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Space Generative AI with Solar Energy Harvesting

Jierui Zhang, Jianhao Huang, Zhanwei Wang, Kaibin Huang

arXiv:2609.01062v1cs.AIcs.NIeess.SP

TL;DR

Solar-powered space generative AI must balance energy-intensive diffusion generation against downlink delivery within short, time-varying orbital energy windows. The paper uses predictable solar-EH dynamics to optimize waiting, transmit power, and generation depth, deriving a low-complexity step-selection policy. Experiments show robust end-to-end gains over static computation- and communication-centric allocations across solar-EH states.

  • Problem

    Space generative AI lacks a joint solution for allocating shared, time-varying solar-EH resources between onboard diffusion generation and result downlink.

  • Method

    The framework first maximizes fixed-step downlink throughput with a waiting-time/transmit-power separation, then derives a Lambert W-based closed-form generation-step policy for joint C^2 optimization.

  • Results

    The proposed joint policy achieves the highest E2E CLIP score across the considered energy range and outperforms fixed computation- and communication-centric schemes, especially in moderate-energy regimes.

  • Takeaways & Limitations

    The policy dynamically shifts toward communication when energy is scarce and toward generation when energy is abundant, while balancing both in moderate-energy conditions.

Abstract

from arXiv · show

Satellites are emerging as promising platforms to extend generative \emph{artificial intelligence} (AI) services to remote areas lacking terrestrial infrastructure. However, deploying space generative AI is fundamentally constrained by the limited, time-varying onboard energy supplied by solar \emph{energy harvesting} (EH). This paper presents a framework for solar-powered space generative AI in which a satellite receives a user prompt, executes a diffusion-based image-generation model, and downlinks the compressed result within a strict time window. We identify the fundamental \emph{computation--communication} (C$^2$) trade-offs governed by the shared harvested-energy budgets. Specifically, increasing the number of generation steps improves intrinsic image quality but depletes energy and time available for downlink transmission, whereas prioritizing communication guarantees reliable delivery but sacrifices semantic quality. To balance these trade-offs and maximize \emph{end-to-end} (E2E) generative performance, we exploit the predictable solar-EH dynamics induced by deterministic orbital motion and develop a joint C$^2$ resource-optimization framework using a tractable two-step approach. First, we characterize the maximum downlink throughput for a fixed generation depth under continuous solar EH. This establishes a separation principle that decouples waiting-time selection from optimal transmit-power control. Next, we formulate a joint C$^2$ utility-maximization problem and derive a closed-form, low-complexity step-selection policy in the dominant constant-power regime. Extensive experiments under realistic orbital dynamics demonstrate that the proposed policy dynamically balances generation quality and transmission reliability. This yields significant E2E performance gains over static computation- and communication-centric baselines across diverse solar-EH states.

I. INTRODUCTION

The paper frames space generative AI as a solar-powered satellite service constrained by a shared, time-varying energy buffer. It develops joint computation–communication optimization to balance diffusion quality, downlink throughput, and timely delivery.

  • Motivation: Satellites can bring generative-AI services to remote areas, but onboard execution is constrained by energy-intensive computation and limited orbital solar harvesting.Harvested power varies with orbital motion, solar geometry, panel orientation, and sunlight–eclipse transitions.
  • Motivation: A short task window forces the satellite to allocate limited harvested energy and time between onboard generation and downlink transmission.The prompt is uploaded to the satellite, which generates a diffusion-model image, compresses it, and transmits the result.
  • Research gap: Increasing diffusion steps can improve image quality but consume resources needed for reliable transmission, creating a coupled computation–communication trade-off.Existing EH communication and satellite computation–communication studies do not fully optimize this generate-and-deliver interaction under solar EH.
  • Method: For fixed generation depth, the framework maximizes downlink throughput under an orbital solar-EH profile by separating waiting-time selection from transmit-power control.The transmit-power policy is derived using the lower convex envelope principle, while deterministic orbital motion enables proactive allocation.
  • Method: The joint optimization decomposes into a throughput subproblem and a reduced step-selection problem, yielding a closed-form, low-complexity rule using the Lambert W function.The rule adapts the generation step to the solar-EH state and system parameters.
  • Results: Experiments under realistic LEO parameters show that the joint policy approaches communication-centric behavior in energy-scarce regimes, computation-centric behavior in energy-abundant regimes, and outperforms both extremes at moderate energy.Across these states, the policy achieves more robust end-to-end generation performance than fixed extreme allocation schemes.

