Physics-informed offline reinforcement learning eliminates catastrophic fuel waste in maritime routing
Organizations: Department of Computer Science, Texas State University, San Marcos, TX 78666, USA · MIT Sea Grant College Program, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Abstract
International shipping produces approximately 3% of global greenhouse gas emissions, yet voyage routing remains dominated by heuristic methods. We present PIER (Physics-Informed, Energy-efficient, Risk-aware routing), an offline reinforcement learning framework that learns fuel-efficient, safety-aware routing policies from physics-calibrated environments grounded in historical vessel tracking data and ocean reanalysis products, requiring no online simulator. Validated on one full year (2023) of AIS data across seven Gulf of Mexico routes (840 episodes per method), PIER reduces mean CO2 emissions by 10% relative to great-circle routing. However, PIER's primary contribution is eliminating catastrophic fuel waste: great-circle routing incurs extreme fuel consumption (>1.5x median) in 4.8% of voyages; PIER reduces this to 0.5%, a 9-fold reduction. Per-voyage fuel variance is 3.5x lower (p<0.001), with bootstrap 95% CI for mean savings [2.9%, 15.7%]. Partial validation against observed AIS vessel behavior confirms consistency with the fastest real transits while exhibiting 23.1x lower variance. Crucially, PIER is forecast-independent: unlike A* path optimization whose wave protection degrades 4.5x under realistic forecast uncertainty, PIER maintains constant performance using only local observations. The framework combines physics-informed state construction, demonstration-augmented offline data, and a decoupled post-hoc safety shield, an architecture that transfers to wildfire evacuation, aircraft trajectory optimization, and autonomous navigation in unmapped terrain.
Figures & tables
| Method | Type | Arrival | Time (h) | Fuel Proxy | HF Exposure |
| Great Circle | Heuristic | 655/840 (78.0%) | 49.8 52.8 | 89.5 94.4 | 55.8 56.1 |
| Greedy Goal | Heuristic | 685/840 (81.5%) | 46.6 42.5 | 78.8 74.9 | 51.7 48.4 |
| BC (expert) | Supervised | 63/840 (7.5%) | 101.1 60.5 | 117.3 81.0 | 83.6 62.7 |
| DQN | Online RL | 3/840 (0.4%) | 70.8 140.0 | 79.5 157.0 | 37.8 75.8 |
| CQL | Offline RL | 643/840 (76.5%) | 49.7 35.0 | 83.9 60.9 | 55.3 46.5 |
| Pier (IQL) | Offline RL | 700/840 (83.3%) | 45.6 26.4 | 78.5 44.9 | 53.2 45.6 |
| Route | Arrival | Time (h) | HF Exposure |
| Brownsville Key West | 100% | 71.1 10.5 | 109.3 38.7 |
| Galveston Key West | 100% | 62.7 2.2 | 85.3 34.1 |
| Corpus Christi Tampa | 93% | 63.2 1.2 | 69.7 32.7 |
| New Orleans Tampa | 98% | 32.6 1.1 | 30.6 29.7 |
| Mobile Tampa | 97% | 27.7 5.1 | 26.9 17.5 |
| Corpus Christi Galveston | 84% | 13.2 1.5 | 10.5 9.9 |
| Variant | Arrival | Time (h) | HF Exposure | Arr |
| IQL (full) | 700/840 (83.3%) | 45.9 21.8 | 56.3 45.4 | - |
| No teacher demos | 675/840 (80.4%) | 46.1 22.3 | 58.1 46.5 | 25 |
| No safety shield | 643/840 (76.9%) | 47.3 21.0 | 59.3 45.7 | 54 |
| No HF-risk features | 659/840 (78.5%) | 49.3 20.7 | 60.3 44.4 | 41 |
| No physics features | 652/840 (77.6%) | 49.0 20.1 | 60.2 45.5 | 48 |
| Metric | Pier (IQL) | Great Circle | Saving | % |
