paramOpt

This is the repository to our paper

Using Gradient-based Optimization for Estimating Process Parameters — A Case Study in Ultrasonic Welding
Jonas Ehrhardt, René Heesch, Björn Ludwig, Sophie Arweiler, Moritz Liesegang, Oliver Niggemann
Paper link coming soon

paramOpt is a gradient-based optimization framework for estimating process parameters from desired product quality specifications.

Overview

Finding suitable process parameters is a central challenge in manufacturing. In many production processes, the forward relationship is known only through data:

process parameters → product quality

However, engineers are often interested in the inverse problem:

desired product quality → suitable process parameters

Since this inverse mapping is generally nonlinear, ill-posed, and not available in closed form, paramOpt solves it by combining supervised learning with gradient-based input optimization in a two step algorithm:

(i) Forward model training A neural network is trained on historical process data, such as Design of Experiment DoE studies, to approximate the mapping from process parameters to quality characteristics. (ii) Input optimization The trained neural network is kept fixed. Instead of optimizing the network weights, paramOpt optimizes selected input parameters so that the model prediction matches a desired target quality.

This makes it possible to exploit the learned functional dependency between process parameters and quality characteristics while searching efficiently in continuous parameter spaces.

Method

The repository includes two variants of paramOpt: $paramOpt_{wb}$ and $paramOpt_{bb}$.

$paramOpt_{wb}$: white-box optimization

For locally available models with access to weights and gradients, paramOpt directly backpropagates the prediction error to the input parameters.

$paramOpt_{bb}$: black-box optimization

For models where gradients are not available, for example hosted foundation models, paramOpt approximates gradients using finite differences. This enables input optimization even when model internals are inaccessible.

Case Study: Ultrasonic Welding

We evaluate paramOpt on process parameter estimation for Ultrasonic Welding.The datasets contain six real-world Design of Experiment studies from two welding processes: Continuous Roll Seam Ultrasonic Welding and Torsional Ultrasonic Welding.

Experiments

The paper evaluates paramOpt in five experiments:

1. Forward model fitting: We compare neural network architectures and a tabular foundation model for learning the mapping from process parameters to lap shear strength.

2. Optimizer comparison: We evaluate different gradient-based optimizers for the second step of paramOpt, including SGD, ASGD, SGD with Nesterov momentum, Adam, and RMSprop.

3. Comparison with search baselines: We benchmark paramOpt against uninformed and heuristic search methods, including a genetic algorithm and beam search.

4. White-box vs. black-box optimization: We compare exact gradients from backpropagation with finite-difference gradient approximations.

5. Real-world validation: We validate an optimized parameter set experimentally in a Continuous Roll Seam Ultrasonic Welding setup.

Overall, the results show that gradient-based parameter estimation can converge faster than search-based baselines and can identify non-intuitive parameter combinations that outperform conventionally estimated process parameters.

The following GIFs illustrate the second optimization step of paramOpt (gt = ground truth, rec = estimated parameter values, guess = optimization starting value).

This is an example for finding only one parameter	This is an example for finding two parameters

Citation

If you use this algorithm, make sure to cite our publication:

License

This project is licensed under the MIT License - see the LICENSE file for details.