arXiv subjects

Lukas Freinberger

Publications and source records attributed to Lukas Freinberger.

3 recordsLinked to original sources

arXiv2026

Adaptive Encoding Strategy for Quantum Annealing in Mixed-Variable Engineering Optimization

Mixed discrete-continuous optimization is central to engineering design, where discrete choices interact with continuous fields. These problems are difficult due to high-dimensional, complex search spaces. To tackle them, Quantum Annealing (QA) is promising, yet its native binary nature supports only discrete variables, making accurate and efficient encodings of continuous quantities a central challenge. Existing approaches either split the coupled problem, mapping discrete decisions to QA while solving continuous fields classically, or use fixed-bit-depth encodings. The former compromises QA's global search advantages; the latter can underrepresent dynamic range or inflate the number of binary variables. We show that simply increasing bit depth can even degrade performance on current QA hardware, underscoring the need for alternative encodings. In response, we introduce an adaptive encoding strategy for continuous variables in QA that enables efficient treatment of coupled mixed-variable problems. We propose an update strategy for the representable ranges of the continuous variables and demonstrate its utility by integrating it into the minimum complementary energy formulation for structural design optimization, which provides a single, coupled constrained problem. We apply a quadratic penalty method where we update the representation of the continuous variables while targeting the full original objective, preserving QA's global search capability. On a published benchmark, the size optimization of a composite rod, our adaptive encoding improves solution quality under a fixed binary variable budget, demonstrating a superior precision-resource trade-off. Since the framework generalizes beyond structural design, it offers practical guidance for encoding continuous variables for QA and indicates that adaptive representations can enhance precision on current hardware.

cs.CE↗

arXiv2025

A Spline-Based Stress Function Approach for the Principle of Minimum Complementary Energy

In computational engineering, ensuring the integrity and safety of structures in fields such as aerospace and civil engineering relies on accurate stress prediction. However, analytical methods are limited to simple test cases, and displacement-based finite element methods (FEMs), while commonly used, require a large number of unknowns to achieve high accuracy; stress-based numerical methods have so far failed to provide a simple and effective alternative. This work aims to develop a novel numerical approach that overcomes these limitations by enabling accurate stress prediction with improved flexibility for complex geometries and boundary conditions and fewer degrees of freedom (DOFs). The proposed method is based on a spline-based stress function formulation for the principle of minimum complementary energy, which we apply to plane, linear elastostatics. The method is first validated against analytical solutions and then tested on two test cases challenging for current state-of-the-art numerical schemes, a bi-layer cantilever with anisotropic material behavior, and a cantilever with a non-prismatic, parabolic-shaped beam geometry. Results demonstrate that our approach, unlike analytical methods, can be easily applied to general geometries and boundary conditions, and achieves stress accuracy comparable to that reported in the literature for displacement-based FEMs, while requiring significantly fewer DOFs. This novel spline-based stress function approach thus provides an efficient and flexible tool for accurate stress prediction, with promising applications in structural analysis and numerical design.

cs.CE↗

arXiv2023

A Formulation of Structural Design Optimization Problems for Quantum Annealing

We present a novel formulation of structural design optimization problems specifically tailored to be solved by quantum annealing (QA). Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where a recently evolving strategy based on quantum mechanical effects is QA. This approach requires the optimization problem to be present, e.g., as a quadratic unconstrained binary optimization (QUBO) model. Thus, we develop a novel formulation of the optimization problem. The latter typically involves an analysis model for the component. Here, we use energy minimization principles that govern the behavior of structures under applied loads. This allows us to state the optimization problem as one overall minimization problem. Next, we map this to a QUBO problem that can be immediately solved by QA. We validate the proposed approach using a size optimization problem of a compound rod under self-weight loading. To this end, we develop strategies to account for the limitations of currently available hardware and find that the presented formulation is suitable for solving structural design optimization problems through QA and, for small-scale problems, already works on today's hardware.

cs.CE↗