Continuous and Differentiable Neural Network Representations of the Surfzone Sea-Surface from Lidar Point Clouds
Abstract
Ocean waves are often analyzed via sea-surface observations. Multi-beam scanning lidar enables two-dimensional measurements of the water surface η(x,y) via sequenced point clouds of sea-surface elevation. Point cloud data, however, have to be gridded, interpolated, or mapped for use in wave analysis. We present and test a method for creating a continuous and differentiable (space and time), but grid-free, representation of the sea-surface from time sequenced lidar point clouds. We use a specific neural network architecture, a SIREN, to represent the sea-surface and to train the network on spatiotemporal 60~s of lidar data collected by a gas-electric UAS (drone) hovering over large (4 m), breaking waves in Monterey, California. The trained SIREN allows estimation of the sea-surface and its derivatives at any location and time. SIREN sea-surface representations tend to filter the highest wave number variability (splash-up and sea-spray). SIREN errors are comparable to instrument errors and insensitive to local data density. The reliability and reproducibility of our approach is tested by training two SIRENs independently on the same data. Differences between the two independent SIRENs are comparable to instrument error, but increase in data-poor regions. SIRENs' potential for directional wave analysis is demonstrated by computing spatial and temporal derivatives and by estimating wave velocity from a SIREN-generated space-time slice of the sea-surface.
Related
- Hide&Seek: Learning to Explain in an End-to-End Differentiable Network
- Continuous representations of the meta Hahn algebra and special functions
- A Continuous digit projector from binary representations of numbers onto A2-representation
- Non-Hitchin Borel Anosov representations from surface groups to SL3kℝ
- Optimal Nonparametric Estimation of Phase-Space Representations for Non-Gaussian Continuous Variable Quantum States
BibTeX
@misc{culver2026continuous,
title = {{Continuous and Differentiable Neural Network Representations of the Surfzone Sea-Surface from Lidar Point Clouds}},
author = {David R. Culver and Matthias Morzfeld and Falk Feddersen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27352},
eprint = {2610.27352},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27352},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Continuous and Differentiable Neural Network Representations of the Surfzone Sea-Surface from Lidar Point Clouds
AU - David R. Culver
AU - Matthias Morzfeld
AU - Falk Feddersen
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27352
UR - https://arxiv.org/abs/2610.27352
AB - Ocean waves are often analyzed via sea-surface observations. Multi-beam scanning lidar enables two-dimensional measurements of the water surface η(x,y) via sequenced point clouds of sea-surface elevation. Point cloud data, however, have to be gridded, interpolated, or mapped for use in wave analysis. We present and test a method for creating a continuous and differentiable (space and time), but grid-free, representation of the sea-surface from time sequenced lidar point clouds. We use a specific neural network architecture, a SIREN, to represent the sea-surface and to train the network on spatiotemporal 60~s of lidar data collected by a gas-electric UAS (drone) hovering over large (4 m), breaking waves in Monterey, California. The trained SIREN allows estimation of the sea-surface and its derivatives at any location and time. SIREN sea-surface representations tend to filter the highest wave number variability (splash-up and sea-spray). SIREN errors are comparable to instrument errors and insensitive to local data density. The reliability and reproducibility of our approach is tested by training two SIRENs independently on the same data. Differences between the two independent SIRENs are comparable to instrument error, but increase in data-poor regions. SIRENs' potential for directional wave analysis is demonstrated by computing spatial and temporal derivatives and by estimating wave velocity from a SIREN-generated space-time slice of the sea-surface.
ER -