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When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the optimization…
This paper presents a global trajectory optimization framework for minimizing lap time in autonomous racing under uncertain vehicle dynamics. Optimizing the trajectory over the full racing horizon is computationally expensive, and tracking…
Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…
For time-dependent PDEs, the numerical schemes can be rendered bound-preserving without losing conservation and accuracy, by a post processing procedure of solving a constrained minimization in each time step. Such a constrained…
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
Accelerating the discovery of mechanical properties in combinatorial materials requires autonomous experimentation that accounts for both instrument behavior and experimental cost. Here, an automated nanoindentation (AE-NI) framework is…
Equilibrium-independent dissipativity (EID) is a recently introduced system property which requires a system to be dissipative with respect to any forced equilibrium configuration. This paper is a detailed examination of EID with quadratic…
The performance of deep (reinforcement) learning systems crucially depends on the choice of hyperparameters. Their tuning is notoriously expensive, typically requiring an iterative training process to run for numerous steps to convergence.…
We consider a continuous-time optimization method based on a dynamical system, where a massive particle starting at rest moves in the conservative force field generated by the objective function, without any kind of friction. We formulate a…
We propose an efficient threshold dynamics method for topology optimization for fluids modeled with the Stokes equation. The proposed algorithm is based on minimization of an objective energy function that consists of the dissipation power…
We present a new formulation of the correlated electron-ion dynamics (CEID) scheme, which systematically improves Ehrenfest dynamics by including quantum fluctuations around the mean-field atomic trajectories. We show that the method can…
Computational Fluid Dynamics (CFD) is an important approach for analyzing flow phenomena and predicting engineering-relevant quantities. The governing physics is formulated as partial differential equations(PDEs) and solved numerically on…
Achieving stable and energy-efficient locomotion is essential for humanoid robots to operate continuously in real-world applications. Existing MPC and RL approaches often rely on energy-related metrics embedded within a multi-objective…
A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. As in standard projection operator methods, a set of resolved variables is…
We develop a structure-preserving computational framework for optimal mixing control in incompressible flows. Our approach exactly conserves the continuous system's key invariants (mass and $L^2$-energy), while also maintaining discrete…
In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…
In this paper, the gentlest ascent dynamics (GAD) developed in [W. E and X. Zhou, Nonlinearity, 24 (2011), pp. 1831--1842] is extended to a constrained gentlest ascent dynamics (CGAD) to find constrained saddle points with any specified…
We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…
The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…