Conditional Normalizing Flow for Gas-Surface Scattering from Thermal to Hypersonic Velocities
Abstract
Accurate aerodynamic modeling of satellites in very low Earth orbit (VLEO) requires gas-surface interaction (GSI) models that capture the full velocity spectrum from thermal to orbital speeds. Atmospheric particles initially strike spacecraft surfaces at hypersonic velocities of 6 000 - 10 000 m/s. Due to surface roughness and complex geometries, especially within air-breathing electric propulsion (ABEP) intake systems, multiple collisions occur, progressively reducing the particle velocities. A recent machine learning framework for deriving scattering kernels from molecular dynamics (MD) simulations has shown promise, but remains limited to high-velocity single impacts and possibly violates fundamental equilibrium principles such as detailed balance. This work extends this machine learning based scattering kernel to cover the complete velocity range using conditional normalizing flows trained with physics-informed constraints, enabling accurate modeling of multi-bounce scenarios in realistic VLEO applications. We train a conditional Real-valued Non-Volume Preserving (cRealNVP) model on expanded molecular dynamics simulations covering velocities from thermal to hypersonic speeds, incorporating a detailed balance loss term. The resulting model demonstrates improved accuracy compared to previous approaches even in the original high-velocity regime, while successfully capturing thermal-velocity scattering. Quantitative assessment shows that thermalization is approximated within acceptable tolerances. This framework provides essential capabilities for accurate ABEP intake optimization and VLEO mission planning while offering a general methodology applicable to broader rarefied gas dynamics problems requiring thermodynamic consistency.
Versions
Related
- Gas-surface scattering and collisional feedback in rarefied hypersonic flow past an inclined flat plate
- Microfacet-based physics-driven framework for single-photon LiDAR rough-surface scattering and detection
- Nonuniform iterative phasing framework and sampling requirements for 3D dynamical inversion from coherent surface scattering imaging
- Andreev Scattering Driven Surface Photogalvanic Effect
- Bottom-Up Surface-Enhanced Raman Scattering for the Detection of Micro-Objects and Globular Analytes
BibTeX
@misc{schutte2026conditional,
title = {{Conditional Normalizing Flow for Gas-Surface Scattering from Thermal to Hypersonic Velocities}},
author = {Miklas Schütte and Stephen Hocker and Hansjörg Lipp and Johannes Roth and Stefanos Fasoulas and Marcel Pfeiffer},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2606.31928},
eprint = {2606.31928},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.31928},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Conditional Normalizing Flow for Gas-Surface Scattering from Thermal to Hypersonic Velocities
AU - Miklas Schütte
AU - Stephen Hocker
AU - Hansjörg Lipp
AU - Johannes Roth
AU - Stefanos Fasoulas
AU - Marcel Pfeiffer
PY - 2026
DA - 2026/07/03
PB - arXiv
DO - 10.48550/arxiv.2606.31928
UR - https://arxiv.org/abs/2606.31928
AB - Accurate aerodynamic modeling of satellites in very low Earth orbit (VLEO) requires gas-surface interaction (GSI) models that capture the full velocity spectrum from thermal to orbital speeds. Atmospheric particles initially strike spacecraft surfaces at hypersonic velocities of 6 000 - 10 000 m/s. Due to surface roughness and complex geometries, especially within air-breathing electric propulsion (ABEP) intake systems, multiple collisions occur, progressively reducing the particle velocities. A recent machine learning framework for deriving scattering kernels from molecular dynamics (MD) simulations has shown promise, but remains limited to high-velocity single impacts and possibly violates fundamental equilibrium principles such as detailed balance. This work extends this machine learning based scattering kernel to cover the complete velocity range using conditional normalizing flows trained with physics-informed constraints, enabling accurate modeling of multi-bounce scenarios in realistic VLEO applications. We train a conditional Real-valued Non-Volume Preserving (cRealNVP) model on expanded molecular dynamics simulations covering velocities from thermal to hypersonic speeds, incorporating a detailed balance loss term. The resulting model demonstrates improved accuracy compared to previous approaches even in the original high-velocity regime, while successfully capturing thermal-velocity scattering. Quantitative assessment shows that thermalization is approximated within acceptable tolerances. This framework provides essential capabilities for accurate ABEP intake optimization and VLEO mission planning while offering a general methodology applicable to broader rarefied gas dynamics problems requiring thermodynamic consistency.
ER -