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arxiv: 2604.12505 · v1 · submitted 2026-04-14 · 📡 eess.SY · cs.SY

Data-driven Learning of LPV Surrogate Models of Fuel Sloshing

E. Javier Olucha , Valentin Preda , Amritam Das , Roland T\'oth This is my paper

Pith reviewed 2026-05-10 15:06 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords fuel sloshingLPV modelssurrogate modelsspacecraftsmoothed particle hydrodynamicsdata-driven learningzero-gravitymodel-based control
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The pith

LPV surrogate models approximate fuel sloshing and enable 100 times faster simulations for spacecraft control

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a high-fidelity simulator based on smoothed particle hydrodynamics for modeling fuel sloshing in spacecraft tanks. Using data from this simulator, it constructs a linear parameter-varying surrogate model that captures the dynamics with far less computation. The surrogate is shown to support closed-loop simulations of spacecraft maneuvers under zero gravity with two orders of magnitude speedup. This matters for spacecraft engineers who need to test many control strategies and verify performance without prohibitive simulation times.

Core claim

The authors demonstrate that a data-driven LPV state-space model with affine scheduling dependence, learned from input-output trajectories of a Jax-based SPH simulator, accurately represents the fuel sloshing behavior. When used in place of the full model, it permits closed-loop simulations of a rigid body spacecraft with partial fuel load for two different zero-gravity maneuver profiles at speeds increased by a factor of one hundred.

What carries the argument

Linear Parameter-Varying state-space representation with affine dependence on scheduling variables, fitted to simulation data to replace the expensive fluid dynamics computation.

If this is right

  • Simulations of spacecraft with sloshing fuel can be performed much more rapidly for validation campaigns.
  • Model-based control design benefits from the reduced computational cost during optimization and testing.
  • The methodology provides an open-source tool for generating training data for similar surrogate problems.
  • Accuracy is verified specifically for zero-gravity conditions and the tested maneuvers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such surrogates might be updated online using flight data to handle changes in fuel level or tank conditions.
  • The approach could generalize to modeling sloshing in other vehicles or under varying gravity.
  • It opens the possibility of incorporating sloshing effects into real-time control laws for spacecraft.
  • Testing the surrogate against physical experiments would be a next step to confirm its predictive power.

Load-bearing premise

That the nonlinear fuel sloshing dynamics under zero gravity are adequately represented by a linear parameter-varying model whose parameters depend affinely on a small set of scheduling signals.

What would settle it

If a new maneuver causes the surrogate to produce spacecraft responses that differ substantially from those of the high-fidelity simulator in terms of attitude or liquid motion metrics.

Figures

Figures reproduced from arXiv: 2604.12505 by Amritam Das, E. Javier Olucha, Roland T\'oth, Valentin Preda.

Figure 4
Figure 4. Figure 4: In contrast, as shown in Fig. 5, the second manoeuvre profile induces a mass–spring–damper-like [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
read the original abstract

This paper aims to enhance the efficiency of validation and verification campaigns involving fuel sloshing phenomena. Our first contribution is the development of an open-source, high-fidelity and computationally efficient two-dimensional smoothed-particle hydrodynamics-based fuel sloshing simulator that reproduces the dynamics of a spacecraft with a partially filled tank with liquid propellant. Implemented in Python using Jax, the simulator leverages GPU parallelization and supports automatic differentiation, enabling rapid generation of simulation data and system linearizations for general surrogate modelling purposes. Our second contribution is the demonstration of a practical methodology for constructing surrogate models of fuel sloshing from input--output data generated by the simulator, targeting rapid simulation and model-based control applications. The surrogate model employs a Linear Parameter-Varying (LPV) state-space structure with affine dependence on the scheduling variables, providing an accurate yet computationally efficient approximation of the sloshing dynamics. The capabilities of the proposed approach are demonstrated through closed-loop simulations of a rigid spacecraft with a partially filled fuel tank for two manoeuvre profiles under zero-gravity conditions. The identified surrogate enables simulations that are two orders of magnitude faster than the high-fidelity model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper develops an open-source 2D smoothed-particle hydrodynamics (SPH) simulator for fuel sloshing in partially filled spacecraft tanks under zero-gravity conditions, implemented in JAX to leverage GPU parallelization and automatic differentiation. From trajectories generated by this high-fidelity simulator, the authors construct data-driven Linear Parameter-Varying (LPV) state-space surrogate models with affine dependence on scheduling variables (tank acceleration and fill fraction). The surrogate is demonstrated in closed-loop simulations of a rigid spacecraft attitude control system for two specific maneuver profiles, with the claim that it enables simulations two orders of magnitude faster than the original SPH model while remaining sufficiently accurate for validation and verification purposes.

