SWR-Viz: AI-Powered Ship Weather Routing

• SWR-Viz is an interactive visual analytics framework integrating physics-informed FNO wave forecasting, RBF-based data assimilation, and SIMROUTE optimization for dynamic maritime routing.
• It achieves a 40% reduction in forecast error by effectively merging sparse observational data with advanced neural operator models and real-time scenario analysis.
• The system’s interactive dashboard enables what-if simulations, detailed emissions tracking, and safety analytics, enhancing operational decision-making in maritime transport.

SWR-Viz is an AI-assisted interactive visual analytics framework designed for ship weather routing. It integrates a physics-informed Fourier Neural Operator (FNO) wave forecast model, robust data assimilation from sparse observations, SIMROUTE-based optimal pathfinding with emissions and safety analytics, and an interactive dashboard for what-if scenario exploration and human-in-the-loop decision support. The framework is tailored to address the operational challenges in maritime transport, particularly those related to forecast latencies, data sparsity, and the need for real-time adaptive routing under dynamically changing ocean conditions. SWR-Viz is evaluated on real-world shipping corridors and demonstrates both forecasting accuracy and practical utility as a decision-support tool (Hazarika et al., 19 Nov 2025).

1. System Architecture

SWR-Viz follows a streaming pipeline architecture composed of four principal components:

1. Fourier Neural Operator (FNO) Wave Forecast Module: Generates data-driven, physics-informed forecasts of ocean state.
2. Data Assimilation Module: Applies Radial Basis Function (RBF)-based corrections using sparse observational data (e.g., buoys, satellites).
3. Routing Engine (SIMROUTE): Implements A* search on a navigation mesh, incorporating vessel model dynamics, wave resistance, emissions, and safety analytics.
4. Interactive Visual Analytics Dashboard: Provides user controls, map visualization, and linked analytics for exploratory scenario assessment.

Data flows as gridded wave fields or vector vessel paths parameterized by each time step. The interface allows users to select initial time/region and configure parameters for forecast generation, data fusion, routing constraints, and analytics visualization.

2. Mathematical Formulations

2.1 Fourier Neural Operator-Based Wave Forecasting

The FNO models the ocean state at time $t$ as a field:

$$u_t(x) = [\mathrm{VHM0},\,\mathrm{VMDR}_x,\,\mathrm{VMDR}_y,\,\mathrm{VTPK}](x) \in \mathbb{R}^4,$$

where $x$ is the spatial coordinate. The FNO learns an operator $\mathcal{G}$ that maps $u_t \rightarrow u_{t+1}$ via a sequence of layers, each combining 2D Fourier transforms with nonlinear activations:

$$v \mapsto \sigma\Bigl(\mathcal{F}^{-1}\{ K(v) \cdot \mathcal{F}(v) \} \Bigr).$$

Stacking $L$ such layers, the FNO outputs are integrated over time using a Predictor–Error–Corrector (PEC) scheme:

$$u_{t+\Delta t} = u_t + \frac{1}{2} \Delta t \bigl[N'(u_t) + N'(u_t + N'(u_t)) \bigr].$$

Training employs two loss components: the masked $L_2$-loss on ocean points and a spectral loss on the first 100 wavenumbers, combined as

$$\mathcal{L} = \mathcal{L}_{\mathrm{ocean}} + \alpha \mathcal{L}_{\mathrm{spec}},$$

with $\alpha \approx 0.1$.

2.2 Data Assimilation with Sparse Observations

Given sparse measurements $\{(x_j,y_j)\}_{j=1}^m$, the ocean forecast $u_t$ is updated via an RBF-corrected adjustment:

$$u_t^{\mathrm{new}}(x) = u_t(x) + \sum_{j=1}^m w_j(x) [y_j - u_t(x_j)],$$

with weights:

$$w_j(x) = \frac{\exp \left( -\|x-x_j\|^2 / \ell^2 \right)}{\sum_{k=1}^m \exp \left( -\|x-x_k\|^2 / \ell^2 \right)},$$

and $\ell$ a typical length-scale (≈20 km). Assimilation is performed every $T_{\mathrm{assim}} \in \{3,6,9,12\}$ hours.

2.3 SIMROUTE Routing Optimization

A ship trajectory is discretized as $\{(x_t,v_t,\theta_t)\}_{t=0}^N$, with $x_t$ the mesh cell, $v_t$ speed, and $\theta_t$ heading. The optimization targets a multi-objective cost over sailing time, fuel/risk costs, and emissions:

$$\min_{\{v_t,\theta_t\}} \sum_{t=0}^{N-1} \underbrace{\Delta t}_{\text{time}} + C_{\mathrm{fuel}}(v_t,\theta_t; H_t) + \lambda\,E(v_t,\theta_t; H_t),$$

subject to vessel dynamics and safety constraints (parametric roll, surf-riding thresholds). Fuel cost and emissions depend on local wave height $H_t$:

$$C_{\mathrm{fuel}} = f_0 v_t^3 (1+\alpha_H H_t^p), \quad E = \gamma_{\mathrm{CO_2}} C_{\mathrm{fuel}} + \cdots$$

with empirically fitted parameters. The A* search algorithm is employed over the discretized mesh.

3. Implementation Characteristics

The FNO is configured with six layers, each preserving 32 Fourier modes and a local channel width of 64, for a total of approximately 2.8 million parameters. Training utilizes 27 years of Copernicus WAVERYS reanalysis (1993–2019) for 3-hourly fields at 0.25° spatial resolution, with validation performed on 2020–2022 data. The optimization uses the Adam optimizer with a learning rate schedule and is executed on an NVIDIA A100 GPU.

Data assimilation hyperparameters include $\ell=20\,\mathrm{km}$ and a default update interval of $T_{\mathrm{assim}}=6$ h, assimilating up to 20% spatial data coverage. The SIMROUTE engine operates at 5 km mesh resolution, with “Panamax” vessel settings and a cruise speed of 24 knots. Emissions are quantified with STEAM2 factors for CO$_2$, NO$_x$, SO$_x$, and particulate matter. All system modules are containerized for deployment, with the interactive dashboard developed in Plotly Dash (Python) and RESTful communication.

Autoregressive forecasts are rolled out at 3-hour intervals; data assimilation draws remote or on-board sensor data at each assimilation step.

4. Interactive Visual Analytics and User Interfaces

SWR-Viz’s user interface is organized into several core panels:

• Sea Surface Control Panel: Date/time selector, forecast horizon (3–48 h), grid resolution, assimilation controls.
• Ship Routing Control Panel: Origin/destination, vessel type, cruise speed, and wave-resistance presets.
• Main Map View: Overlays wave height (colormap), direction glyphs, optimized versus baseline routes, safety hot-spots, and a timeline slider.
• Route Analytics Panel: Stacked bar charts of segment-wise emissions, engine power time series, and summary tables for voyage statistics.
• Digital Rehearsal Tab: Enables freeform avoidance zone definition via lasso/rectangle tools, recomputation of up to five alternate routes, and side-by-side analytics for comparative scenario assessment.

Interactive features include what-if scenario editing, emission segment highlighting (selecting a bar highlights the corresponding map segment), linked brushing between time-series and map, and export functionality for routes and tables as CSV/GeoJSON. Visualizations and controls are tightly linked via Dash callbacks, enabling real-time analytic feedback as inputs or scenario constraints are changed.

5. Forecast and Routing Performance Evaluation

5.1 Forecast Skill

• Anomaly Correlation Coefficient (ACC) for significant wave height (VHM0) exceeds 0.5 up to approximately 33 hours lead time, outperforming a persistence baseline (≈12 hours).
• Cosine similarity for mean wave direction (VMDR) remains above 0.8 for 48 hours.
• Spectral energy retention: First 100 wavenumbers remain within 5% error of reanalysis, indicating no unstable growth in high-frequency modes.
• Normalized RMSE: At 24 hours, single-shot forecasts achieve 0.18; assimilation reduces this to 0.11, a ∼40% error reduction.

5.2 Routing Accuracy

A summary of routing results for a Tokyo–Hakodate passage (Jan 2022, 24 knots):

Wave Data	Time (h)	Fuel (mT)	CO₂ (mT)	Safety (%)
WAVERYS (truth)	19.69	57.30	150.14	55.0
Single-Shot	19.76	58.97	153.10	17.1
DA(@3 h,20%)	19.69	57.31	150.20	55.0
DA(@6 h,20%)	19.70	57.37	151.01	52.1

RBF-assimilated forecasts produce routes nearly indistinguishable from those generated with reanalysis wave data (Δ fuel and CO₂ <0.1%). Single-shot forecasts (no assimilation) overestimate fuel by approximately 3% and generate riskier paths. Gulf of Mexico evaluations show similar forecast skill; longer stable weather windows yield up to 2% additional fuel savings.

6. Expert Feedback and Operational Usability

Feedback from maritime operators, navigation officers, and sustainability professionals indicates the following:

• Immediate local forecasts mitigate dependence on delayed external products.
• Interactive digital rehearsal capabilities support rapid, human-in-the-loop rerouting, cited as “game-changing” for operational decision making.
• Segment-specific emission analysis (local savings of 8–10%) provides more actionable KPIs than aggregate voyage averages.
• There is significant interest in integrating SWR-Viz widgets into existing bridge software.

The consensus is that SWR-Viz fulfills operational requirements for real-time, user-driven, and sustainability-oriented ship routing, combining fast AI forecasting, established routing analytics, and interactive visualization in one unified system (Hazarika et al., 19 Nov 2025).