 0.369 | 0.337 | 0.364 | 0.389 | 0.404 | 0.410 | 0.391 | 0.398 | 0.431 | 0.439 | 0.390 | 0.424 | |||
336 | 0.361 | 0.384 | 0.370 | 0.388 | 0.385 | 0.415 | 0.417 | 0.423 | 0.427 | 0.421 | 0.487 | 0.480 | 0.454 | 0.461 | |||
720 | 0.415 | 0.414 | 0.427 | 0.422 | 0.448 | 0.457 | 0.511 | 0.471 | 0.497 | 0.459 | 0.630 | 0.572 | 0.515 | 0.491 | |||
ETTm2 | 96 | 0.163 | 0.250 | 0.165 | 0.257 | 0.178 | 0.272 | 0.189 | 0.266 | 0.182 | 0.265 | 0.190 | 0.286 | 0.190 | 0.284 | ||
192 | 0.220 | 0.291 | 0.223 | 0.301 | 0.236 | 0.310 | 0.252 | 0.307 | 0.253 | 0.309 | 0.264 | 0.337 | 0.256 | 0.324 | |||
336 | 0.273 | 0.325 | 0.290 | 0.351 | 0.299 | 0.351 | 0.321 | 0.349 | 0.311 | 0.347 | 0.329 | 0.377 | 0.327 | 0.365 | |||
720 | 0.356 | 0.379 | 0.403 | 0.423 | 0.432 | 0.450 | 0.417 | 0.405 | 0.409 | 0.402 | 0.451 | 0.454 | 0.435 | 0.425 | |||
ETTh1 | 96 | 0.363 | 0.388 | 0.375 | 0.399 | 0.416 | 0.430 | 0.389 | 0.412 | 0.397 | 0.414 | 0.560 | 0.524 | 0.375 | 0.414 | ||
192 | 0.407 | 0.414 | 0.416 | 0.427 | 0.448 | 0.464 | 0.440 | 0.442 | 0.448 | 0.438 | 0.602 | 0.547 | 0.426 | 0.447 | |||
336 | 0.419 | 0.421 | 0.460 | 0.462 | 0.615 | 0.578 | 0.500 | 0.471 | 0.479 | 0.452 | 0.634 | 0.562 | 0.459 | 0.465 | |||
720 | 0.445 | 0.456 | 0.481 | 0.495 | 0.625 | 0.596 | 0.515 | 0.493 | 0.489 | 0.484 | 0.629 | 0.576 | 0.487 | 0.494 | |||
ETTh2 | 96 | 0.266 | 0.333 | 0.279 | 0.344 | 0.297 | 0.361 | 0.332 | 0.370 | 0.315 | 0.361 | 0.396 | 0.447 | 0.342 | 0.385 | ||
192 | 0.319 | 0.369 | 0.360 | 0.401 | 0.463 | 0.467 | 0.400 | 0.410 | 0.376 | 0.397 | 0.476 | 0.486 | 0.434 | 0.441 | |||
336 | 0.313 | 0.375 | 0.466 | 0.473 | 0.515 | 0.498 | 0.455 | 0.451 | 0.421 | 0.433 | 0.523 | 0.521 | 0.502 | 0.494 | |||
720 | 0.380 | 0.421 | 0.380 | 0.421 | 0.620 | 0.558 | 0.896 | 0.690 | 0.438 | 0.450 | 0.460 | 0.463 | 0.537 | 0.537 | 0.480 | 0.485 | |
ILI | 24 | 1.409 | 0.744 | 1.964 | 0.975 | 2.684 | 1.112 | 2.088 | 0.943 | 1.512 | 0.803 | 3.072 | 1.166 | 3.300 | 1.268 | ||
36 | 1.325 | 0.742 | 2.080 | 0.998 | 2.669 | 1.069 | 2.854 | 1.047 | 1.594 | 0.826 | 3.291 | 1.241 | 2.615 | 1.058 | |||
48 | 1.453 | 0.809 | 2.064 | 1.003 | 2.562 | 1.054 | 2.411 | 0.951 | 1.650 | 0.860 | 3.361 | 1.252 | 2.586 | 1.067 | |||
60 | 1.559 | 0.848 | 2.274 | 1.076 | 2.750 | 0.110 | 2.230 | 0.975 | 1.791 | 0.861 | 3.261 | 1.229 | 2.845 | 1.153 |
Tab. 3 Comparison of experimental results of different models
