Related papers: Regularized dynamical parametric approximation
Numerous Optimization Algorithms have a time-varying update rule thanks to, for instance, a changing step size, momentum parameter or, Hessian approximation. In this paper, we apply unrolled or automatic differentiation to a time-varying…
We consider systems of stochastic evolutionary equations of the type $$du=\mathrm{div}\,S(\nabla u)\,dt+\Phi(u)dW_t$$ where $S$ is a non-linear operator, for instance the $p$-Laplacian $$S(\xi)=(1+|\xi|)^{p-2}\xi,\quad \xi\in\mathbb…
We study the problem of inferring sparse time-varying Markov random fields (MRFs) with different discrete and temporal regularizations on the parameters. Due to the intractability of discrete regularization, most approaches for solving this…
Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional-order (non-integer) derivatives into differential models of natural phenomena, such as…
In this paper, we study optimization problems where the cost function contains time-varying parameters that are unmeasurable and evolve according to linear, yet unknown, dynamics. We propose a solution that leverages control theoretic tools…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
Standard quantum mechanics relies on two distinct dynamical principles: unitary evolution and collapse. A mathematically self-contained variational framework is presented that replaces this dualism with a single principle, in which…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
The theory of Wasserstein gradient flows in the space of probability measures has made an enormous progress over the last twenty years. It constitutes a unified and powerful framework in the study of dissipative partial differential…
Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…
We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two…
A regularized optimization problem over a large unstructured graph is studied, where the regularization term is tied to the graph geometry. Typical regularization examples include the total variation and the Laplacian regularizations over…
We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on a bounded spatial domain.…
In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a…
Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…
Nonlinear evolution equation at small x with impact parameter dependence is analyzed numerically. Saturation scales and the radius of expansion in impact parameter are extracted as functions of rapidity. Running coupling is included in this…
In this paper, we propose a direct parallel-in-time (PinT) algorithm for time-dependent problems with first- or second-order derivative. We use a second-order boundary value method as the time integrator that leads to a tridiagonal time…
Estimating equations arise in a wide range of statistical applications, including longitudinal and clustered data analysis, survival analysis, econometrics, and semiparametric inference. In high-dimensional settings, adding…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features…