🤖 machine learning

Reducing Experimental Testing in Space Propulsion Film Cooling Analyses by Pixelwise Generative Image Interpolation

This paper proposes a lightweight, knowledge-informed machine learning approach using pixelwise generative image interpolation to reconstruct high-fidelity film cooling data from sparse experimental measurements, thereby reducing the need for extensive physical testing in space propulsion system development.

Original authors: Adam T. Müller, Philipp J. Teuffel, Konstantin Manassis, Nicolaj C. Stache

Published 2026-05-29

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CC BY 4.0

Original authors: Adam T. Müller, Philipp J. Teuffel, Konstantin Manassis, Nicolaj C. Stache

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

Imagine you are trying to figure out how a specific type of "invisible shield" (a film of coolant) spreads over a hot engine wall to keep it from melting. In the real world, to see this shield, engineers have to build expensive engines, inject dangerous chemicals, and run hundreds of tests. It's like trying to learn how to bake the perfect cake by baking 500 different cakes, tasting each one, and throwing them all away. It's slow, costly, and wasteful.

This paper introduces a clever shortcut using a computer program called PixCOIN. Think of PixCOIN as a super-smart artist who has learned to paint these coolant shields just by looking at a few sketches and a list of instructions.

Here is how it works, broken down into simple concepts:

1. The Problem: Too Many Tests

Engineers need to know how the coolant film behaves when they change things like the angle of the spray, the pressure, or the size of the nozzle. Usually, they have to test every single combination to be sure. If you have 5 settings for 5 different knobs, that's thousands of tests. The authors wanted to see if they could skip most of the tests and still get the full picture.

2. The Solution: The "Pixel-by-Pixel" Artist

Instead of trying to guess the whole picture at once, PixCOIN looks at the image one tiny dot (pixel) at a time.

The Input: You tell the computer two things:
1. The Recipe: The physical settings (e.g., "spray at 15 degrees," "pressure is 10 bar").
2. The Location: "I want to know what the shield looks like at this specific spot on the wall."
The Output: The computer predicts how thick or visible the coolant is at that exact spot.

By doing this for every single spot on the wall, the computer builds a complete, high-quality image of the coolant shield without ever seeing the real thing for that specific setting. It's like having a chef who can taste a soup and tell you exactly how it would taste if you added a pinch more salt, without actually adding the salt.

3. The "Magic Trick": Learning from Less

The researchers tested this by feeding the computer only a fraction of the usual data.

The Experiment: They gave the computer real photos of coolant films from only 30% of the usual test settings.
The Result: The computer filled in the missing 70% of the pictures so well that they looked almost identical to the real ones.
- The "blur" between the real and fake images was less than 8% (very small).
- The "structure" of the image (how the lines and shapes looked) was over 93% similar.

It's like showing a child three different drawings of a cat, and then asking them to draw a cat with a hat. Even though they've never seen a cat with a hat, they can guess what it looks like because they understand the rules of how cats are built.

4. The "Expert Helper" (The Knowledge Extension)

Sometimes, the computer makes small mistakes, like missing a tiny drop of water or getting the edge of the film slightly wrong. This happened because the original photos used to teach the computer had some "blurry" parts.

To fix this, the authors added a smart assistant (using a tool called Grad-CAM).

How it works: Imagine a teacher grading the computer's homework. The teacher looks at the drawing and says, "You got the body right, but you missed the tail."
The Fix: The computer then focuses only on fixing the tail, ignoring the rest of the drawing which is already perfect. This allows the system to correct specific errors based on human expert knowledge without retraining the whole system from scratch.

5. Why This Matters

The main takeaway is that this method allows engineers to skip about 30% of their physical tests and still get a very accurate picture of how their engines will behave.

Real-world impact: They can test more designs faster and cheaper.
The Analogy: Instead of driving a car to every possible destination to map the roads, you use a GPS that learns the road rules from a few trips and then predicts the rest of the map for you.

Summary

The paper claims that by using a lightweight neural network (a type of AI) that looks at images pixel-by-pixel, engineers can generate accurate images of coolant films for new engine settings based on very few real-world tests. They also showed that if the computer makes a mistake in a specific area, human experts can guide it to fix just that spot, making the final result even better. This saves time, money, and resources in building safer, more efficient rocket engines.

Technical Summary: Reducing Experimental Testing in Space Propulsion Film Cooling Analyses by Pixelwise Generative Image Interpolation

1. Problem Statement

Film cooling is a critical thermal management strategy in aerospace propulsion systems, protecting components like combustion chamber walls and nozzles from extreme thermal loads. However, optimizing these systems requires understanding complex interactions between design parameters (injector geometry, coolant properties) and operating conditions. Capturing these interactions experimentally demands extensive physical testing, which is often constrained by time, cost, and resources, particularly when scaling to high-dimensional parameter spaces. Traditional data reduction methods, such as scalar approximations or response surface modeling, struggle to capture local anomalies, discontinuities, and turbulent features inherent in real-world film cooling behavior.