数据集 | 预测长度 | PatchLG | PatchTST | DLinear | MICN | TimesNet | BasisFormer | ETSformer | FEDformer | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | ||
Weather | 96 | 0.145 | 0.187 | 0.175 | 0.236 | 0.166 | 0.236 | 0.170 | 0.220 | 0.172 | 0.213 | 0.215 | 0.311 | 0.251 | 0.339 | ||
192 | 0.188 | 0.229 | 0.220 | 0.281 | 0.224 | 0.287 | 0.226 | 0.266 | 0.221 | 0.257 | 0.402 | 0.462 | 0.302 | 0.360 | |||
336 | 0.240 | 0.271 | 0.264 | 0.318 | 0.275 | 0.335 | 0.281 | 0.304 | 0.276 | 0.296 | 0.397 | 0.459 | 0.347 | 0.385 | |||
720 | 0.319 | 0.326 | 0.319 | 0.324 | 0.363 | 0.337 | 0.380 | 0.359 | 0.354 | 0.354 | 0.347 | 0.575 | 0.562 | 0.406 | 0.417 | ||
Electricity | 96 | 0.130 | 0.222 | 0.130 | 0.222 | 0.140 | 0.237 | 0.161 | 0.168 | 0.168 | 0.271 | 0.168 | 0.263 | 0.204 | 0.324 | 0.188 | 0.303 |
192 | 0.147 | 0.237 | 0.153 | 0.250 | 0.183 | 0.290 | 0.191 | 0.293 | 0.180 | 0.272 | 0.226 | 0.342 | 0.197 | 0.311 | |||
336 | 0.162 | 0.253 | 0.169 | 0.267 | 0.189 | 0.300 | 0.199 | 0.301 | 0.194 | 0.287 | 0.240 | 0.356 | 0.214 | 0.329 | |||
720 | 0.199 | 0.287 | 0.203 | 0.300 | 0.215 | 0.326 | 0.227 | 0.323 | 0.234 | 0.318 | 0.261 | 0.371 | 0.244 | 0.353 | |||
ETTm1 | 96 | 0.286 | 0.336 | 0.303 | 0.346 | 0.314 | 0.363 | 0.335 | 0.377 | 0.353 | 0.382 | 0.393 | 0.418 | 0.364 | 0.413 | ||
192 | 0.328 | 0.363 | 0.369 | 0.337 | 0.364 | 0.389 | 0.404 | 0.410 | 0.391 | 0.398 | 0.431 | 0.439 | 0.390 | 0.424 | |||
336 | 0.361 | 0.384 | 0.370 | 0.388 | 0.385 | 0.415 | 0.417 | 0.423 | 0.427 | 0.421 | 0.487 | 0.480 | 0.454 | 0.461 | |||
720 | 0.415 | 0.414 | 0.427 | 0.422 | 0.448 | 0.457 | 0.511 | 0.471 | 0.497 | 0.459 | 0.630 | 0.572 | 0.515 | 0.491 | |||
ETTm2 | 96 | 0.163 | 0.250 | 0.165 | 0.257 | 0.178 | 0.272 | 0.189 | 0.266 | 0.182 | 0.265 | 0.190 | 0.286 | 0.190 | 0.284 | ||
192 | 0.220 | 0.291 | 0.223 | 0.301 | 0.236 | 0.310 | 0.252 | 0.307 | 0.253 | 0.309 | 0.264 | 0.337 | 0.256 | 0.324 | |||
336 | 0.273 | 0.325 | 0.290 | 0.351 | 0.299 | 0.351 | 0.321 | 0.349 | 0.311 | 0.347 | 0.329 | 0.377 | 0.327 | 0.365 | |||
720 | 0.356 | 0.379 | 0.403 | 0.423 | 0.432 | 0.450 | 0.417 | 0.405 | 0.409 | 0.402 | 0.451 | 0.454 | 0.435 | 0.425 | |||
ETTh1 | 96 | 0.363 | 0.388 | 0.375 | 0.399 | 0.416 | 0.430 | 0.389 | 0.412 | 0.397 | 0.414 | 0.560 | 0.524 | 0.375 | 0.414 | ||
192 | 0.407 | 0.414 | 0.416 | 0.427 | 0.448 | 0.464 | 0.440 | 0.442 | 0.448 | 0.438 | 0.602 | 0.547 | 0.426 | 0.447 | |||
