Related papers: Computational enhancement of discrete gradient met…
Quantum reservoir computing is a promising paradigm for processing temporal data. So far, the primary focus has been on univariate time series. However, the most relevant and complex real-world data is multidimensional. In this paper, we…
Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…
Reservoir computing (RC) systems can efficiently forecast chaotic time series using nonlinear dynamical properties of an artificial neural network of random connections. The versatility of RC systems has motivated further research on both…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…
Our aim in this note is to extend the semi discrete technique by combine it with the split step method. We apply our new method to the Ait-Sahalia model and propose an explicit and positivity preserving numerical scheme.
We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…
Quantum reservoir computing (QRC) is an emerging paradigm for harnessing the natural dynamics of quantum systems as computational resources that can be used for temporal machine learning tasks. In the current setup, QRC is difficult to deal…
We show that the primal-dual gradient method, also known as the gradient descent ascent method, for solving convex-concave minimax problems can be viewed as an inexact gradient method applied to the primal problem. The gradient, whose exact…
The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient…
We present a new particle filtering algorithm for nonlinear systems in the discrete-time setting. Our algorithm is based on the Stein variational gradient descent (SVGD) framework, which is a general approach to sample from a target…
We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose the…
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 use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
We demonstrate how the dynamical coarse-graining approach can be systematically extended to higher orders in the coupling between system and reservoir. Up to second order in the coupling constant we explicitly show that dynamical…
Quantum machine learning is a rapidly advancing discipline that leverages the features of quantum mechanics to enhance the performance of computational tasks. Quantum reservoir processing, which allows efficient optimization of a single…
We propose a modified non-Markovian quantum jump method to overcome the obstacle of dramatically increased trajectory number in conventional quantum trajectory simulations. In our method the trajectories are classified into the trajectory…