Forward and inverse prediction of micro-channel topographies in abrasive slurry jet machining: a machine learning framework and a graphical web-based tool

Technical Summary: Forward and Inverse Prediction of Micro-Channel Topographies in Abrasive Slurry Jet Machining

Problem Statement
Abrasive Slurry Jet Micro-machining (ASJM) is a strategic process for creating high-aspect-ratio micro-features in hard, brittle, or temperature-sensitive materials without a heat-affected zone. Despite its potential for biomedical devices, MEMS, and aerospace cooling channels, industrial adoption is hindered by the difficulty in predicting and controlling the machined topography. The forward problem (predicting the eroded profile from process parameters) is complicated by high jet turbulence, nonlinear particle erosion dynamics, and a multitude of interdependent operating parameters. The inverse problem (determining the process parameters required to achieve a desired topography) is even more challenging and has rarely been addressed. Existing numerical methods, such as Computational Fluid Dynamics (CFD), offer high fidelity but are computationally expensive and difficult to invert for real-time control. Conversely, previous machine learning (ML) applications in abrasive jet machining have been limited to predicting scalar outputs like surface roughness or depth of cut, rather than full surface profiles.

Methodology
The study employs a data-driven approach using a comprehensive dataset generated from a full factorial design of experiments (DOE) involving 270 unique combinations of operating parameters on AA6061-T6 aluminum. The independent variables were pump pressure ($P$), nozzle traverse speed ($V$), standoff distance ($SOD$), and the number of machining passes ($N$). The target output was a 220-dimensional vector representing the cross-sectional depth profile of the micro-channel.

Four supervised learning models were developed and compared:

1. Polynomial Regression: A parametric baseline using feature expansion to capture nonlinearities.
2. Random Forest (RF): A non-parametric ensemble method enhanced with domain-informed feature engineering (e.g., cumulative erosive potential $P \times N$).
3. Artificial Neural Network (ANN): A fully connected deep learning model designed to map inputs to the full profile vector.
4. Convolutional Neural Network (1D-CNN): A deep learning architecture utilizing convolutional layers to capture local spatial correlations within the profile.

All models were trained on 85% of the data and evaluated on a held-out test set using Mean Squared Error (MSE), Mean Absolute Error (MAE), and the coefficient of determination ($R^2$). The study also investigated model sensitivity to dataset size (25% to 100%) and input noise.

For the inverse problem, an ANN was trained to infer process parameters ($P, SOD, V, N$) from a target geometry. To address the "many-to-one" nature of the inverse problem (where multiple parameter sets can yield the same geometry), the authors employed a "forward-consistency" loss. The predicted parameters were passed through the pre-trained forward ANN to generate a simulated profile, which was then compared to the target geometry. This ensured the inverse model produced physically consistent parameters. A probabilistic inverse framework using Monte-Carlo dropout was also implemented to generate a distribution of feasible solutions rather than a single deterministic guess.

Key Contributions

1. Full-Profile Prediction: This work presents the first ML framework capable of predicting the full vector-valued cross-sectional profile of ASJM-machined micro-channels, moving beyond scalar metrics like roughness or depth.
2. Physics-Informed Feature Engineering: The study incorporates a monotonicity-aware training scheme using engineered features (e.g., $P \times N$, $SOD \times V$, $P/V$) to encode known erosion-rate dependencies, ensuring fair model comparisons.
3. Probabilistic Inverse Design: The authors developed a constraint-aware inverse framework that returns a set of feasible parameter combinations with uncertainty estimates, explicitly addressing the non-uniqueness of the inverse problem.
4. Real-Time Applicability Assessment: The study quantifies inference latency, demonstrating that deep learning surrogates can operate within the millisecond-per-pass budget required for closed-loop process control, unlike traditional CFD simulations.
5. Open-Source Tool: The trained models and experimental dataset are released as a free, browser-based web application, allowing operators without programming experience to utilize the tools.

Results

• Forward Prediction: All models successfully predicted micro-channel profiles with aspect ratios ranging from 0.06 to ~2. The ANN achieved the highest accuracy ($R^2 = 0.817$, MAE = 0.00339 mm), followed closely by the 1D-CNN ($R^2 = 0.807$). Traditional models (Polynomial Regression and RF) performed reasonably well ($R^2 \approx 0.76$) but were less accurate on high-aspect-ratio features.
• Dataset Sensitivity: Performance improved with dataset size, plateauing after 75% of the data was used. The ANN demonstrated the highest robustness, maintaining an $R^2$ of 0.7 even with only 25% of the dataset, whereas the Random Forest model degraded significantly ($R^2 = 0.32$) under the same conditions.
• Noise Robustness: Deep learning models (ANN and CNN) showed high tolerance to input noise, with MAE increasing only mildly (from 3.5 µm to 4.1 µm) under 10% Gaussian noise. In contrast, the polynomial model produced non-physical values under similar noise conditions.
• Inverse Prediction: The inverse ANN successfully predicted process parameters for target geometries. When using only depth and width as inputs, the model achieved an $R^2$ of 0.94 for depth and 0.55 for width. When using the full profile as input, accuracy decreased ($R^2 \approx 0.77$) due to input dimensionality and redundancy. The probabilistic inverse approach successfully identified feasible parameter sets with median absolute depth errors of 0.94 µm.
• Latency: Inference times on a single CPU ranged from 0.22 ms (Polynomial) to ~100 ms (Deep Learning), making them suitable for real-time control, whereas the Random Forest model took ~10.9 seconds per sample, rendering it unsuitable for real-time applications.

Significance
The paper claims that this work bridges the gap between empirical testing and real-time predictive manufacturing in ASJM. By reducing prediction time from hours (CFD) to microseconds/milliseconds, the proposed ML surrogates remove the computational barrier preventing physics-based models from being embedded in closed-loop controllers. The framework enables "one-shot" specification of process parameters for desired geometries, facilitating automated process planning, digital twin integration, and rapid qualification of new material-abrasive combinations without exhaustive design-of-experiments campaigns. The authors position this as a pioneering effort to demonstrate the feasibility of ML for complex, nonlinear material removal patterns in abrasive jet machining, with the trained models and tools made publicly available to accelerate adoption in the field.