⚡ electrical engineering

GrainArtist: A Physics-Informed Multi-Engine Framework for Solid Rocket Propellant Grain Inverse Design

This paper introduces GrainArtist, a physics-informed multi-engine framework that integrates diverse computational methods to rapidly and accurately perform the inverse design of solid rocket propellant grains, achieving high ballistic tracking accuracy across various regimes while efficiently filtering infeasible geometries through analytical safety guards.

Original authors: Mostafa Bheary

Published 2026-09-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Mostafa Bheary

Original paper licensed under CC BY 4.0 (https://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

Solid rocket motors are the workhorses of spaceflight, powering everything from missile interceptors to the upper stages of launch vehicles that carry satellites into orbit. Unlike liquid-fueled engines that can be throttled or shut down, a solid rocket motor is a simple, robust cylinder packed with a single block of energetic material. Once lit, it burns until the fuel is gone, and its entire performance is dictated by the shape of the hole carved through the center of that fuel block. As the fire eats away at the surface of this hole, the area of the burning surface changes, which in turn changes the pressure inside the engine and the amount of thrust it produces. Engineers face a difficult puzzle: if they need a specific pattern of thrust—perhaps a sharp burst to escape the atmosphere followed by a steady push to reach orbit—they must design a hole shape that creates exactly that pattern as it burns away. This is known as inverse design, and it is notoriously difficult because the relationship between the shape and the resulting fire is complex, non-linear, and constrained by strict safety rules. If the shape has sharp, inward-pointing corners, the intense heat and pressure of ignition can cause the fuel to crack and the motor to fail catastrophically.

A research team led by Mostafa Bheary at Beni-Suef University has introduced a new system called GrainArtist to solve this design puzzle. Rather than relying on a single method to guess the right shape, GrainArtist acts as a multi-engine workshop that runs five different design strategies simultaneously. These strategies range from searching through a library of known shapes and using deep learning to predict new ones, to applying strict mathematical formulas and evolving random shapes through computer simulation. Before any of these strategies are allowed to run a full, time-consuming computer simulation of the fire, the system subjects every potential design to a rapid, physics-based safety check. This check, derived from established aerospace safety principles, instantly rejects designs that are too thin, have dangerous sharp corners, or would cause the engine to choke on its own exhaust. By filtering out over 99% of impossible or dangerous ideas before they consume computing power, the system ensures that only viable candidates are tested in detail.

The system was tested against three distinct mission profiles to see how well it could reverse-engineer the correct fuel shape. In one test, it had to create a shape that produced a steadily increasing thrust, known as a progressive burn. In another, it needed a shape that maintained a constant, flat thrust level, typical for air-to-air missiles. The third and most challenging test required a dual-thrust profile: a high-pressure burst at the start followed by a sharp drop to a lower, steady pressure. For the first two scenarios, the system successfully synthesized complex, multi-lobed shapes that matched the target thrust curves with an accuracy exceeding 98%. For the dual-thrust mission, which had stumped previous methods that relied on simple, smooth curves, a specialized analytical engine within the system found a solution in just 7.36 seconds. This solution used a gear-like toothed pattern that burned rapidly at first and then transitioned smoothly into a steady burn, a shape that standard design templates could not produce.

The researchers found that no single design method worked best for every situation. The deep learning approach could generate a shape in less than a second, but it sometimes produced results that were physically impossible or inaccurate. The evolutionary search, which mimics natural selection, was robust but slow, often taking over two minutes to converge on a solution. The analytical engine, which used a specific mathematical formula for the gear-like shape, was the fastest and most accurate for the dual-thrust mission but struggled with the constant-thrust mission. By running all these engines at once and letting a computer judge the best result, the system achieved high accuracy across all test cases. The entire process, from defining the mission requirements to finding the final grain shape, took less than two minutes for complex evolutionary searches and just a few seconds for the analytical solutions.

