Related papers: Learning filtered discretization operators: non-in…

Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…

We develop a theoretical analysis for special neural network architectures, termed operator recurrent neural networks, for approximating nonlinear functions whose inputs are linear operators. Such functions commonly arise in solution…

Robotic manipulation in unstructured environments requires the generation of robust and long-horizon trajectory-level policy with conditions of perceptual observations and benefits from the advantages of SE(3)-equivariant diffusion models…

Accurate estimation of the states of a nonlinear dynamical system is crucial for their design, synthesis, and analysis. Particle filters are estimators constructed by simulating trajectories from a sampling distribution and averaging them…

We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…

We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gradient flow, we discretize the dynamics by a fully implicit…

Neural network architectures have been extensively employed in the fair representation learning setting, where the objective is to learn a new representation for a given vector which is independent of sensitive information. Various…

Traditional discriminative computer vision relies predominantly on static projections, mapping input features to outputs in a single computational step. Although efficient, this paradigm lacks the iterative refinement and robustness…

We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…

We consider linear structural equation models with explicitly modelled latent variables. In such models, observed and latent variables solve linear equations including stochastic noise terms. The goal of our work is to identify the direct…

Federated learning (FL) scenarios inherently generate a large communication overhead by frequently transmitting neural network updates between clients and server. To minimize the communication cost, introducing sparsity in conjunction with…

For many of the physical phenomena around us, we have developed sophisticated models explaining their behavior. Nevertheless, inferring specifics from visual observations is challenging due to the high number of causally underlying physical…

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…

Non-linear filtering approaches allow to obtain decompositions of images with respect to a non-classical notion of scale, induced by the choice of a convex, absolutely one-homogeneous regularizer. The associated inverse scale space flow can…

Measurements acquired from distributed physical systems are often sparse and noisy. Therefore, signal processing and system identification tools are required to mitigate noise effects and reconstruct unobserved dynamics from limited sensor…

Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…

We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

Non-blind image deblurring is typically formulated as a linear least-squares problem regularized by natural priors on the corresponding sharp picture's gradients, which can be solved, for example, using a half-quadratic splitting method…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…