💻 computer science

Geometry-Aware Surrogate for Real-Time Hydrodynamics Estimation of Autonomous Ground Vehicles in Amphibious Environments

This paper introduces a real-time, geometry-aware neural network surrogate trained on high-fidelity CFD data that accurately predicts hydrodynamic forces for autonomous ground vehicles in amphibious environments, enabling the embedding of physically grounded dynamics into simulation and planning loops.

Original authors: Ammar Waheed, Luke Gallantree, Zohaib Hasnain

Published 2026-05-19

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Ammar Waheed, Luke Gallantree, Zohaib Hasnain

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to teach a robot car how to drive through a flooded street. To do this safely, the car needs to know exactly how the water is pushing against it. Is the water slowing it down? Is it lifting the car up? Is it pushing it sideways?

The problem is that figuring out these water forces is like trying to predict the weather: it's incredibly complex.

The Old Ways: Too Slow or Too Simple
Currently, engineers have two bad options:

The Supercomputer Method: They use high-powered simulations (like a digital wind tunnel for water) to calculate the forces. This is very accurate, but it takes hours to simulate just a few seconds of driving. It's like trying to solve a math problem by hand when you need the answer right now to avoid a crash.
The "Game Engine" Method: They use simple rules, like "water always pushes back with 10% force." This is instant, but it's wrong. It doesn't account for the shape of the car or how deep the water is. It's like guessing the weight of a suitcase just by looking at its color.

The New Solution: The "Smart Water Calculator"
This paper introduces a new "surrogate" model. Think of this as a super-smart student who has spent months studying millions of hours of those slow, perfect supercomputer simulations. Now, this student can answer the question "How hard is the water pushing?" in less than one millisecond (faster than a human eye blink).

Here is how it works, using some creative analogies:

1. The "Lego Car" Approach

Most old models treated the car as one giant, solid block. They guessed the total push on the whole thing.
This new model treats the car like a Lego set. It breaks the vehicle down into many small, individual pieces (the front bumper, the wheels, the sides, the bottom).

Why? Because water pushes on the front wheel differently than it pushes on the back bumper. By calculating the force on each Lego piece separately and then adding them up, the model gets a much clearer picture of the total force.

2. The "Underwater Map" (SDF)

To know how much water is hitting each Lego piece, the model uses a digital "underwater map" called a Signed Distance Field (SDF).

The Analogy: Imagine the car is a submarine. The SDF is a 3D grid that knows exactly where the metal of the car is and where the empty air is. When the water level rises, the model checks this map to see exactly which Lego pieces are underwater and how deep they are. It doesn't just guess; it measures the exact geometry.

3. The "Student's Homework" (Training)

The model was trained entirely on data from two very different vehicles: a small, boxy robot (the Husky) and a larger, rugged military-style vehicle (the Warthog).

The Magic: The model didn't just memorize the answers. It learned the rules of how water interacts with shapes. Because it learned the rules, it can handle new situations it hasn't seen before.

4. The "Real-World Test"

The researchers didn't just trust the computer. They took the real Warthog vehicle and drove it through a water channel at different speeds and depths. They used high-speed cameras to track the car's movement perfectly.

The Result: Even though the model was never explicitly told the laws of physics (like "drag increases with the square of speed"), it discovered them on its own.
- When they plotted the data, the drag force followed the perfect curve of physics ( $Force \propto Speed^2$ ).
- The lifting force (buoyancy) increased perfectly in line with how deep the water was.
- It's as if the student took a test without studying the textbook, yet got every answer right because they truly understood the subject.

Why This Matters

This technology acts as a bridge. It allows engineers to put a "physics-accurate" water simulator inside a real-time control loop.

Before: Engineers had to choose between a slow, accurate simulation (useless for real-time driving) or a fast, inaccurate one (dangerous for real-world driving).
Now: They have a tool that is both fast enough for real-time and accurate enough to trust.

In short, this paper presents a way to give autonomous vehicles a "sixth sense" for water, allowing them to navigate floods and shallow rivers safely without needing a supercomputer on board to do the math.

Technical Summary: Geometry-Aware Surrogate for Real-Time Hydrodynamics Estimation

Problem Statement
Autonomous ground vehicles (AGVs) operating in amphibious environments, such as shallow water or flood-prone terrains, require dynamic models that accurately account for hydrodynamic forces (drag, buoyancy, added mass). Current simulation and planning tools face a dichotomy: high-fidelity Computational Fluid Dynamics (CFD) solvers provide physical accuracy but are computationally prohibitive for real-time use (often requiring hours for seconds of simulation), while simplified models (e.g., fixed drag coefficients or primitive buoyancy) run in real-time but lack the fidelity to capture geometry-dependent interactions, leading to significant sim-to-real gaps. Existing data-driven approaches often treat the vehicle as a monolithic body, failing to resolve how loading varies across specific geometric surfaces as submersion depth and flow direction change.

