Related papers: High-dimensional experiments for the downward cont…

The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches. While producing state-of-the-art results, this methodology is…

We consider a class of inverse problems where it is possible to aggregate the results of multiple experiments. This class includes problems where the forward model is the solution operator to linear ODEs or PDEs. The tremendous size of such…

Within the framework of scalar-non-metricity gravity, we introduce a steep potential together with a power-law coupling function and investigate whether the acceleration phases of the universe can be consistently described by this model. In…

Typical geophysical inversion problems are ill-posed, non-linear and non-unique. Sometimes the problem is trans-dimensional, where the number of unknown parameters is one of the unknowns, which makes the inverse problem even more…

Gaussian Processes (GPs) has experienced tremendous success in geoscience in general and for bio-geophysical parameter retrieval in the last years. GPs constitute a solid Bayesian framework to formulate many function approximation problems…

The Einstein Equivalence Principle (EEP) underpins all metric theories of gravity. One of its key aspects is the local position invariance (LPI) of non-gravitational experiments, which is captured by the gravitational red-shift. The iconic…

To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…

Diffusion models have shown strong performances in solving inverse problems through posterior sampling while they suffer from errors during earlier steps. To mitigate this issue, several Decoupled Posterior Sampling methods have been…

Analogue gravity is a research programme that explores analogues of general relativistic gravitational fields within other physical systems, particularly but not exclusively in condensed matter systems, with the aim of gaining new insights…

The detection of gravitational waves by the LIGO-Virgo-KAGRA collaboration has ushered in a new era of observational astronomy, emphasizing the need for rapid and detailed parameter estimation and population-level analyses. Traditional…

An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…

In this lecture I address the issue of possible large distance modification of gravity and its observational consequences. Although, for the illustrative purposes we focus on a particular simple generally-covariant example, our conclusions…

Lagrangian trajectory or particle dispersion models as well as semi-Lagrangian advection schemes require meteorological data such as wind, temperature and geopotential at the exact spatio-temporal locations of the particles that move…

Imputation of missing data in large regions of satellite imagery is necessary when the acquired image has been damaged by shadows due to clouds, or information gaps produced by sensor failure. The general approach for imputation of missing…

Earth observation satellites have been continuously monitoring the earth environment for years at different locations and spectral bands with different modalities. Due to complex satellite sensing conditions (e.g., weather, cloud,…

Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \mid y)$. While posterior sampling is valuable for capturing uncertainty and multi-modality, many classical and practical…

The GRACE mission has been providing valuable new information on time variations in the Earth's gravity field since 2002. In addition, the GRACE Follow-On mission is scheduled to be flown soon after the end of life of the GRACE mission in…

In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem…

Reference systems and frames are crucial for high precision absolute astrometric work, and their foundations must be well-defined. The current frame, the International Celestial Reference Frame, will be discussed: its history, the use of…

With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of…