Browsing by Author "Sel, Bilgehan"
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- Derivative-Free Meta-Blackbox Optimization on ManifoldSel, Bilgehan (Virginia Tech, 2024-06)Solving a sequence of high-dimensional, nonconvex, but potentially similar optimization problems poses a significant computational challenge in various engineering applications. This thesis presents the first meta-learning framework that leverages the shared structure among sequential tasks to improve the computational efficiency and sample complexity of derivative-free optimization. Based on the observation that most practical high-dimensional functions lie on a latent low-dimensional manifold, which can be further shared among problem instances, the proposed method jointly learns the meta-initialization of a search point and a meta-manifold. This novel approach enables the efficient adaptation of the optimization process to new tasks by exploiting the learned meta-knowledge. Theoretically, the benefit of meta-learning in this challenging setting is established by proving that the proposed method achieves improved convergence rates and reduced sample complexity compared to traditional derivative-free optimization techniques. Empirically, the effectiveness of the proposed algorithm is demonstrated in two high-dimensional reinforcement learning tasks, showcasing its ability to accelerate learning and improve performance across multiple domains. Furthermore, the robustness and generalization capabilities of the meta-learning framework are explored through extensive ablation studies and sensitivity analyses. The thesis highlights the potential of meta-learning in tackling complex optimization problems and opens up new avenues for future research in this area.
- Learning-to-Learn to Guide Random Search: Derivative-Free Meta Blackbox Optimization on ManifoldSel, Bilgehan; Tawaha, Ahmad; Ding, Yuhao; Jia, Ruoxi; Ji, Bo; Lavaei, Javad; Jin, Ming (2023-01-01)Solving a sequence of high-dimensional, nonconvex, but potentially similar optimization problems poses a computational challenge in engineering applications. We propose the first meta-learning framework that leverages the shared structure among sequential tasks to improve the computational efficiency and sample complexity of derivative-free optimization. Based on the observation that most practical high-dimensional functions lie on a latent low-dimensional manifold, which can be further shared among instances, our method jointly learns the meta-initialization of a search point and a meta-manifold. Theoretically, we establish the benefit of meta-learning in this challenging setting. Empirically, we demonstrate the effectiveness of the proposed algorithm in two high-dimensional reinforcement learning tasks.
- Magnetic field mapping of inaccessible regions using physics-informed neural networksCoskun, Umit H.; Sel, Bilgehan; Plaster, Brad (Nature Portfolio, 2022-07-27)A difficult problem concerns the determination of magnetic field components within an experimentally inaccessible region when direct field measurements are not feasible. In this paper, we propose a new method of accessing magnetic field components using non-disruptive magnetic field measurements on a surface enclosing the experimental region. Magnetic field components in the experimental region are predicted by solving a set of partial differential equations (Ampere's law and Gauss' law for magnetism) numerically with the aid of physics-informed neural networks (PINNs). Prediction errors due to noisy magnetic field measurements and small number of magnetic field measurements are regularized by the physics information term in the loss function. We benchmark our model by comparing it with an older method. The new method we present will be of broad interest to experiments requiring precise determination of magnetic field components, such as searches for the neutron electric dipole moment.
- SOS-Based Nonlinear Observer Design for Simultaneous State and Disturbance Estimation Designed for a PMSM ModelSel, Artun; Sel, Bilgehan; Coskun, Umit; Kasnakoglu, Cosku (MDPI, 2022-08-26)In this study, a type of nonlinear observer design is studied for a class of nonlinear systems. For the construction of the nonlinear observer, SOS-based optimization tools are utilized, which for some nonlinear dynamical systems have the advantage of transforming the problem into a more tractable one. The general problem of nonlinear observer design is translated into an SOS polynomial optimization which can be turned into an SDP problem. For a study problem, simultaneous state and disturbance estimation is considered, a cascaded nonlinear observer using a certain parameterization is constructed, and computation techniques are discussed. Cascade nonlinear observer structure is a design strategy that decomposes the problem into its components resulting in dimension reduction. In this paper, SOS-based methods using the cascade design technique are represented, and a simultaneous state and disturbance signal online estimation algorithm is constructed. The method with its smaller components is given in detail, the efficacy of the method is demonstrated by means of numerical simulations performed in MATLAB, and the observer is designed using numerical optimization tools YALMIP, MOSEK, and PENLAB.