336 | 0.419 | 0.421 | 0.460 | 0.462 | 0.615 | 0.578 | 0.500 | 0.471 | 0.479 | 0.452 | 0.634 | 0.562 | 0.459 | 0.465 | |||
720 | 0.445 | 0.456 | 0.481 | 0.495 | 0.625 | 0.596 | 0.515 | 0.493 | 0.489 | 0.484 | 0.629 | 0.576 | 0.487 | 0.494 | |||
ETTh2 | 96 | 0.266 | 0.333 | 0.279 | 0.344 | 0.297 | 0.361 | 0.332 | 0.370 | 0.315 | 0.361 | 0.396 | 0.447 | 0.342 | 0.385 | ||
192 | 0.319 | 0.369 | 0.360 | 0.401 | 0.463 | 0.467 | 0.400 | 0.410 | 0.376 | 0.397 | 0.476 | 0.486 | 0.434 | 0.441 | |||
336 | 0.313 | 0.375 | 0.466 | 0.473 | 0.515 | 0.498 | 0.455 | 0.451 | 0.421 | 0.433 | 0.523 | 0.521 | 0.502 | 0.494 | |||
720 | 0.380 | 0.421 | 0.380 | 0.421 | 0.620 | 0.558 | 0.896 | 0.690 | 0.438 | 0.450 | 0.460 | 0.463 | 0.537 | 0.537 | 0.480 | 0.485 | |
ILI | 24 | 1.409 | 0.744 | 1.964 | 0.975 | 2.684 | 1.112 | 2.088 | 0.943 | 1.512 | 0.803 | 3.072 | 1.166 | 3.300 | 1.268 | ||
36 | 1.325 | 0.742 | 2.080 | 0.998 | 2.669 | 1.069 | 2.854 | 1.047 | 1.594 | 0.826 | 3.291 | 1.241 | 2.615 | 1.058 | |||
48 | 1.453 | 0.809 | 2.064 | 1.003 | 2.562 | 1.054 | 2.411 | 0.951 | 1.650 | 0.860 | 3.361 | 1.252 | 2.586 | 1.067 | |||
60 | 1.559 | 0.848 | 2.274 | 1.076 | 2.750 | 0.110 | 2.230 | 0.975 | 1.791 | 0.861 | 3.261 | 1.229 | 2.845 | 1.153 |
数据集 | 预测长度 | PatchLG | R-Local-Global | R-Local | R-Global | ||||
---|---|---|---|---|---|---|---|---|---|
MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | ||
Weather | 96 | 0.145 | 0.187 | 0.152 | 0.197 | 0.151 | 0.197 | 0.149 | 0.194 |
192 | 0.188 | 0.229 | 0.196 | 0.240 | 0.194 | 0.237 | 0.194 | 0.236 | |
336 | 0.240 | 0.271 | 0.254 | 0.284 | 0.246 | 0.278 | 0.248 | 0.277 | |
720 | 0.319 | 0.326 | 0.328 | 0.335 | 0.324 | 0.333 | 0.327 | 0.332 | |
Electricity | 96 | 0.130 | 0.222 | 0.133 | 0.221 | 0.131 | 0.225 | 0.131 | 0.224 |
192 | 0.147 | 0.237 | 0.148 | 0.239 | 0.150 | 0.241 | 0.151 | 0.240 | |
336 | 0.162 | 0.253 | 0.167 | 0.257 | 0.166 | 0.258 | 0.168 | 0.258 | |
720 | 0.199 | 0.287 | 0.200 | 0.288 | 0.204 | 0.292 | 0.203 | 0.291 | |
ETTm1 | 96 | 0.286 | 0.336 | 0.292 | 0.344 | 0.292 | 0.345 | 0.296 | 0.344 |
192 | 0.328 | 0.363 | 0.334 | 0.367 | 0.330 | 0.369 | 0.327 | 0.365 | |
336 | 0.361 | 0.384 | 0.372 | 0.394 | 0.362 | 0.391 | 0.360 | 0.387 | |
720 | 0.417 | 0.415 | 0.429 | 0.426 | 0.419 | 0.424 | 0.415 | 0.415 | |
ETTm2 | 96 | 0.163 | 0.250 | 0.178 | 0.262 | 0.171 | 0.256 | 0.173 | 0.255 |
192 | 0.220 | 0.291 | 0.241 | 0.305 | 0.235 | 0.301 | 0.231 | 0.298 | |