| Mean CO 2 (t/voyage) | 171.6 | 189.8 | 18.2 | 9.6% |
| Median CO 2 (t/voyage) | 216.9 | 218.2 | 1.3 | 0.6% |
| 90th percentile CO 2 (t) | 240.9 | 243.2 | 2.3 | 0.9% |
| 95th percentile CO 2 (t) | 242.9 | 259.5 | 16.6 | 6.4% |
| Max CO 2 (worst voyage, t) | 470.8 | 1,560.4 | 1,089.6 | 69.8% |
| Std deviation CO 2 (t) | 76.4 | 141.9 | - | - |
| Route | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Ann. | |
| Bro→Key | Arr% | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 (98) |
| HF | 135 | 128 | 117 | 143 | 144 | 58 | 70 | 49 | 76 | 98 | 175 | 118 | 109 | |
| CC→Gal | Arr% | 100 | 60 | 70 | 100 | 60 | 100 | 70 | 80 | 80 | 100 | 90 | 100 | 84 (92) |
| HF | 4 | 33 | 4 | 4 | 3 | 12 | 2 | 4 | 11 | 25 | 20 | 6 | 11 | |
| CC→Tam | Arr% | 100 | 100 | 100 | 90 | 100 | 100 | 90 | 90 | 70 | 90 | 80 | 100 | 92 (82) |
| HF | 56 | 106 | 66 | 74 | 66 | 67 | 26 | 14 | 65 | 134 | 89 | 71 | 70 |
| Vessel | MCR (kW) | (kn) | SFOC | VLSFO | HFO | MGO | |||
| IQL | GC | IQL | GC | IQL | GC | ||||
| Panamax Bulk | 10000 | 14.0 | 153 | 0.15 | 0.17 | 0.15 | 0.17 | 0.16 | 0.17 |
| 170 | 0.17 | 0.19 | 0.17 | 0.19 | 0.17 | 0.19 | |||
| 187 | 0.19 | 0.21 | 0.19 | 0.21 | 0.19 | 0.21 | |||
| Handymax Bulk | 7500 | 13.0 | 153 | 0.14 | 0.16 | 0.14 | 0.16 | 0.15 | 0.16 |
| 170 | 0.16 | 0.18 | 0.16 | 0.18 | 0.16 | 0.18 | |||
| Method | Mean | Median | Std | P95 | Max | Time (h) | 1.5 med | |
| CO 2 per voyage (tonnes) | mean std | |||||||
| A* (Balanced) | 60 | 175.5 | 220.7 | 78.0 | 251.2 | 251.5 | 50.5 22.5 | 0.0% |
| Pier (IQL) | 569 | 171.6 | 216.9 | 76.4 | 242.9 | 470.8 | 45.6 26.4 | 0.5% |
| Great Circle | 563 | 189.8 | 218.2 | 141.9 | 259.5 | 1,560.4 | 49.8 52.8 | 4.8% |
| Statistical tests (Levene’s test for variance equality): | ||||||||
| A* vs Great Circle: , (ns); A* vs IQL: , (ns) | ||||||||
| Method | Time (h) | CO 2 (t) | HF Exposure | |
| AIS (direct transits) | 4 | 93.0 78.2 | 315.0 348.2 | 270.5 149.5 |
| AIS (all voyages) | 6 | 257.2 257.6 | 257.2 301.2 | 219.8 141.7 |
| Great Circle | 92 | 52.3 56.0 | 185.3 195.1 | 36.8 35.2 |
| CQL | 119 | 27.8 5.4 | 96.3 15.1 | 28.4 18.9 |
| Pier (IQL) | 116 | 27.7 5.1 | 95.2 15.1 | 26.9 17.5 |
| Variance ratio (AIS direct / IQL): | ||||
| Forecast noise | Approx. | Arrival (%) | Mean HF | ||
| horizon | A* | IQL | A* | IQL | |
| 0.00 | Perfect | 75 | 93 | 3.7 | 22.9 |
| 0.10 | 24 h | 72 | 93 | 7.9 | 22.9 |
| 0.25 | 48 h | 77 | 93 | 8.9 | 22.9 |
| 0.50 | 72 h | 85 | 93 | 12.1 | 22.9 |
| 0.75 | 96 h | 88 | 93 | 14.1 | 22.9 |
| Route | Arrived | Time (h) | Fuel (t) | HF Exp. | Shield Int. |
| S1 (Open Water) | ✓ | 16.0 | 12.3 | 2.63 | 0 |
| S2 (Corridor) | ✓ | 16.0 | 16.1 | 3.56 | 0 |
| S3 (Storm) | ✓ | 17.0 | 16.0 | 3.73 | 1 |
| Time (h) | Fuel (t) | HF Exp. | Arrived | |||||||||
| Config | S1 | S2 | S3 | S1 | S2 | S3 | S1 | S2 | S3 | S1 | S2 | S3 |
| Full Pier | 16 | 16 | 17 | 12.3 | 16.1 | 16.0 | 2.63 | 3.56 | 3.73 | ✓ | ✓ | ✓ |
| Full (100ep) | 15 | 10 | 9 | 12.0 | 8.7 | 8.0 | 2.61 | 1.34 | 1.28 | ✓ | ||
| Teacher | 15 | 6 | 17 | 11.8 | 5.5 | 16.1 | 2.52 | 0.81 | 3.77 | ✓ | ✓ | |
| Shield | 15 | 19 | 9 | 12.0 | 18.1 | 8.1 | 2.63 | 3.96 | 1.29 | ✓ | ✓ | |
| HF Risk | 7 | 24 | 9 | 5.1 | 23.4 | 8.1 | 0.98 | 4.52 | 1.27 | ✓ | ||