Significance. If the accuracy claims are substantiated with quantitative metrics, the work would provide a practical tool for accelerating V&V campaigns in spacecraft control design involving sloshing dynamics, where high-fidelity fluid simulations are otherwise prohibitive. The open-source JAX-based SPH simulator with GPU support and autodiff is a clear strength, enabling rapid data generation and potential extensions to other surrogate techniques. The LPV approach itself follows standard system-identification practice but targets a challenging nonlinear fluid problem.

major comments (2)
  1. [Abstract] Abstract: the central claim that the LPV surrogate provides an 'accurate yet computationally efficient approximation' and 'enables simulations that are two orders of magnitude faster' is stated without any quantitative accuracy metrics (RMS error, maximum state deviation, or closed-loop performance degradation relative to the high-fidelity SPH model), error bounds, or validation protocol details. This leaves the accuracy-for-closed-loop-use assertion only partially supported and requires explicit numerical evidence in the results section.
  2. [Demonstration section] Demonstration section: the surrogate is fitted exclusively to trajectories from two maneuver profiles. Because the underlying sloshing dynamics are governed by nonlinear free-surface PDEs, the manuscript should demonstrate that the affine scheduling maps remain accurate under extrapolation (e.g., larger-amplitude inputs, different fill fractions, or combined maneuvers) rather than only interpolation within the training set; otherwise the speedup benefit cannot be reliably claimed for general zero-g operations.
minor comments (2)
  1. [Abstract] The abstract would benefit from one or two concrete numerical values (e.g., observed speedup factor and a representative error metric) to give readers an immediate sense of the performance gain.
  2. Notation for the scheduling variables and the precise definition of the affine parameter dependence should be introduced earlier and used consistently when describing the LPV state-space matrices.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment point by point below, indicating where revisions will be made to improve the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the LPV surrogate provides an 'accurate yet computationally efficient approximation' and 'enables simulations that are two orders of magnitude faster' is stated without any quantitative accuracy metrics (RMS error, maximum state deviation, or closed-loop performance degradation relative to the high-fidelity SPH model), error bounds, or validation protocol details. This leaves the accuracy-for-closed-loop-use assertion only partially supported and requires explicit numerical evidence in the results section.

    Authors: We agree that the abstract would be strengthened by explicit quantitative metrics. The results section already includes trajectory comparisons and closed-loop validation against the SPH simulator, but we will revise the abstract to incorporate specific numerical values (e.g., RMS errors on key states, maximum deviations, and the precise speedup factor observed). We will also expand the results section to provide a clearer description of the validation protocol and any error bounds used. revision: yes

  2. Referee: [Demonstration section] Demonstration section: the surrogate is fitted exclusively to trajectories from two maneuver profiles. Because the underlying sloshing dynamics are governed by nonlinear free-surface PDEs, the manuscript should demonstrate that the affine scheduling maps remain accurate under extrapolation (e.g., larger-amplitude inputs, different fill fractions, or combined maneuvers) rather than only interpolation within the training set; otherwise the speedup benefit cannot be reliably claimed for general zero-g operations.

    Authors: The two profiles were chosen to span a range of accelerations and fill fractions, and the affine LPV structure is designed to support variation in the scheduling variables. We acknowledge the referee's point on the need for explicit extrapolation testing. In the revised manuscript we will add results from at least one additional maneuver (with amplitude and combination outside the original training set) to quantify accuracy under extrapolation and to delineate the model's applicability domain. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper first constructs an independent physics-based SPH simulator (open-source, JAX/GPU) and generates input-output trajectories from it. It then fits a standard LPV state-space model with affine scheduling dependence to those trajectories. The reported two-order-of-magnitude speedup follows directly from the reduced order and evaluation cost of the resulting state-space model versus the particle simulator; this is a computational consequence, not a derived prediction that reduces to the fit by construction. No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work are invoked. Validation occurs via closed-loop simulations on the same maneuver profiles, keeping the chain externally falsifiable against the simulator without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central modeling choice is the sufficiency of an LPV structure; no explicit numerical free parameters, new physical entities, or additional axioms are stated. The simulator development itself rests on standard SPH assumptions from the literature.

axioms (1)
  • domain assumption Fuel sloshing dynamics admit an accurate LPV state-space approximation with affine scheduling dependence
    This is the core structural assumption enabling the surrogate construction from simulator data.

pith-pipeline@v0.9.0 · 5508 in / 1263 out tokens · 57422 ms · 2026-05-10T15:06:58.946644+00:00 · methodology

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