336 | 0.273 | 0.325 | 0.284 | 0.334 | 0.282 | 0.334 | 0.282 | 0.332 | |
720 | 0.356 | 0.379 | 0.367 | 0.385 | 0.368 | 0.386 | 0.366 | 0.386 | |
ETTh1 | 96 | 0.363 | 0.388 | 0.382 | 0.406 | 0.373 | 0.398 | 0.376 | 0.399 |
192 | 0.407 | 0.414 | 0.419 | 0.424 | 0.412 | 0.422 | 0.414 | 0.421 | |
336 | 0.419 | 0.421 | 0.428 | 0.429 | 0.424 | 0.430 | 0.436 | 0.438 | |
720 | 0.445 | 0.456 | 0.448 | 0.461 | 0.459 | 0.468 | 0.454 | 0.466 | |
ETTh2 | 96 | 0.266 | 0.333 | 0.284 | 0.346 | 0.294 | 0.351 | 0.312 | 0.354 |
192 | 0.319 | 0.369 | 0.370 | 0.400 | 0.362 | 0.399 | 0.359 | 0.387 | |
336 | 0.313 | 0.375 | 0.338 | 0.388 | 0.363 | 0.402 | 0.373 | 0.403 | |
720 | 0.380 | 0.421 | 0.405 | 0.439 | 0.388 | 0.428 | 0.402 | 0.432 | |
ILI | 24 | 1.409 | 0.744 | 1.464 | 0.791 | 2.058 | 0.942 | 1.879 | 0.891 |
36 | 1.325 | 0.742 | 1.515 | 0.787 | 2.112 | 0.955 | 1.988 | 1.010 | |
48 | 1.453 | 0.809 | 1.469 | 0.802 | 2.182 | 1.015 | 2.105 | 0.959 | |
60 | 1.559 | 0.848 | 1.608 | 0.829 | 2.206 | 0.998 | 2.321 | 1.029 |
Tab. 4 Ablation experimental results of PatchLG model
数据集 | 预测长度 | PatchLG | R-Local-Global | R-Local | R-Global | ||||
---|---|---|---|---|---|---|---|---|---|
MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | ||
Weather | 96 | 0.145 | 0.187 | 0.152 | 0.197 | 0.151 | 0.197 | 0.149 | 0.194 |
192 | 0.188 | 0.229 | 0.196 | 0.240 | 0.194 | 0.237 | 0.194 | 0.236 | |
336 | 0.240 | 0.271 | 0.254 | 0.284 | 0.246 | 0.278 | 0.248 | 0.277 | |
720 | 0.319 | 0.326 | 0.328 | 0.335 | 0.324 | 0.333 | 0.327 | 0.332 | |
Electricity | 96 | 0.130 | 0.222 | 0.133 | 0.221 | 0.131 | 0.225 | 0.131 | 0.224 |
192 | 0.147 | 0.237 | 0.148 | 0.239 | 0.150 | 0.241 | 0.151 | 0.240 | |
336 | 0.162 | 0.253 | 0.167 | 0.257 | 0.166 | 0.258 | 0.168 | 0.258 | |
720 | 0.199 | 0.287 | 0.200 | 0.288 | 0.204 | 0.292 | 0.203 | 0.291 | |
ETTm1 | 96 | 0.286 | 0.336 | 0.292 | 0.344 | 0.292 | 0.345 | 0.296 | 0.344 |
192 | 0.328 | 0.363 | 0.334 | 0.367 | 0.330 | 0.369 | 0.327 | 0.365 | |
336 | 0.361 | 0.384 | 0.372 | 0.394 | 0.362 | 0.391 | 0.360 | 0.387 | |
720 | 0.417 | 0.415 | 0.429 | 0.426 | 0.419 | 0.424 | 0.415 | 0.415 | |
ETTm2 | 96 | 0.163 | 0.250 | 0.178 | 0.262 | 0.171 | 0.256 | 0.173 | 0.255 |
192 | 0.220 | 0.291 | 0.241 | 0.305 | 0.235 | 0.301 | 0.231 | 0.298 | |
336 | 0.273 | 0.325 | 0.284 | 0.334 | 0.282 | 0.334 | 0.282 | 0.332 | |
720 | 0.356 | 0.379 | 0.367 | 0.385 | 0.368 | 0.386 | 0.366 | 0.386 | |
