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Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through…
The robustness of machine learning models has been questioned by the existence of adversarial examples. We examine the threat of adversarial examples in practical applications that require lightweight models for one-class classification.…
We criticize Colbeck and Renner's (CR's) statement that "any hidden variable model can only be compatible with quantum mechanics if its local part is trivial" [Phys. Rev. Lett. 101, 050403 (2008)]. We note that CR's attempt to divide a…
The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. Here, a novel, implicit, particle-in-cell based…
The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard…
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles…
This contribution presents an integration method based on the Simpson quadrature. The integrator is designed for finite-dimensional nonlinear mechanical systems that derive from variational principles. The action is discretized using…
The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. It…
As we exhaust methods that reduces variance without introducing bias, reducing variance in experiments often requires accepting some bias, using methods like winsorization or surrogate metrics. While this bias-variance tradeoff can be…
Adversarial imitation learning has become a popular framework for imitation in continuous control. Over the years, several variations of its components were proposed to enhance the performance of the learned policies as well as the sample…
We employ a port-Hamiltonian approach to model nonlinear rigid multibody systems subject to both position and velocity constraints. Our formulation accommodates Cartesian and redundant coordinates, respectively, and captures kinematic as…
This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of…
In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…
The linearization of the meteorological equations around a specified reference state, usually applied in NWP to define the linear system of constant-coefficients semi-implicit schemes, is outlined as an unnecessarily restrictive approach…
This paper presents a Lie-Trotter splitting for inertial Langevin equations (Geometric Langevin Algorithm) and analyzes its long-time statistical properties. The splitting is defined as a composition of a variational integrator with an…
This is a companion note to our recent study of the weak convergence properties of constrained emphatic temporal-difference learning (ETD) algorithms from a theoretic perspective. It supplements the latter analysis with simulation results…
Model-based reinforcement learning has attracted much attention due to its high sample efficiency and is expected to be applied to real-world robotic applications. In the real world, as unobservable disturbances can lead to unexpected…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
For a non-linear MIMO feedback system, the robustness against uncertain time-variations in the feedback loop is investigated in an input-output framework. A general sufficient condition in terms of a bound on average rates of time-variation…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…