From Dimensions to Formulas: How Machine Learning help Reverse Engineering

Automating Formula Discovery: Using Machine Learning to Uncover Dimensional Relationships in Product Design

-Raghu Vasanth

In industries with extensive product catalogs, especially those involving standardized parts with slight variations (e.g., furniture components, building materials, or machinery parts), accurately deriving or predicting key product parameters based on dimensional inputs can save time and resources. Traditionally, engineers and designers use predefined formulas for such calculations. However, with thousands of similar products, each with slightly different dimensions, manual formula creation can become impractical. Here’s where machine learning (ML) steps in as a powerful tool to automatically identify relationships between dimensions and desired parameters, revealing insights and even formulas that are otherwise hard to detect.

This blog covers a practical guide on using machine learning to discover or approximate formulas for predicting product parameters based on dimensional data.

Why Use Machine Learning?

For businesses handling thousands of similar parts with varied dimensions, finding a formula that can predict product characteristics such as weight, volume, or structural stability based on dimensions alone can be invaluable. Machine learning can learn from data, generalize patterns, and predict parameters for new products without manual calculations.

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Step-by-Step Guide: Discovering Dimensional Formulas with Machine Learning

1. Data Collection and Preparation

• Data Gathering: Start by collecting dimensions and any other relevant characteristics for each product. Organize the data in a structured format, such as a spreadsheet or CSV file. Each row should represent a product, and each column should correspond to a dimension (like length, width, height) or other physical properties.
• Data Cleaning: Ensure there are no missing values or outliers in the data that could distort the model.
• Feature Engineering: Depending on the product, you may want to create derived features. For instance, aspect ratios, surface areas, or even volume might reveal useful relationships, especially if there are more complex dependencies within the data.

2. Define the Output (Target Parameter)

• Determine the specific parameter you want to predict. It could be a measurable physical attribute (e.g., weight or volume) or a performance characteristic (e.g., load-bearing capacity, strength).
• By clearly defining the target, you help the model focus on the right aspects of the input dimensions.

3. Choosing a Suitable Machine Learning Model

• Linear Regression: Start simple if you suspect a linear relationship between dimensions and the target parameter. Linear regression can help you find relationships like Parameter = a × length + b × width + c × height + d.
• Polynomial Regression: For non-linear relationships, polynomial regression may capture quadratic or cubic relationships between dimensions, which are often seen in physical properties like volume or mass.
• Decision Trees and Random Forests: These models are excellent for non-linear relationships and can reveal which dimensions are most influential in determining the output.
• Neural Networks: If the relationships between dimensions are highly complex, consider neural networks. They excel at handling multi-dimensional data but may require more data and tuning.

4. Training the Model

• Split your dataset into training and test sets (e.g., 80% training and 20% testing). This division allows you to evaluate the model’s performance on unseen data.
• Train the model on the training data by providing the dimensions as input features and the target parameter as the output label.
• Experiment with different model types and configurations to see which one provides the most accurate and consistent predictions.

5. Interpreting the Model

• After training, analyze the model to understand the relationships it has identified:
• Linear Regression: Directly interpretable through coefficients, which indicate the influence of each dimension on the output.
• Decision Trees and Random Forests: Use feature importance scores to identify which dimensions are most influential. This can often reveal patterns that might serve as components of a formula.
• Neural Networks: Use techniques like SHAP values (SHapley Additive exPlanations) to interpret the effect of each dimension on the output. Although neural networks are less interpretable, SHAP values can offer insights into key relationships.

6. Formulate a Formula

• With simpler models, you might derive a clear formula for calculating the parameter based on input dimensions. For example, a linear regression model might yield a formula like:

  Parameter = 2.5 × length + 1.2 × width + 0.8 × height + 5

• For more complex models (like neural networks), the formula may be too intricate for direct human interpretation. In such cases, consider saving the model as a predictive function that can be used as a virtual formula for new data.

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Example Use Case: Predicting Volume Based on Dimensions

Let’s say you have thousands of box-like products with three dimensions: length, width, and height. You want to predict their volume accurately.

1. Data Preparation: Gather length, width, and height for each product.
2. Model Selection: Start with multiple linear regression, as the relationship between volume and dimensions is typically linear (Volume = length × width × height).
3. Training and Interpretation: After training, check if the model's coefficients reflect the expected relationships or if additional features (e.g., volume ratios) improve accuracy.
4. Formula Extraction: If the results align, you now have a direct formula for volume prediction based on dimensional inputs.

Conclusion

Using machine learning to identify formulas based on dimensions is a transformative approach for industries dealing with large product inventories and complex part structures. By following a structured approach, you can leverage ML models to identify, approximate, or even generate formulas that relate dimensions to key parameters, saving time and reducing manual calculations.

Whether you are working with physical measurements or performance metrics, machine learning offers a systematic, data-driven way to streamline formula discovery, making it a powerful tool for design and manufacturing optimization.