The work presented in this thesis lies at the intersection of Machine Learning (ML) and control theory.
The first part is dedicated to the design of Deep Neural Network (DNN) architectures with specific numerical properties, inspired by dynamical systems m ...
This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time -dependent partial differential equations (PDEs) on domains with geometric structure. By introducing positional embeddings based on eigenfunctions of the ...
We consider control of dynamical systems through the lens of competitive analysis. Most prior work in this area focuses on minimizing regret, that is, the loss relative to an ideal clairvoyant policy that has noncausal access to past, present, and future d ...
We introduce the elliptical Ornstein-Uhlenbeck (OU) process, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex plane, which are obse ...
The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical systems, it is possible ...
Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...
Tokamak devices aim to magnetically confine a hydrogen plasma at sufficiently high pressure to achieve net energy production from nuclear fusion of light isotopes. Predictive modeling and optimization is crucial for reliable operation of tokamak reactors, ...
We consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled and recentred solution converges to the Cole-Hopf solution of the KPZ equati ...
This letter proposes a parallelizable algorithm for linear-quadratic model predictive control (MPC) problems with state and input constraints. The algorithm itself is based on a parallel MPC scheme that has originally been designed for systems with input c ...
In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...
The optimization of surface finish to improve performance, such as adhesion, friction, wear, fatigue life, or interfacial transport, occurs largely through trial and error, despite significant advancements in the relevant science. There are three central c ...
In real-time optimization, the solution quality depends on the model ability to predict the plant KarushKuhn-Tucker (KKT) conditions. In the case of non-parametric plant-model mismatch, one can add input-affine modifiers to the model cost and constraints a ...
We consider an optimal control problem (OCP) for a partial differential equation (PDE) with random coefficients. The optimal control function is a deterministic, distributed forcing term that minimizes an expected quadratic regularized loss functional. For ...
