Differentiable Parametric CAD System Using Neural Network Gradients
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Solution Overview
Problem
Current CAD tools lack the ability to efficiently compute the Jacobian matrix, which is essential for gradient-based optimization of CAD models, as existing methods are either resource-intensive, fail to respect implicit constraints, or are limited to specific operations, making them impractical for general-purpose use.
Innovation Solution
A differentiable parametric CAD system utilizing an artificial neural network that can be applied on top of existing CAD software, allowing the computation of gradients of shape point positions with respect to CAD parameters, thereby enabling gradient-based optimization while maintaining the benefits of mainstream CAD tools.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If finite difference methods are used to approximate the Jacobian matrix, then the computation can be implemented with existing CAD tools, but the computational cost increases significantly and convergence properties deteriorate
Solution Approach 1:
The patent replaces the mechanical finite difference approximation method with a neural network-based automatic differentiation system. The neural network learns the Jacobian matrix computation task, substituting the traditional numerical differentiation approach with a learned model that provides both accuracy and efficiency.
Solution Approach 2:
The patent transforms the static CAD parameter system into a dynamic differentiable system by introducing neural network parameters. The CAD parameters are embedded within a neural network framework that learns optimal parameter transformations, enabling gradient computation while maintaining the original parameter semantics.
2Measurement precision
If automatic differentiation frameworks are used, then exact gradients can be computed, but the framework is restricted to specific operations and difficult to implement as a general-purpose CAD tool
Solution Approach 1:
The patent creates a universal system that combines the precision of automatic differentiation with the versatility of mainstream CAD tools. The neural network framework can handle various CAD operations (extrusion, revolution, lofting, etc.) while maintaining differentiability, making it applicable to general-purpose CAD design tasks.
Solution Approach 2:
The patent introduces a neural network as an intermediary layer between CAD parameters and geometry representation. This intermediary enables gradient flow through operations that would otherwise be non-differentiable, bridging the gap between exact gradient computation and broad CAD operation support.
3Ease of manufacture
If handcrafted parametrisation is used to make Jacobian computation easily implementable, then the computation becomes feasible, but it is time and resource consuming to implement for every new case and not feasible for all problems
Solution Approach 1:
The patent performs preliminary action by training the neural network to learn the Jacobian computation task in advance. Once trained, the network can rapidly compute gradients for new CAD cases without requiring manual Jacobian derivation or implementation, saving significant time and resources for each new design problem.
Solution Approach 2:
The patent creates a learned copy of the Jacobian computation process within the neural network. Instead of implementing the actual mathematical derivation for each CAD operation, the network learns to copy the essential gradient computation patterns, providing fast and accurate results without repetitive manual work.
Data Source
AI summary
A computer-implemented method is proposed in a computer-assisted design (CAD) system. In one embodiment, the method obtains gradients of an objective with respect to CAD parameters of a shape in a coordinate space, where the shape is obtained from the CAD parameters. The obtained gradients may then be used to modify the CAD parameters by applying a gradient descent algorithm aimed to maximise or minimise the objective. The present invention thus proposes a differentiable parametric CAD system comprising an artificial neural network, and which can be applied on top of any CAD software tool.