A Car-Following Model considering the Effect of Following Vehicles under the Framework of Physics-Informed Deep Learning

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left">Parameters</td><td class="align_center">Value</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left"><span style="width: 42.0523ptpx;"><svg height="13.8595pt" id="M92" style="vertical-align:-2.2681pt" version="1.1" viewbox="-0.0498162 -11.5914 42.0523 13.8595" width="42.0523pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g 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class="align_center">0.73</td></tr><tr><td class="align_left"><span style="width: 22.3347ptpx;"><svg height="11.5564pt" id="M93" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 22.3347 11.5564" width="22.3347pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.285,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.783,0)"><path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 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transform="matrix(.013,0,0,-0.013,38.638,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,43.999,0)"><path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z"></path></g><g transform="matrix(.013,0,0,-0.013,48.875,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg></span></td><td class="align_center">30</td></tr><tr><td class="align_left"><span style="width: 30.465ptpx;"><svg height="12.5794pt" id="M95" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 30.465 12.5794" 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transform="matrix(.013,0,0,-0.013,15.515,0)"><path d="M766 88L752 113C719 83 690 64 681 64C674 64 672 74 679 103L724 292C758 436 724 448 701 448C680 448 666 442 639 429C594 407 514 350 441 252H439L447 289C476 423 450 448 419 448C398 448 379 441 355 427C307 400 234 344 162 249H160L180 324C203 409 197 448 170 448C144 448 82 413 23 349L35 321C57 343 96 374 108 374C115 374 117 371 111 341C87 227 57 112 24 -6L32 -12C53 -4 81 4 108 6C119 68 134 128 149 171C177 229 309 383 364 383C387 383 388 355 373 282C354 190 330 92 303 -6L309 -12C332 -4 356 3 386 6C396 63 411 122 424 171C458 236 590 383 642 383C658 383 664 369 652 315L603 91C587 20 593 -12 619 -12C642 -12 708 23 766 88Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.773,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg></span></td><td class="align_center">2</td></tr><tr><td class="align_left"><span style="width: 40.7605ptpx;"><svg 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<div>The ground truth value of each parameter.</div>

Journal of Advanced Transportation

tab5

Table 5

Table 5: A Car-Following Model considering the Effect of Following Vehicles under the Framework of Physics-Informed Deep Learning 