B. Onboard Generative AI Model

The framework uses a latent diffusion model for onboard text-to-image generation, followed by compression and downlink transmission within the task window. Computation time and energy depend on DDIM steps and fixed computation power, while communication uses predictable orbital channels.

  • Generative AI Model: A lightweight prompt is processed onboard by a latent diffusion model that iteratively denoises random latent noise using DDIM steps.The pipeline also includes prompt encoding and remaining operations such as VAE decoding.
  • Computation Model: With fixed computation power, increasing DDIM steps increases computation time and cumulative computation energy.The computation model parameterizes per-step and remaining-operation FLOPs through the computation speed.
  • Operations and Protocol: The satellite performs waiting, image generation, compression, and result transmission within a short task execution window.The prompt uplink is negligible, so the larger generated image is compressed before downlink.
  • Space-ground Communication Model: The delivery capacity is the number of bits transmitted over [a, b], using a power policy determined from predictable orbital and channel evolution.The channel gain depends on time-varying satellite-ground distance and is modeled through Shannon-rate transmission.

D. Performance Metrics

Performance is evaluated through intrinsic generation quality and downlink throughput, which jointly determine received-image quality under a shared solar-EH budget. The resulting computation–communication trade-off motivates throughput optimization with fixed computation before joint optimization.

  • Performance Metrics: The E2E CLIP score measures semantic similarity between the prompt and the image received at the ground device.It depends jointly on generation, compression, and downlink transmission, making direct closed-form characterization difficult.
  • Performance Metrics: The onboard CLIP score measures intrinsic image quality and empirically increases with the number of DDIM steps.It captures semantic similarity before compression and transmission.
  • Performance Metrics: Communication throughput is the total number of bits delivered over the communication window, with higher throughput enabling lower compression.Throughput depends on waiting time, computation time, and the transmit-power policy.
  • C2 Trade-off: Under solar-EH constraints, allocating more energy to generation improves intrinsic quality but leaves less energy for downlink transmission.The reverse allocation favors communication and motivates separate fixed-computation throughput analysis followed by joint C2 optimization.
  • Throughput Optimization: For fixed generation steps, the throughput problem fixes n and therefore fixes the communication-phase duration t2.Direct optimization remains complex because waiting time and continuous transmit power are jointly variable.
  • Optimal Solution Structure: The optimal waiting time is the minimum feasible value, after which transmit power can be optimized independently without reducing throughput.This separation principle reduces complexity by determining waiting time before power control.

C. Optimal Waiting Time and Transmit Power

The optimal communication policy first selects the minimum feasible waiting time and then shapes transmit power from the residual harvested-energy curve. Depending on orbital timing and curve geometry, the resulting policy is constant-power or cosine-power control.

  • General Setup: The closed-form analysis assumes Pcomp t2 < P0 and derives solutions from the harvested-energy curve over the communication interval.The relevant cases depend on task-request time and whether the curve is concave or convex.
  • Task Starts from Orbital Noon: For a task starting at orbital noon, immediate computation is feasible when causality permits; otherwise waiting is chosen to make the computation constraint tight at the window end.The positive-wait case is characterized by the condition P0/ω sin(ωt2) < Pcomp t2.
  • Concave-Energy Case: When the residual harvested-energy curve is concave, its lower convex envelope is affine, yielding constant optimal transmit power.The constant-power policy is illustrated in Fig. 2(a) for representative parameters.
  • Convex-Energy Case: When the residual harvested-energy curve is convex, a supporting-line tangent construction determines the optimal policy.An interior tangency is found by an equal-slope condition and can be solved efficiently by bisection; otherwise the boundary case yields constant power.
  • Task Starts from Orbital Dawn: For orbital-dawn task requests, the computation constraint permits zero waiting, so t1* = 0.The corresponding transmit-power policy is shown in Fig. 2(b).
  • General Case: The general solution extends the two special cases by selecting the appropriate constant-power or tangent-based policy from the orbital energy profile.The construction provides the basic structure for arbitrary task-request times.

3) Optimal Solutions:

The optimal solution is governed by a virtual energy threshold and the curvature of the harvested-energy profile. These conditions determine the minimum feasible start and whether constant-power or tangent-based control applies.