While the system successfully designs shapes that work in computer simulations, the researchers note that these designs are currently limited to two-dimensional cross-sections. A real rocket motor is a three-dimensional object, and manufacturing a complex shape often requires pulling a solid metal core out of the fuel, a process that demands specific angles to prevent the tool from getting stuck. The current system guarantees that the 2D shape is safe and will not crack, but it does not yet verify if the 3D version can be physically cast or if it can be made using newer additive manufacturing techniques. The author suggests that the next step is to expand the system to handle full three-dimensional motors with multiple fuel segments stacked along the length of the engine. Until then, GrainArtist serves as a powerful screening tool, allowing engineers to explore a vast universe of fuel shapes and identify the most promising candidates before committing to the expensive and dangerous process of building and firing a real rocket motor.

Technical Summary: GrainArtist – A Physics-Informed Multi-Engine Framework for Solid Rocket Propellant Grain Inverse Design

Problem Statement
The inverse design of solid rocket motor (SRM) propellant grains involves determining the initial port geometry ( $\Omega_0$ ) that produces a prescribed chamber pressure or thrust-time history ( $P^*(t)$ or $F^*(t)$ ). This is an inherently ill-posed, high-dimensional, and multi-constraint optimization problem. The nonlinearity arises from the coupled thermodynamic-geometric feedback loop governed by Saint-Robert's burning rate law ( $r = aP_c^n$ ), where the instantaneous burning surface area ( $A_b$ ) dictates the chamber pressure.

Existing methodologies face significant limitations:

Classical Analytical Methods: Constrained to rigid "primitive" templates (e.g., star, BATES, Finocyl), preventing the synthesis of complex dual-thrust or arbitrary profiles.
Stochastic Evolutionary Algorithms: Require excessive computational resources ( $10^4$ – $10^5$ forward evaluations) and suffer from "cold-start" inefficiencies and premature stagnation.
Implicit Topological Methods: Offer topological freedom but often generate unmanufacturable geometries (acute cusps, internal voids) and incur high computational costs ( $O(N^3)$ in 3D).
Deep Learning Approaches: Provide rapid inference but risk "physical hallucinations" (e.g., negative web thicknesses) and lack adherence to strict aerospace safety standards (e.g., NASA SP-8076/8064) when operating without analytical guards.

Furthermore, practical engineering imposes stringent constraints: structural integrity (minimum fillet curvature $r_{fillet} \ge 2.22$ mm to prevent stress singularities), aerodynamic stability (port-to-throat ratio $A_p/A_t \ge 1.50$ to suppress erosive burning), and manufacturability (casing clearance and draft angles).

Methodology: The GrainArtist Framework
GrainArtist addresses these challenges through a physics-informed, multi-engine concurrent architecture. Rather than relying on a single paradigm, it integrates five synthesis engines operating under a unified analytical safety guard layer and evaluated by a high-fidelity GPU-accelerated forward simulator.