ETTh1 | 96 | 0.363 | 0.388 | 0.382 | 0.406 | 0.373 | 0.398 | 0.376 | 0.399 |
192 | 0.407 | 0.414 | 0.419 | 0.424 | 0.412 | 0.422 | 0.414 | 0.421 | |
336 | 0.419 | 0.421 | 0.428 | 0.429 | 0.424 | 0.430 | 0.436 | 0.438 | |
720 | 0.445 | 0.456 | 0.448 | 0.461 | 0.459 | 0.468 | 0.454 | 0.466 | |
ETTh2 | 96 | 0.266 | 0.333 | 0.284 | 0.346 | 0.294 | 0.351 | 0.312 | 0.354 |
192 | 0.319 | 0.369 | 0.370 | 0.400 | 0.362 | 0.399 | 0.359 | 0.387 | |
336 | 0.313 | 0.375 | 0.338 | 0.388 | 0.363 | 0.402 | 0.373 | 0.403 | |
720 | 0.380 | 0.421 | 0.405 | 0.439 | 0.388 | 0.428 | 0.402 | 0.432 | |
ILI | 24 | 1.409 | 0.744 | 1.464 | 0.791 | 2.058 | 0.942 | 1.879 | 0.891 |
36 | 1.325 | 0.742 | 1.515 | 0.787 | 2.112 | 0.955 | 1.988 | 1.010 | |
48 | 1.453 | 0.809 | 1.469 | 0.802 | 2.182 | 1.015 | 2.105 | 0.959 | |
60 | 1.559 | 0.848 | 1.608 | 0.829 | 2.206 | 0.998 | 2.321 | 1.029 |
数据集 | 预测长度 | PatchLG | CrossGNN | FourierGNN | |||
---|---|---|---|---|---|---|---|
MSE | MAE | MSE | MAE | MSE | MAE | ||
Weather | 96 | 0.145 | 0.187 | 0.175 | 0.227 | 0.165 | 0.216 |
192 | 0.188 | 0.229 | 0.208 | 0.259 | 0.206 | 0.252 | |
336 | 0.240 | 0.271 | 0.256 | 0.297 | 0.258 | 0.289 | |
720 | 0.319 | 0.326 | 0.337 | 0.347 | 0.328 | 0.338 | |
Electricity | 96 | 0.130 | 0.222 | 0.164 | 0.268 | 0.156 | 0.257 |
192 | 0.147 | 0.237 | 0.178 | 0.280 | 0.174 | 0.274 | |
336 | 0.162 | 0.253 | 0.195 | 0.295 | 0.193 | 0.291 | |
720 | 0.199 | 0.287 | 0.233 | 0.325 | 0.231 | 0.321 | |
ETTm1 | 96 | 0.286 | 0.336 | 0.294 | 0.344 | 0.313 | 0.360 |
192 | 0.328 | 0.363 | 0.329 | 0.363 | 0.352 | 0.384 | |
336 | 0.361 | 0.384 | 0.371 | 0.385 | 0.389 | 0.405 | |
720 | 0.417 | 0.415 | 0.418 | 0.414 | 0.440 | 0.433 | |
ETTm2 | 96 | 0.163 | 0.250 | 0.165 | 0.256 | 0.182 | 0.265 |
192 | 0.220 | 0.291 | 0.224 | 0.297 | 0.244 | 0.309 | |
336 | 0.273 | 0.325 | 0.280 | 0.336 | 0.296 | 0.344 | |
720 | 0.356 | 0.379 | 0.370 | 0.393 | 0.384 | 0.400 | |
ETTh1 | 96 | 0.363 | 0.388 | 0.370 | 0.392 | 0.489 | 0.471 |
192 | 0.407 | 0.414 | 0.409 | 0.419 | 0.513 | 0.486 | |
336 | 0.419 | 0.421 | 0.432 | 0.432 | 0.503 | 0.487 | |
720 | 0.445 | 0.456 | 0.451 | 0.460 | 0.540 | 0.521 | |
ETTh2 | 96 | 0.266 | 0.333 | 0.295 | 0.346 | 0.327 | 0.380 |
192 | 0.319 | 0.369 | 0.357 | 0.392 | 0.383 | 0.416 | |
336 | 0.313 | 0.375 | 0.402 | 0.427 | 0.365 | 0.413 | |
720 | 0.380 | 0.421 | 0.432 | 0.452 | 0.427 | 0.452 |
