SIMROUTE-Based Routing

• SIMROUTE-based routing is a computational framework that models ship voyages as constrained shortest-path problems with dynamic vessel speed and wave resistance.
• It integrates A* search with physics-informed Fourier Neural Operator wave forecasts and kernel-based data assimilation to optimize routes in real time.
• The approach supports interactive scenario exploration and emissions analytics, enabling precise, safe, and environmentally conscious voyage planning.

SIMROUTE-based routing is a computational framework for dynamic ship weather routing that operationalizes the voyage planning problem as a constrained shortest-path optimization on a high-resolution navigation mesh. This approach is distinguished by the explicit modeling of dynamic vessel speed via empirical wave-resistance formulas and tight integration with real-time or AI-generated sea-state forecasts. Notably, in the SWR-Viz platform, SIMROUTE operates as the pathfinding core, synergized with physics-informed Fourier Neural Operator (FNO) wave forecasts, interactive scenario exploration, emissions analytics, and real-time data assimilation (Hazarika et al., 19 Nov 2025).

1. Problem Formulation and Optimization Framework

SIMROUTE recasts ship routing as a discrete optimization problem over a geospatial mesh. Given a route $r = \{x_0, x_1, ..., x_N\}$, each segment's cost, typically sailing time, is

$$\Delta t_i = \frac{d(x_i, x_{i+1})}{v_{\rm eff}(x_i)},$$

where $d(\cdot, \cdot)$ denotes the great-circle distance and $v_{\rm eff}(x_i)$ is the local effective speed accounting for wave-induced resistance. The objective functional for route optimization is

$$J[r] = \min_{r}\ \sum_{i=0}^{N-1} \Delta t_i = \min_{r}\ \sum_{i=0}^{N-1} \frac{d(x_i, x_{i+1})}{v_{\rm eff}(x_i)}.$$

SIMROUTE employs the A* search algorithm, using a heuristic $h(x)$—commonly the straight-line time at nominal speed—to guide traversal through the navigation graph. This structure supports explicit incorporation of oceanographic constraints and dynamic vessel performance penalties (Hazarika et al., 19 Nov 2025).

2. Vessel Dynamics, Wave-Resistance, and Safety Constraints

Vessel response to sea state is modeled via empirical wave-resistance relationships, parameterized by local wave height $H(x_i)$, wave encounter angle $\psi(x_i)$, and vessel-specific constants (e.g., length $L$, beam $B$, deadweight $D$): $$R_{\rm wave}(x_i) = \alpha H(x_i)^\beta \cos(\psi(x_i)),$$ with effective speed given by

$$v_{\rm eff}(x_i) = v_{\rm nom} [1 - C_R R_{\rm wave}(x_i)].$$

Here, $C_R$ is a vessel-specific constant, with the constraint $0 < v_{\rm eff}(x_i) \le v_{\rm nom}$ ensuring feasibility.

Safety and sea-state limits are encoded as hard constraints: $$H(x_i) \le H_{\max}, \quad P_{\rm roll}(x_i) = \Pr\{\text{parametric rolling}\} \le P_{\rm safe}.$$ Nodes violating these are either pruned from the mesh or assigned infinite traversal cost, strictly enforcing navigational safety (Hazarika et al., 19 Nov 2025).

3. Integration with Physics-Informed FNO Wave Forecasting

The operational efficacy of SIMROUTE-based routing in SWR-Viz is enhanced by real-time querying of a physics-informed FNO wave field, which supplies high-resolution near-term forecasts for significant wave height $H(t,x)$, direction $\psi(t,x)$, and period $T_p(t,x)$. The FNO rollout is agnostic to grid and resolution, enabling evaluation of $H(x_i)$ at any mesh node without retraining.

Forecast uncertainty is mitigated through periodic assimilation of sparse ocean observations. The assimilation technique applies a kernel-based correction: $$H^{\text{new}}(x) = H^{\text{forecast}}(x) + \sum_{j=1}^M w_j \phi(\|x - y_j\|),$$ where the weights $w_j$ ensure consistency with observations at locations $y_j$, and $\phi$ is an RBF kernel. This method preserves the spectral energy of the FNO and is computationally efficient and mesh-agnostic.