Analytical Safety Guard Layer: Before any GPU simulation, candidate geometries are filtered in CPU memory ( $\approx 22.89 \mu s$ per candidate) using five predicates derived from NASA SP-8076 and SP-8064 principles:
- Casing wall separation ( $w_{web} \ge 5.0$ mm).
- Void coalescence prevention.
- Fillet curvature radius ( $r_{fillet} \ge 2.22$ mm).
- Port-to-throat aerodynamic stability ( $A_p/A_t \ge 1.50$ ).
- Volumetric loading constraints ( $V_f/V_c \in [0.35, 0.88]$ ).
  This layer purges 99.05% of infeasible designs, ensuring zero GPU overhead on invalid candidates.
Five Concurrent Synthesis Engines:
- Engine I (Vector Database Retrieval): Retrieves nearest-neighbor seeds from a stratified dataset of 5,000 validated designs across 10 geometric families.
- Engine II (Deep Neural Inverse Brain): A Multi-Layer Perceptron (MLP) maps target trajectories (pressure, slope, impulse) to a 36-dimensional latent Signed Distance Field (SDF) manifold via PCA, providing zero-shot predictions in sub-second time.
- Engine III (Dual-Stage Polar-Gear Optimizer): A specialized closed-form analytical engine using four parameters ( $N_t, r_{in}, d_{tooth}, w_r$ ) to synthesize Boost-Sustain profiles through geometric stage transitions.
- Engine IV (Generative Freeform Sculptor): A continuous 25-degree-of-freedom engine combining harmonic contours with Gaussian jet emitters and satellite voids for non-standard, asymmetric profiles.
- Engine V (Neuro-GA Evolutionary Engine): A surrogate-accelerated genetic algorithm utilizing dual-tier warm-starts (database + neural) and uncertainty-guided $k$ -NN filtering to reduce GPU evaluations.
GPU-Accelerated Forward Simulator:
The framework employs a CuPy-accelerated Euclidean Distance Transform (EDT) solver on a $1000 \times 1000$ grid. It executes forward burnback calculations with Sutton post-burnout gas blowdown in $\approx 0.59$ s. The simulator validates geometries against a composite fitness function balancing pressure tracking accuracy ( $R^2$ , MAE), peak pressure error, burnout duration, and residual sliver mass.
Tournament Arbiter:
An automated multi-metric arbiter evaluates outputs from all five engines and selects the "champion" design based on active-regime accuracy, structural compliance, and computational efficiency.

Key Contributions

Multi-Engine Architecture: The first unified framework integrating database retrieval, neural inversion, analytical optimization, generative sculpting, and evolutionary search.
Polar-Gear Analytical Engine: A deterministic, closed-form solver for dual-thrust (Boost-Sustain) missions, achieving 98.24% accuracy in 7.36 s.
Analytical Safety Guards: A pre-flight filtering system that eliminates 99.05% of infeasible geometries in CPU memory, strictly enforcing NASA-derived structural and aerodynamic constraints.
Surrogate-Accelerated Search: A Neuro-GA engine that reduces full GPU forward evaluations by 77.6% through uncertainty-guided $k$ -NN filtering and MD5 caching.
High-Fidelity Simulation: A GPU-accelerated EDT solver that matches analytical circular-port predictions within 0.28% while executing full simulations in under one second.

Results
The framework was validated across three canonical ballistic regimes:

Progressive Regime (6-Lobe Star): Achieved 98.81% active-regime accuracy (98.74% full-trajectory MAE) with a convergence time of $\approx 111.6$ s.
Neutral Regime (Concentric Rod-and-Tube): Achieved 98.61% active-regime accuracy (93.94% full MAE) in $\approx 118.1$ s.
Dual-Thrust Boost-Sustain Regime (Polar-Gear): Achieved 98.24% active-regime accuracy with deterministic convergence in 7.36 s.

Ablation studies confirmed that the dual-tier warm-start and surrogate filtering reduced total wall-clock runtime by a factor of 4.46x compared to a standard cold-start GA, while maintaining solution quality. The multi-engine tournament demonstrated that no single engine dominates all regimes; the Polar-Gear engine excelled at dual-thrust profiles, while the Neuro-GA engine was superior for neutral profiles.

Significance and Claims
The paper claims that GrainArtist resolves the fundamental trade-off between geometric expressiveness, convergence speed, and strict adherence to aerospace safety heuristics. By treating inverse design as a competitive multi-engine problem, the framework avoids the "primitive trap" of analytical methods and the "cold-start dilemma" of evolutionary algorithms.

The author emphasizes that while the framework guarantees 2D planar casing clearance and fillet curvature (necessary conditions), physical 3D manufacturability (e.g., draft angles for casting) requires downstream validation or additive manufacturing workflows. The system is positioned as a high-fidelity computational screening tool that drastically reduces the design search space prior to physical prototyping, capable of synthesizing mission-tailored geometries for diverse ballistic profiles with active-regime tracking accuracies consistently exceeding 98%.

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