Tab. 5 Performance comparison of spatio-temporal dependency modeling methods and PatchLG
数据集 | 预测长度 | PatchLG | CrossGNN | FourierGNN | |||
---|---|---|---|---|---|---|---|
MSE | MAE | MSE | MAE | MSE | MAE | ||
Weather | 96 | 0.145 | 0.187 | 0.175 | 0.227 | 0.165 | 0.216 |
192 | 0.188 | 0.229 | 0.208 | 0.259 | 0.206 | 0.252 | |
336 | 0.240 | 0.271 | 0.256 | 0.297 | 0.258 | 0.289 | |
720 | 0.319 | 0.326 | 0.337 | 0.347 | 0.328 | 0.338 | |
Electricity | 96 | 0.130 | 0.222 | 0.164 | 0.268 | 0.156 | 0.257 |
192 | 0.147 | 0.237 | 0.178 | 0.280 | 0.174 | 0.274 | |
336 | 0.162 | 0.253 | 0.195 | 0.295 | 0.193 | 0.291 | |
720 | 0.199 | 0.287 | 0.233 | 0.325 | 0.231 | 0.321 | |
ETTm1 | 96 | 0.286 | 0.336 | 0.294 | 0.344 | 0.313 | 0.360 |
192 | 0.328 | 0.363 | 0.329 | 0.363 | 0.352 | 0.384 | |
336 | 0.361 | 0.384 | 0.371 | 0.385 | 0.389 | 0.405 | |
720 | 0.417 | 0.415 | 0.418 | 0.414 | 0.440 | 0.433 | |
ETTm2 | 96 | 0.163 | 0.250 | 0.165 | 0.256 | 0.182 | 0.265 |
192 | 0.220 | 0.291 | 0.224 | 0.297 | 0.244 | 0.309 | |
336 | 0.273 | 0.325 | 0.280 | 0.336 | 0.296 | 0.344 | |
720 | 0.356 | 0.379 | 0.370 | 0.393 | 0.384 | 0.400 | |
ETTh1 | 96 | 0.363 | 0.388 | 0.370 | 0.392 | 0.489 | 0.471 |
192 | 0.407 | 0.414 | 0.409 | 0.419 | 0.513 | 0.486 | |
336 | 0.419 | 0.421 | 0.432 | 0.432 | 0.503 | 0.487 | |
720 | 0.445 | 0.456 | 0.451 | 0.460 | 0.540 | 0.521 | |
ETTh2 | 96 | 0.266 | 0.333 | 0.295 | 0.346 | 0.327 | 0.380 |
192 | 0.319 | 0.369 | 0.357 | 0.392 | 0.383 | 0.416 | |
336 | 0.313 | 0.375 | 0.402 | 0.427 | 0.365 | 0.413 | |
720 | 0.380 | 0.421 | 0.432 | 0.452 | 0.427 | 0.452 |
模型 | 指标 | Weather | ETTm1 | ETTm2 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
T=96 | T=192 | T=336 | T=720 | T=96 | T=192 | T=336 | T=720 | T=96 | T=192 | T=336 | T=720 | |||
PatchLG | 0 | MSE | 0.145 | 0.188 | 0.240 | 0.319 | 0.286 | 0.328 | 0.361 | 0.417 | 0.163 | 0.220 | 0.273 | 0.356 |
MAE | 0.187 | 0.229 | 0.271 | 0.326 | 0.336 | 0.363 | 0.384 | 0.415 | 0.250 | 0.291 | 0.325 | 0.379 | ||
1 | MSE | 0.146 | 0.190 | 0.241 | 0.323 | 0.287 | 0.327 | 0.365 | 0.419 | 0.165 | 0.223 | 0.278 | 0.359 | |
MAE | 0.190 | 0.230 | 0.272 | 0.330 | 0.338 | 0.365 | 0.389 | 0.420 | 0.254 | 0.295 | 0.331 | 0.380 | ||
5 | MSE | 0.146 | 0.192 | 0.242 | 0.323 | 0.287 | 0.332 | 0.372 | 0.425 | 0.166 | 0.226 | 0.282 | 0.367 | |
MAE | 0.191 | 0.234 | 0.272 | 0.331 | 0.337 | 0.368 | 0.393 | 0.431 | 0.258 | 0.298 | 0.334 | 0.387 | ||
