Related papers: Stochastic subgrid-scale parameterization for one-…

Graph convolutional networks have been successfully applied in various graph-based tasks. In a typical graph convolutional layer, node features are updated by aggregating neighborhood information. Repeatedly applying graph convolutions can…

Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…

The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…

We address the application of stochastic optimization methods for the simultaneous control of parameter-dependent systems. In particular, we focus on the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro, and on the…

Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…

Numerous early warning systems based on rainfall measurements have been designed over the last decades to forecast the onset of rainfall-induced shallow landslides. However, their use over large areas poses challenges due to uncertainties…

We consider a data-driven formulation of the classical discrete-time stochastic control problem. Our approach exploits the natural structure of many such problems, in which significant portions of the system are uncontrolled. Employing the…

Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow networks, which tend to get stuck in…

Fine resolution estimates of demographic and socioeconomic attributes are crucial for planning and policy development. While several efforts have been made to produce fine-scale gridded population estimates, socioeconomic features are…

Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires…

We study the implicit regularization of mini-batch stochastic gradient descent, when applied to the fundamental problem of least squares regression. We leverage a continuous-time stochastic differential equation having the same moments as…

A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…

We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…

Hydrodynamical simulations are the most accurate way to model structure formation in the universe, but they often involve a large number of astrophysical parameters modeling subgrid physics, in addition to cosmological parameters. This…

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…

Can stochastic gradient methods track a moving target? We study the problem of tracking multidimensional time-varying parameters under noisy observations and possible model misspecification. Gradient-based filters update the time-varying…

State-of-the-art methods for Convolutional Sparse Coding usually employ Fourier-domain solvers in order to speed up the convolution operators. However, this approach is not without shortcomings. For example, Fourier-domain representations…

We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize…