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This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Earth observation from satellite sensory data poses challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression has excelled in biophysical parameter estimation tasks from…

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…

Inverse problems in granular flows, such as landslides and debris flows, involve estimating material parameters or boundary conditions based on target runout profile. Traditional high-fidelity simulators for these inverse problems are…

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…

We present a geometric framework for regression on structured high-dimensional data that shifts the analysis from the ambient space to a geometric object capturing the data's intrinsic structure. The method addresses a fundamental challenge…

Inspired by recent work on extended image volumes that lays the ground for randomized probing of extremely large seismic wavefield matrices, we present a memory frugal and computationally efficient inversion methodology that uses techniques…

Acquisition cost is a crucial bottleneck for seismic workflows, and low-rank formulations for data interpolation allow practitioners to `fill in' data volumes from critically subsampled data acquired in the field. Tremendous size of seismic…

When solving inverse problems in geophysical imaging, deep generative models (DGMs) may be used to enforce the solution to display highly structured spatial patterns which are supported by independent information (e.g. the geological…

To help understand our universe better, researchers and scientists currently run extreme-scale cosmology simulations on leadership supercomputers. However, such simulations can generate large amounts of scientific data, which often result…

Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…

This paper pushes the performance of cloth simulation, making the simulation interactive even for high-resolution garment models while keeping every triangle untangled. The penetration-free guarantee is inspired by the interior point…

Recent advancements in 3D Gaussian Splatting (3DGS) have shifted the focus toward balancing reconstruction fidelity with computational efficiency. In this work, we propose ImprovedGS+, a high-performance, low-level reinvention of the…

Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…

Gravimetric methods are expected to play a decisive role in geophysical modeling of the regional crustal structure applied to geoneutrino studies. GIGJ (GOCE Inversion for Geoneutrinos at JUNO) is a 3D numerical model constituted by ~46 x…

The success of building a high-resolution velocity model using machine learning is hampered by generalization limitations that often limit the success of the approach on field data. This is especially true when relying on neural operators…

We present the numerical methods and GPU-accelerated implementation underlying a Total Lagrangian finite element framework for finite-deformation flexible multibody dynamics, introduced in the companion paper [1]. The framework supports…

We propose a local-to-global representation learning algorithm for 3D point cloud data, which is appropriate to handle various geometric transformations, especially rotation, without explicit data augmentation with respect to the…

Geometric computing with chain complexes allows for the computation of the whole chain of linear spaces and (co)boundary operators generated by a space decomposition into a cell complex. The space decomposition is stored and handled with…

We introduce a Graph Transformer framework that serves as a general inverse physics engine on meshes, demonstrated through the challenging task of reconstructing aerodynamic flow fields from sparse surface measurements. While deep learning…