Device Shape Optimization via BEM and Adjoint Gradients
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Solution Overview
Problem
Existing methods for optimizing device shape, such as in charged particle optics and trapped ion quantum computing, are computationally burdensome and fail to provide highly accurate gradients needed for effective optimization, especially with complex geometric shapes.
Innovation Solution
A system comprising a forward and reverse system, where the forward system uses a boundary element method (BEM) and additional physical rules like Verlet Integration to model device behavior, and the reverse system employs adjoint variable methods for automatic differentiation to calculate gradients and optimize device shape parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional differentiated physics solvers (FEM, FDM) are used to optimize device shape, then the optimization process can be automated, but the gradients obtained are not highly accurate for complex geometric shapes
Solution Approach 1:
The patent changes the mathematical parameters and solution approach by using boundary element method (BEM) formulations with automatic differentiation, transforming the problem from volume-based FEM/FDM to surface-based BEM, which provides both high gradient accuracy and computational efficiency for complex geometries
Solution Approach 2:
The patent substitutes conventional numerical differentiation methods with automatic differentiation technology, replacing manual finite difference approximations with exact analytical derivatives computed through computational graph-based algorithms, thereby achieving both accuracy and efficiency
2Device complexity
If manual shape variation and iterative simulation are used to optimize device shape, then the optimization can be performed with simple tools, but the process is computationally burdensome and incapable of meaningful optimization for complex devices
Solution Approach 1:
The patent transforms the optimization approach by implementing automatic differentiation with BEM, changing from manual iterative simulation to automated gradient-based optimization, which reduces computational burden while handling complex geometries effectively
Solution Approach 2:
The system performs self-optimization by automatically computing gradients and updating design parameters without manual intervention, using the computational model to guide the optimization process autonomously
3Measurement precision
If spline-based differentiated BEM algorithm is used to optimize devices, then the optimization accuracy can be improved, but the method is incompatible with mesh-based design
Solution Approach 1:
The patent creates a universal optimization framework that works with both mesh-based and spline-based representations by implementing automatic differentiation that operates on the computational graph regardless of the underlying geometric representation, thereby achieving both accuracy and compatibility
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables efficient and automated optimization of device shapes, improving performance by iteratively adjusting design parameters to achieve desired performance metrics, such as reduced electrostatic fields or optimized electromagnetic wave interactions.
Implementation Method 1
a model characterizing the device features according to appropriate physical rules. The model may be comprised of a boundary element method (BEM) for partial differential equations, e.g., Laplace, Maxwell, Helmholtz
Implementation Method 2
The forward system may also receive a desired performance (and/or manner to determine performance to evaluate the actual performance)
Implementation Method 3
other numerical approaches for physical equations, e.g., the Verlet Integration Method to solve the nonlinear system of Newton's and Coulomb's law
Implementation Method 4
the Verlet Integration Method to solve the nonlinear system of Newton's and Coulomb's law in conjunction
Implementation Method 5
The reverse system calculates the manner by which the device shape (e.g., 2D or 3D shape) or other device attributes such as an applied voltage has to change in order to achieve the desired performance. The computation performed by the reverse system may be referred to as adjoint variable method or automatic differentiation
Data Source
AI summary
A method includes receiving/processing a device geometry data for a device based on a boundary element method (BEM) to generate a surface physics solution and further to generate a first intermediate data; applying additional underlying physics rule to the generated surface solution and generating a second intermediate data; evaluating performance of the device based on the applying; generating a gradient between the evaluated performance of the device and a desired performance; storing the intermediate data in a memory component; applying the additional underlying physics rule to the generated gradient and to the second intermediate data to generate a gradient of the parameters of the physics rules; processing the gradient of the parameters of the physics rules based on the BEM and the first intermediate data to generate a gradient of the generated surface solution; and updating the device geometry data based on the gradient of the generated surface boundary.