2. Methodology: PixCOIN

The authors propose PixCOIN (Pixel-based Conditional Image Interpolation), a machine learning approach designed to reconstruct image data from sparse experimental measurements. Unlike conventional interpolation or surface modeling, PixCOIN operates directly in pixel space to generate complex, spatially detailed images without relying on geometric assumptions.

Core Architecture

Model Type: A lightweight, fully connected feed-forward neural network (FFNN) with ReLU activations.
Input Features: The network accepts two primary inputs:
1. Physical Operating Parameters ( $p$ ): Such as injection angle, mass flow rate, and pressure.
2. Positional Encoding: Normalized pixel coordinates $(x, y)$ are explicitly integrated as input features. This allows the model to learn spatially dependent patterns directly without using convolutional architectures.
Training Strategy: Instead of training on full images, the dataset is decomposed into pixel-level entries. Each training sample consists of normalized coordinates, associated physical parameters, and the target pixel intensity. This approach prevents overfitting to image-level structures and ensures broad exposure across the dataset.
Loss Function: The model is trained using Mean Squared Error (MSE) loss.
Inference: At inference, physical parameters are fixed to a desired operating point. The network sequentially evaluates all spatial coordinates $(x, y)$ to produce intensity predictions, which are assembled into a 2D image representing the predicted film distribution.

Knowledge-Informed Extension

To address local segmentation errors (e.g., in the Radial Flow Zone), the authors propose an extension integrating expert domain knowledge:

Mechanism: A lightweight CNN classifier detects segmentation faults in synthesized images.
Adaptation: Using Gradient-weighted Class Activation Mapping (Grad-CAM), the system localizes faulty regions. During backpropagation, pixels flagged as faulty are trained using a modified loss function targeting a reference foreground intensity, while other pixels use standard MSE. This enables targeted correction without altering the base network architecture.

3. Experimental Setup and Data

The method was validated using both synthetic data and real-world cold flow experiments conducted at the German Aerospace Center (DLR).

Real Data: Experiments utilized a semi-open combustion chamber with a single coolant injector. High-speed imaging (1024x1024, 50 FPS) captured fluid film behavior. Demineralized water with ink was used as a surrogate for High-Test Peroxide (HTP).
Preprocessing: Images underwent geometric normalization (rectification of the semi-cylindrical chamber), temporal denoising (averaging 10 consecutive frames), and segmentation (background subtraction and adaptive thresholding). All images were downsampled to 120x84 pixels for training.
Parameters: Five key parameters were investigated: manufacturing method, combustion chamber diameter, injector nozzle diameter, injection angle, and pressure. The full dataset comprised 480 unique operating points with 10 images each (4,800 total data points).

4. Key Results

The model was evaluated using quantitative metrics including Root Mean Squared Error (RMSE), Structural Similarity Index (SSIM), Peak Signal-to-Noise Ratio (PSNR), Cosine Similarity, and Perceptual Hashing.

Performance with Reduced Data: The study demonstrated that PixCOIN maintains high accuracy even with significantly reduced experimental data.
- Reducing the number of mass flow settings from 5 to 3 resulted in a marginal RMSE increase of 0.95% and an SSIM decrease of 1.54%.
- Reducing to only 2 settings (minimum and maximum) caused RMSE to rise to ~9.0% and SSIM to drop to ~90.9%, yet performance remained within acceptable limits (RMSE < 10%).
- A random reduction of 30% of operating points yielded RMSE < 8% and SSIM > 93%.
Interpolation vs. Extrapolation: The model performs robustly in interpolation scenarios. However, as expected with data-driven methods, extrapolation to unseen parameter values (e.g., an injection angle of 0° not present in training) resulted in noticeably higher errors and lower image quality compared to interpolated cases.
Synthetic Validation: On synthetic datasets, the model successfully regressed underlying functions, capturing fine details such as single-pixel-wide structures and smooth grayscale gradients.
Computational Efficiency: Training a medium-sized model (~3.5M parameters) took approximately 7 minutes per epoch on an NVIDIA RTX 3500 Ada GPU. Inference for a single image took approximately 6 seconds.

5. Significance and Contributions

The paper claims the following contributions:

Efficient Experimental Reduction: The approach enables a 30% reduction in measurements while preserving high-quality data (RMSE < 8%, SSIM > 93%), offering a scalable solution for experimental campaigns where image-based diagnostics are central.
Pixelwise Interpolation: It provides a general, lightweight method for pixel-wise image interpolation based on positional encoding, capable of generating complex spatial patterns without geometric assumptions.
Expert-Guided Refinement: The proposed knowledge-informed extension allows for the local refinement of generated images based on expert domain knowledge, addressing specific failure modes like segmentation errors in critical flow zones.
Practical Application: The method facilitates more agile exploration of the design space in propulsion development, reducing reliance on costly test campaigns and enabling efficient optimization of coolant injector configurations.

The authors conclude that while challenges remain regarding systematic experimental inconsistencies and segmentation quality, PixCOIN demonstrates robust potential for reducing the experimental burden in space propulsion research while maintaining high-fidelity data representation.