  • Optimal Policy by Curvature: When the energy curve is concave over [a, b], constant power applies.This is the regime associated with the constant-power solution.
  • Optimal Policy by Curvature: When the energy curve is convex over [a, b], the tangent construction applies and yields the corresponding transmit-power solution.The applicable request-time range is 2π/ω − T ≤ treq ≤ 2π/ω − T as stated in the supplied passage.

D. Discussion

τ0 is a virtual threshold identifying when computation can begin without violating energy causality. Positive τ0 requires waiting; nonpositive τ0 permits immediate computation.

  • D. Discussion: τ0 is defined by the endpoint-tightness condition E(τ0+t2) = Pcompt2.It identifies the earliest computation-start threshold implied by the harvested-energy curve.
  • D. Discussion: If τ0 > 0, starting computation before τ0 violates the computation energy-causality constraint.The satellite must wait until τ0.
  • D. Discussion: If τ0 ≤ 0, immediate computation is feasible within the considered task horizon.The threshold lies before the task horizon.

2) Constant-Power Control Versus Cosine-Power Control:

The paper compares constant-power and cosine-power transmission under solar EH, while modeling CLIP-score saturation to restrict feasible DDIM steps and forming a joint C2 utility.

  • Constant-Power Control Versus Cosine-Power Control:: The optimal transmit-power structure is determined by the convexity of the harvested-energy curve E(t).
  • Constant-Power Control Versus Cosine-Power Control:: For convex E(t), the least concave envelope is a chord, yielding constant-power control.
  • Constant-Power Control Versus Cosine-Power Control:: For concave E(t) in the stated regime, the policy is constant initially and then follows cosine-power control Pcomm(t) = P0 cos(ωt).
  • Constant-Power Control Versus Cosine-Power Control:: Constant-power control applies in most cases, covering approximately three quarters of the task-start range.Cosine-power control can track the orbital solar-EH profile.
  • Constant-Power Control Versus Cosine-Power Control:: The framework targets joint C2 utility by balancing onboard CLIP score against communication throughput with coefficient λ.
  • Constant-Power Control Versus Cosine-Power Control:: Because CLIP score gains saturate at additional DDIM steps, the analysis restricts n to an effective set N.

2) Approximation of CLIP Score:

The closed-form analysis characterizes the computation–communication trade-off through a concave utility and reduces joint optimization to step selection, culminating in a Lambert-W policy with constant online complexity.

  • 2) Approximation of CLIP Score:: The joint problem optimizes DDIM steps, waiting time, and transmit-power control under energy causality.
  • 2) Approximation of CLIP Score:: Decomposing by DDIM step reduces the problem to an outer search over n and an inner communication-throughput maximization.
  • 2) Approximation of CLIP Score:: The resulting exhaustive search over N yields an exact solution while separating computation from communication control.
  • 2) Approximation of CLIP Score:: In the constant-power regime, Theorem 2 derives a closed-form DDIM-step solution using the Lambert W function and candidate-set evaluation.
  • 2) Approximation of CLIP Score:: R(n) is concave and decreases monotonically with n because additional generation consumes energy otherwise available for transmission.
  • 2) Approximation of CLIP Score:: The utility U(n) is concave and exhibits unimodal behavior as computational investment improves S(n) but degrades throughput R(n).
  • 2) Approximation of CLIP Score:: The Lambert W branches produce different parameter responses in communication- and computation-dominant power regimes.
  • 2) Approximation of CLIP Score:: The closed-form rule evaluates at most two candidate integers, giving online complexity O(1) versus O(|N|) for exhaustive search.

V. EXPERIMENTAL RESULTS

Experiments evaluate throughput, E2E CLIP score, solver optimality, and joint-control gains under realistic space and solar-EH settings. The proposed strategy achieves the highest throughput across tested panel areas and solar elevation angles.

  • V. EXPERIMENTAL RESULTS: The evaluation averages communication throughput and E2E CLIP score across diverse channel realizations and multiple queries.
  • V. EXPERIMENTAL RESULTS: The solver benchmark compares the closed-form solution with exhaustive search over feasible DDIM steps to verify optimality and complexity reduction.
  • V. EXPERIMENTAL RESULTS: The computation-centric baseline fixes n = nmax, whereas the communication-centric baseline uses the minimal required step n = nmin.
  • V. EXPERIMENTAL RESULTS: The proposed strategy achieves the highest communication throughput across the full tested ranges of panel area A and solar elevation angle β.
  • V. EXPERIMENTAL RESULTS: Throughput grows logarithmically with A and remains stable at low β before degrading as β approaches 90°.The degradation reflects reduced effective solar harvesting area.
  • V. EXPERIMENTAL RESULTS: The persistent gap over baselines supports minimizing the waiting phase and adopting the LCE principle.