4. Practical Implementation in SWR-Viz

SWR-Viz operationalizes SIMROUTE routing within an AI-assisted, interactive analytics platform. Key workflow components include:

• Data Assimilation: After FNO prediction, buoy or satellite wave-height data are assimilated using the aforementioned RBF kernel, enabling rapid adjustment of wave fields while maintaining spectral fidelity.
• Interactive What-If Exploration: Users can designate spatial avoidance zones using lasso or rectangle selection, which translates to region-specific cost augmentations or node exclusions in the navigation mesh. The system computes multiple alternative "digital rehearsal" routes within seconds, facilitating direct comparison of travel time, fuel, emissions, and safety metrics.
• Emissions Analytics: For each computed route $r$, the engine load and wave-induced power requirements are sampled per segment and processed via the STEAM2 emissions model. For pollutant species $p$ (e.g., $$\mathrm{CO}_2, \mathrm{NO}_x, \mathrm{SO}_x, \mathrm{PM}$$), total emitted mass is computed as

$$E_p(r) = \sum_{i=0}^{N-1} \dot m_p(v_{\rm eff}(x_i), R_{\rm wave}(x_i)) \Delta t_i,$$

with results integrated into the route analytics pane (Hazarika et al., 19 Nov 2025).

5. Performance Metrics and Comparative Results

Evaluation of SWR-Viz and SIMROUTE-based routing demonstrates several key performance attributes:

• Forecast Stability: Anomaly correlation for significant wave height remains above 0.5 for approximately 33 hours, while wave direction cosine similarity remains robust over a 48-hour horizon.
• Spectral Consistency: The FNO's forecast retains spectral energy distribution across the first 100 wavenumbers, avoiding high-frequency blow-up observed in less regularized models.
• Operational Accuracy with Data Assimilation: Incorporating 20% observational coverage every 6–9 hours reduces single-shot rollout RMSE, matching reanalysis-equivalent levels.

For a Tokyo–Hakodate route at 24 knots, routing based on the FNO forecast with 20% assimilation yields nearly identical metrics to reanalysis:

• WAVERYS (reanalysis): 19.69 h, 57.30 mT fuel, 150.14 mT CO₂, safety 55%
• FNO single-shot: 19.76 h, 58.97 mT fuel, 153.10 mT CO₂, safety 17.1%
• FNO+DA: 19.70 h, 57.37 mT fuel, 151.01 mT CO₂, safety 52.1%

Emission reduction analysis indicates voyage-level savings are modest (few percent), but segment-level reductions of 8–10% are achievable via interactive analytics (Hazarika et al., 19 Nov 2025).

6. Algorithmic Extensions in SWR-Viz

SIMROUTE’s standard A* implementation is augmented in SWR-Viz by four principal extensions:

• Integration with a Fourier Neural Operator for on-demand, resolution-independent wave predictions.
• Mesh-agnostic, kernel-based data assimilation for rapid ingestion of sparse observational data.
• User-driven “digital rehearsal” workflow for constraint injection and rapid alternate route computation.
• Real-time emissions and safety analytics synchronized with routing, all within a visual analytics interface.

These enhancements underpin a comprehensive decision-support pipeline marrying physics-based maritime operation models, machine learning forecasts, and interactive human-in-the-loop exploration (Hazarika et al., 19 Nov 2025).

7. Significance and Broader Implications

The SIMROUTE-based routing approach, particularly as instantiated in the SWR-Viz framework, constitutes an operationally viable methodology for efficient, safe, and environmentally conscious voyage planning. Its modular synthesis of dynamic environmental modeling, high-performance graph search, and interactive analytics represents a substantive advance in ship-weather routing technology. More broadly, the demonstrated workflow illustrates a generalizable paradigm by which lightweight AI forecasting models, data assimilation, and human-centered visual insights can be composed into practical decision-support systems for complex geospatial and environmental domains (Hazarika et al., 19 Nov 2025).