10 | MSE | 0.154 | 0.200 | 0.247 | 0.329 | 0.292 | 0.334 | 0.381 | 0.436 | 0.175 | 0.237 | 0.290 | 0.378 | |
MAE | 0.195 | 0.242 | 0.279 | 0.335 | 0.339 | 0.372 | 0.402 | 0.445 | 0.273 | 0.309 | 0.342 | 0.398 | ||
PatchTST | 0 | MSE | 0.152 | 0.197 | 0.250 | 0.319 | 0.293 | 0.331 | 0.365 | 0.414 | 0.164 | 0.221 | 0.278 | 0.367 |
MAE | 0.200 | 0.243 | 0.284 | 0.335 | 0.343 | 0.369 | 0.392 | 0.420 | 0.254 | 0.294 | 0.329 | 0.385 | ||
1 | MSE | 0.162 | 0.203 | 0.261 | 0.326 | 0.301 | 0.341 | 0.372 | 0.425 | 0.168 | 0.229 | 0.282 | 0.386 | |
MAE | 0.208 | 0.255 | 0.298 | 0.346 | 0.351 | 0.378 | 0.405 | 0.431 | 0.259 | 0.299 | 0.338 | 0.392 | ||
5 | MSE | 0.163 | 0.211 | 0.277 | 0.351 | 0.305 | 0.352 | 0.385 | 0.442 | 0.173 | 0.238 | 0.295 | 0.413 | |
MAE | 0.220 | 0.261 | 0.309 | 0.362 | 0.358 | 0.387 | 0.412 | 0.446 | 0.268 | 0.308 | 0.348 | 0.409 | ||
10 | MSE | 0.175 | 0.228 | 0.291 | 0.376 | 0.319 | 0.366 | 0.408 | 0.468 | 0.188 | 0.251 | 0.312 | 0.425 | |
MAE | 0.239 | 0.278 | 0.326 | 0.385 | 0.368 | 0.401 | 0.432 | 0.475 | 0.279 | 0.322 | 0.368 | 0.431 | ||
MICN | 0 | MSE | 0.166 | 0.224 | 0.275 | 0.337 | 0.314 | 0.364 | 0.385 | 0.448 | 0.178 | 0.236 | 0.299 | 0.432 |
MAE | 0.236 | 0.287 | 0.355 | 0.380 | 0.363 | 0.389 | 0.415 | 0.457 | 0.272 | 0.310 | 0.351 | 0.450 | ||
1 | MSE | 0.171 | 0.240 | 0.303 | 0.356 | 0.318 | 0.371 | 0.392 | 0.459 | 0.183 | 0.245 | 0.311 | 0.441 | |
MAE | 0.240 | 0.302 | 0.376 | 0.390 | 0.368 | 0.394 | 0.426 | 0.461 | 0.274 | 0.318 | 0.362 | 0.462 | ||
5 | MSE | 0.179 | 0.258 | 0.329 | 0.381 | 0.323 | 0.378 | 0.406 | 0.471 | 0.192 | 0.257 | 0.326 | 0.458 | |
MAE | 0.243 | 0.316 | 0.399 | 0.406 | 0.371 | 0.404 | 0.438 | 0.480 | 0.280 | 0.329 | 0.376 | 0.478 | ||
10 | MSE | 0.187 | 0.258 | 0.313 | 0.385 | 0.332 | 0.395 | 0.426 | 0.501 | 0.202 | 0.371 | 0.339 | 0.486 | |
MAE | 0.253 | 0.349 | 0.428 | 0.439 | 0.381 | 0.415 | 0.457 | 0.503 | 0.291 | 0.352 | 0.393 | 0.500 |
Tab. 6 Experimental results on robustness of different models
模型 | 指标 | Weather | ETTm1 | ETTm2 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
T=96 | T=192 | T=336 | T=720 | T=96 | T=192 | T=336 | T=720 | T=96 | T=192 | T=336 | T=720 | |||
PatchLG | 0 | MSE | 0.145 | 0.188 | 0.240 | 0.319 | 0.286 | 0.328 | 0.361 | 0.417 | 0.163 | 0.220 | 0.273 | 0.356 |
MAE | 0.187 | 0.229 | 0.271 | 0.326 | 0.336 | 0.363 | 0.384 | 0.415 | 0.250 | 0.291 | 0.325 | 0.379 | ||