Methodology
The authors propose a per-surface neural network surrogate trained entirely on high-fidelity CFD data to predict spatially distributed hydrodynamic forces at real-time rates.

Data Generation: High-fidelity CFD simulations were conducted on two geometrically distinct platforms (Clearpath Husky A200 and Clearpath Warthog) using a Volume of Fluid (VOF) formulation with a fixed-body, moving-fluid strategy. The parameter space varied velocity, flow angle, fluid density, and water depth.
Geometry Representation: The vehicle geometry is decomposed into semantically meaningful surface patches (e.g., front, rear, sides, wheels, underbody). A Signed Distance Field (SDF) is precomputed from the vehicle mesh to calculate precise submergence metrics (submerged fraction and normalized mean depth) for each patch based on the water level.
Neural Network Architecture: The model is a Multi-Layer Perceptron (MLP) with shared weights across all surface patches.
- Inputs: Global features (velocity, density, depth, dimensionless numbers like Froude and Reynolds) and per-surface features (semantic type, centroid, normal, area, and dynamic submergence metrics).
- Outputs: Three-component hydrodynamic forces ( $F_x, F_y, F_z$ ) for each surface patch, normalized by fluid density to encourage generalization across different fluids.
Loss Function: The training objective combines a hybrid per-surface loss (MSE and relative error), a net-force consistency loss (ensuring the sum of surface forces matches the total CFD force), and a physics-violation penalty (penalizing forces on dry surfaces).
Validation: The model was validated experimentally using a full-scale Warthog vehicle in a water channel. Motion capture data provided kinematic inputs (velocity and water level), and the model's predictions were tested against established hydrodynamic scaling laws rather than direct force measurements (which are difficult to isolate on a driven vehicle).

Key Contributions

Per-Surface Decomposition: Unlike previous surrogates that predict a single aggregate force vector, this model resolves forces at the individual surface patch level. This allows the model to capture how specific body regions contribute to net load as a function of depth and flow direction.
Cross-Platform Generalization: The model was trained on two distinct vehicle geometries and demonstrated the ability to generalize across scales and shapes without vehicle-specific retraining, utilizing normalized geometric and physics features.
Emergent Physical Consistency: The model was trained solely on CFD data without explicit encoding of physical scaling laws. However, experimental validation showed that the model naturally reproduced fundamental hydrodynamic relationships (quadratic drag scaling and linear buoyancy-depth scaling) that were not part of the training loss.
Real-Time Performance: The surrogate achieves inference times under 0.9 ms per sample on a single CPU core, making it suitable for integration into real-time simulation and control loops.

Results

CFD Accuracy: On held-out CFD data, the surrogate achieved a symmetric Mean Absolute Percentage Error (sMAPE) of approximately 13% for longitudinal force ( $F_x$ ) and 3–12% for vertical force ( $F_z$ ) across both vehicle platforms.
Inference Latency: Median inference latency was 0.826 ms (Husky) and 0.833 ms (Warthog) on an Intel i7-13700HX CPU, with 95th percentile latencies below 0.90 ms.
Experimental Validation:
- Drag Scaling: Predicted drag forces followed a quadratic relationship with speed ( $R^2 \geq 0.97$ ) across different submersion depths.
- Buoyancy Scaling: Predicted vertical forces showed a linear relationship between buoyancy intercepts and water depth ( $R^2 = 0.973$ ).
- Sim-to-Real Transfer: The model successfully transferred from simulation to real-world conditions, reproducing physical laws without explicit programming, confirming the geometry-aware architecture's ability to learn underlying fluid-structure interactions.

Significance and Claims
The paper claims to bridge the gap between physical fidelity and computational speed in amphibious vehicle simulation. By providing a geometry-resolved force estimation at interactive rates, the framework enables the embedding of physically grounded hydrodynamics into simulation and planning pipelines that currently rely on oversimplified models. The authors emphasize that the model's ability to generalize across different vehicle geometries and reproduce emergent physical scaling laws (drag and buoyancy) without explicit constraints demonstrates a robust sim-to-real transfer capability. This approach offers a pathway for improving the reliability of autonomous vehicle behavior in fluid-affected terrains while reducing the need for expensive field testing and repeated CFD simulations. The work is presented as a step toward real-time, physics-consistent control and planning for amphibious autonomy, though the authors note limitations regarding quasi-steady assumptions (lack of history-dependent dynamics) and the rigid-body approximation of the geometry.