C. Evaluation of the Closed-form Solution for (P4)

The closed-form step-selection rule closely matches exhaustive search and adapts generation depth to energy, orbital position, and available time. Across evaluations, joint computation–communication control improves end-to-end quality by balancing generation and reliable downlink transmission.

  • C. Evaluation of the Closed-form Solution for (P4): The pre-rounding closed-form solution closely tracks the exhaustive-search optimum across the considered system settings.This preserves solution accuracy while reducing computational complexity.
  • D. Performance Evaluation: The proposed joint C2 policy achieves the highest E2E CLIP score across the considered energy range.It reduces DDIM steps at low energy and increases generation resources at high energy.
  • D. Performance Evaluation: In moderate-energy regimes, the joint policy outperforms computation-centric and communication-centric extremes by balancing onboard generation and downlink throughput.Neither extreme allocation is optimal in this regime.
  • 1) Comparison with Other Schemes:: Below each scheme’s feasibility threshold, insufficient post-generation energy remains for downlink transmission, causing transmission failure.The threshold depends on the scheme’s resource allocation.
  • 1) Comparison with Other Schemes:: Across orbital angles, the joint policy maintains the highest E2E CLIP score by increasing generation in sunlight and reducing computation during eclipse.The computation-centric baseline can fail during eclipse, while the communication-centric baseline remains quality-limited.
  • 2) Impact of Orbital Position:: Solar EH substantially improves E2E CLIP score in resource-constrained regimes by supporting minimum feasibility, larger DDIM steps, or higher downlink throughput.When initial energy is sufficiently large, solar-EH and no-EH curves converge.
  • 3) Impact of Solar EH:: Discrete DDIM-step selection produces steplike E2E CLIP transitions when harvested energy crosses the threshold for an additional step with reliable transmission.The step increase occurs only after both generation and transmission remain feasible.
  • VI. CONCLUDING REMARKS: The framework identifies adaptive generation depth as most beneficial under moderate energy, where computation- and communication-centric extremes are both suboptimal.The conclusion frames this as task-oriented generative service provisioning under orbital constraints.

APPENDIX

The appendix models solar-energy harvesting from orbital geometry. It relates the satellite’s rotating body frame and Sun vector to instantaneous harvested power through the effective projection area.

  • APPENDIX: The satellite body frame rotates relative to the orbital frame with angular velocity ω, represented by a time-dependent rotation matrix.The rotation matrix maps the orbital-frame geometry into the body frame.
  • APPENDIX: The Sun vector in the satellite body frame is obtained by applying the rotation matrix to the orbital-frame Sun vector.This provides the time-varying solar direction used by the harvesting model.
  • APPENDIX: Instantaneous harvested power is proportional to the solar-panel effective projection area.Only the positive alignment between the panel normal and body-frame Sun vector contributes to harvested power.
  • APPENDIX: The harvested-power expression uses efficiency η, solar parameter γ, area A, and max(n · Sb(t), 0) to enforce nonnegative illumination.The inner product determines the instantaneous geometric projection.

C. Proof of Theorem 2

The proof transforms the optimization into a stationary-point equation and solves it with the Lambert W function. Concavity then restricts the optimal integer generation depth to a finite candidate set.

  • C. Proof of Theorem 2: Introducing u = T − t1 − c1n − c2 converts the optimization over generation depth n into an equivalent single-variable problem.The inverse relation n = a1 − a2u recovers the generation depth from u.
  • C. Proof of Theorem 2: The stationary-point equation is transformed into Lambert W form, with branch selection determined by the sign of ΔE and domain constraints.The principal branch W0 applies for ΔE > 0, while W−1 applies for ΔE < 0.
  • C. Proof of Theorem 2: Because the objective is concave, the optimal integer solution n* is guaranteed to lie in the candidate set S defined in Theorem 2.Substituting the recovered stationary point yields the closed-form result.
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