Related papers: Algorithmic regularization with velocity-dependent…
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…
Regularization is a powerful technique for extracting useful information from noisy data. Typically, it is implemented by adding some sort of norm constraint to an objective function and then exactly optimizing the modified objective…
The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but is difficult to implement with high-order numerical methods. The regularized…
We present a new entropy-based moment method for the velocity discretization of kinetic equations. This method is based on a regularization of the optimization problem defining the original entropy-based moment method, and this gives the…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
This paper is devoted to the understanding of regularisation process in the shape optimization approach to the so-called Dirichlet inverse obstacle problem for elliptic operators. More precisely, we study two different regularisations of…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…
We first discuss two-body and chain regularization methods for direct N-body simulations on HARP-2 and GRAPE-6. The former is used for accurate integration of perturbed binaries and hierarchies, whereas the latter deals with strong…
A new algorithm is introduced to integrate the equations of rotational motion. The algorithm is derived within a leapfrog framework and the quantities involved into the integration are mid-step angular momenta and on-step orientational…
Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous…
We present an adaptive regularization algorithm that can be effectively applied to the optimization problem in deep learning framework. Our regularization algorithm aims to take into account the fitness of data to the current state of model…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
Entropy regularized algorithms such as Soft Q-learning and Soft Actor-Critic, recently showed state-of-the-art performance on a number of challenging reinforcement learning (RL) tasks. The regularized formulation modifies the standard RL…
A second order explicit one-step numerical method for the initial value problem of the general ordinary differential equation is proposed. It is obtained by natural modifications of the well-known leapfrog method, which is a second order,…
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…
We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…
In this paper we consider ill-posed inverse problems, both linear and nonlinear, by a heavy ball method in which a strongly convex regularization function is incorporated to detect the feature of the sought solution. We develop ideas on how…
We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…