Quantum for Topology Optimization

With an initial interest in Topology (which comes from Topological Insulators with some remarkable properties that are topologically protected), I recently searched about Topology Optimization to advance my understanding.

Topology Optimization (TO) has evolved simultaneously with the computing technology available in the market. As a result, it has become a powerful tool to improve system efficiency and performance, reduce fuel consumption, decrease structures' weight and durability, and many more.

A study found that complicated designs and Multiphysics problems require more computational resources for TO in classical computing systems. Therefore, HPC and computational acceleration techniques have been applied together to boost the process of TO in classical computing.

Earlier research shows acceleration techniques were CPU-based, whereas the latest research indicates GPU -based computational acceleration techniques. However, both use classical computing principles and hardware as well. As a result, Topology optimization has been facing computational and mathematical complexities.?

What about changing approaches (algorithms) that follow (emulate) different principles?

A new insight that inspired me is a nested approach based on Quantum-Inspired Optimization (1). This approach establishes a more efficient topology optimization framework. Furthermore, quantum annealing strategies help determine design variable search direction without gradient information, and the quantum evolutionary algorithm ensures diverse search exploration. Topology optimization of continuum structures is the most technically challenging job; however, it's the most beneficial for industries (cost and safety).

A common strategy for this is the design space discretized into finite elements (FE), and loading/boundary conditions are defined accordingly. Optimization focuses on determining the material-containing elements for the structure and void elements representing empty space.

Global Optimization:

Researchers have pointed out that in real-world TO problems finding the globally best solution in the feasible regions is challenging. However, previously many global optimization methods are developed (such as Genetic Algorithms) for Topology Optimization.

These methods' significant limitations are that they require higher computational costs and financial constraints for the given optimization problems. Specifically, when the function evaluation is complete FEA (finite element analysis) in each iteration, it becomes highly challenging.

Quantum-Inspired Algorithm -

In QIEA (Quantum Inspired Evolutionary Algorithm), a solution is represented by a quantum bit (quantum encoding), a pair of probability amplitudes encode 0-1 linear superposition. It allows for a large solution space even with a small population and increases the chances of finding the global optimum.

Additionally, Quantum gates, such as NOT, AND, OR, NAND, Hadamard, and rotation gates, can modify the state of a quantum bit. The quantum gate can be applied to change the quantum bits' state, ultimately helping converge to the optimal solution faster.?

QIEA for Topology Optimization:

Quantum Annealing-

?Quantum annealing is an effective non-gradient optimization technique. It is known for its high performance on various optimization problems. It utilizes quantum fluctuations in frustrated systems or networks to anneal the system down to its minimum cost state (ground state), gradually tuning the quantum fluctuation to zero.

It considers parameters as particles in Quantum systems whereas objective function as the P.E of Hamiltonian. Kinetic energies are then reduced for quantum transitions. With iterative inversions, the objective function reaches the global minima.

According to a previous study on the use cases of QIEA, it was more convenient for manufacturing (ex: Wing rib structure) and had greater rigidity and endurance with critical loads. QIEA-based TO needs lesser iterations, making it affordable with significant exploration capabilities.?

For more engineering use cases:https://www.bosonqpsi.com/post/topology-optimization-powered-by-quantum-for-more-thoughtful-faster-engineering-simulations

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