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Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models…
Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…
Sparse-view synthesis remains a challenging problem due to the difficulty of recovering accurate geometry and appearance from limited observations. While recent advances in 3D Gaussian Splatting (3DGS) have enabled real-time rendering with…
Real-time fluid and aeroacoustic simulation on complex surfaces can have interactive applications - from globe-based weather visualizations to immersive computer games with physically accurate wind and sound. However, conventional…
In this paper, we address the problem of predicting a response variable in the context of both, spatially correlated and high-dimensional data. To reduce the dimensionality of the predictor variables, we apply the sufficient dimension…
While computer science has seen remarkable advancements in foundation models, which remain underexplored in geoscience. Addressing this gap, we introduce a workflow to develop geophysical foundation models, including data preparation, model…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function…
Many real-world dynamical systems can be described as State-Space Models (SSMs). In this formulation, each observation is emitted by a latent state, which follows first-order Markovian dynamics. A Probabilistic Deep SSM (ProDSSM)…
The growing availability of large and complex datasets has increased interest in temporal stochastic processes that can capture stylized facts such as marginal skewness, non-Gaussian tails, long memory, and even non-Markovian dynamics.…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
Simulation-based inference (SBI) enables parameter inference by training neural networks on forward simulations. It is being applied both for intractable likelihoods as well as under time constraints on the posterior sampling. After…
We present an approximate calculation of the full Bayesian posterior probability distribution for the local non-Gaussianity parameter $f_{\text{nl}}$ from observations of cosmic microwave background anisotropies within the framework of…
High accuracy complex computer models, or simulators, require large resources in time and memory to produce realistic results. Statistical emulators are computationally cheap approximations of such simulators. They can be built to replace…
Achieving real-time Simultaneous Localization and Mapping (SLAM) based on 3D Gaussian splatting (3DGS) in large-scale real-world environments remains challenging, as existing methods still struggle to jointly achieve low-latency pose…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
Reconstructing the structural geology and mineral composition of the first few kilometers of the Earth's subsurface from sparse or indirect surface observations remains a long-standing challenge with critical applications in mineral…
Continuous-time approximation of Stochastic Gradient Descent (SGD) is a crucial tool to study its escaping behaviors from stationary points. However, existing stochastic differential equation (SDE) models fail to fully capture these…