Related papers: Reconstruction from projections using dynamics: No…

Recovering continuous-time dynamics from discrete observations is difficult because local supervision (e.g., pointwise regression targets, derivative approximations, or equation residuals) loses fidelity as the observation interval grows.…

We present an approach to learn the dynamics of multiple objects from image sequences in an unsupervised way. We introduce a probabilistic model that first generate noisy positions for each object through a separate linear state-space…

Computed tomography has propelled scientific advances in fields from biology to materials science. This technology allows for the elucidation of 3-dimensional internal structure by the attenuation of x-rays through an object at different…

We present an algorithm for reconstructing the radiance field of a large-scale scene from a single casually captured video. The task poses two core challenges. First, most existing radiance field reconstruction approaches rely on accurate…

Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…

We present results of the investigations of the statistical properties of a joint density and velocity divergence probability distribution function (PDF) in the mildly non-linear regime. For that purpose we use both perturbation theory…

A theoretically interesting and practically important question in cosmology is the reconstruction of the initial density distribution provided a late-time density field. This is a long-standing question with a revived interest recently,…

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily…

These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…

Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for…

Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…

The evolution of inhomogeneities in a spherical collapse model is studied by expanding the Einstein equation in powers of inverse radial parameter. In the linear regime, the density contrast is obtained for flat, closed and open universes.…

We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…

Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…

This paper deals with non-parametric density estimation on $\bR^2$ from i.i.d observations. It is assumed that after unknown rotation of the coordinate system the coordinates of the observations are independent random variables whose…

Reconstruction of deformable scenes from endoscopic videos is important for many applications such as intraoperative navigation, surgical visual perception, and robotic surgery. It is a foundational requirement for realizing autonomous…

It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…

We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…