1 | MSE | 0.146 | 0.190 | 0.241 | 0.323 | 0.287 | 0.327 | 0.365 | 0.419 | 0.165 | 0.223 | 0.278 | 0.359 | |
MAE | 0.190 | 0.230 | 0.272 | 0.330 | 0.338 | 0.365 | 0.389 | 0.420 | 0.254 | 0.295 | 0.331 | 0.380 | ||
5 | MSE | 0.146 | 0.192 | 0.242 | 0.323 | 0.287 | 0.332 | 0.372 | 0.425 | 0.166 | 0.226 | 0.282 | 0.367 | |
MAE | 0.191 | 0.234 | 0.272 | 0.331 | 0.337 | 0.368 | 0.393 | 0.431 | 0.258 | 0.298 | 0.334 | 0.387 | ||
10 | MSE | 0.154 | 0.200 | 0.247 | 0.329 | 0.292 | 0.334 | 0.381 | 0.436 | 0.175 | 0.237 | 0.290 | 0.378 | |
MAE | 0.195 | 0.242 | 0.279 | 0.335 | 0.339 | 0.372 | 0.402 | 0.445 | 0.273 | 0.309 | 0.342 | 0.398 | ||
PatchTST | 0 | MSE | 0.152 | 0.197 | 0.250 | 0.319 | 0.293 | 0.331 | 0.365 | 0.414 | 0.164 | 0.221 | 0.278 | 0.367 |
MAE | 0.200 | 0.243 | 0.284 | 0.335 | 0.343 | 0.369 | 0.392 | 0.420 | 0.254 | 0.294 | 0.329 | 0.385 | ||
1 | MSE | 0.162 | 0.203 | 0.261 | 0.326 | 0.301 | 0.341 | 0.372 | 0.425 | 0.168 | 0.229 | 0.282 | 0.386 | |
MAE | 0.208 | 0.255 | 0.298 | 0.346 | 0.351 | 0.378 | 0.405 | 0.431 | 0.259 | 0.299 | 0.338 | 0.392 | ||
5 | MSE | 0.163 | 0.211 | 0.277 | 0.351 | 0.305 | 0.352 | 0.385 | 0.442 | 0.173 | 0.238 | 0.295 | 0.413 | |
MAE | 0.220 | 0.261 | 0.309 | 0.362 | 0.358 | 0.387 | 0.412 | 0.446 | 0.268 | 0.308 | 0.348 | 0.409 | ||
10 | MSE | 0.175 | 0.228 | 0.291 | 0.376 | 0.319 | 0.366 | 0.408 | 0.468 | 0.188 | 0.251 | 0.312 | 0.425 | |
MAE | 0.239 | 0.278 | 0.326 | 0.385 | 0.368 | 0.401 | 0.432 | 0.475 | 0.279 | 0.322 | 0.368 | 0.431 | ||
MICN | 0 | MSE | 0.166 | 0.224 | 0.275 | 0.337 | 0.314 | 0.364 | 0.385 | 0.448 | 0.178 | 0.236 | 0.299 | 0.432 |
MAE | 0.236 | 0.287 | 0.355 | 0.380 | 0.363 | 0.389 | 0.415 | 0.457 | 0.272 | 0.310 | 0.351 | 0.450 | ||
1 | MSE | 0.171 | 0.240 | 0.303 | 0.356 | 0.318 | 0.371 | 0.392 | 0.459 | 0.183 | 0.245 | 0.311 | 0.441 | |
MAE | 0.240 | 0.302 | 0.376 | 0.390 | 0.368 | 0.394 | 0.426 | 0.461 | 0.274 | 0.318 | 0.362 | 0.462 | ||
5 | MSE | 0.179 | 0.258 | 0.329 | 0.381 | 0.323 | 0.378 | 0.406 | 0.471 | 0.192 | 0.257 | 0.326 | 0.458 | |
MAE | 0.243 | 0.316 | 0.399 | 0.406 | 0.371 | 0.404 | 0.438 | 0.480 | 0.280 | 0.329 | 0.376 | 0.478 | ||
10 | MSE | 0.187 | 0.258 | 0.313 | 0.385 | 0.332 | 0.395 | 0.426 | 0.501 | 0.202 | 0.371 | 0.339 | 0.486 | |
MAE | 0.253 | 0.349 | 0.428 | 0.439 | 0.381 | 0.415 | 0.457 | 0.503 | 0.291 | 0.352 | 0.393 | 0.500 |
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