Related papers: A stochastic domain decomposition method for time …
A fast method is presented for adaptive moving mesh generation in multi-dimensions using a domain decomposition parabolic Monge-Amp\`ere approach. The domain decomposition procedure employed here is non-iterative and involves splitting the…
We present a fast method for generating random samples according to a variable density Poisson-disc distribution. A minimum threshold distance is used to create a background grid array for keeping track of those points that might affect any…
We present a geometric multigrid solver based on adaptive smoothed aggregation suitable for Discontinuous Galerkin (DG) discretisations. Mesh hierarchies are formed via domain decomposition techniques, and the method is applicable to fully…
Mesh generation remains a key technology in many areas where numerical simulations are required. As numerical algorithms become more efficient and computers become more powerful, the percentage of time devoted to mesh generation becomes…
Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary…
Generating temporal data under conditions is crucial for forecasting, imputation, and generative tasks. Such data often has metadata and partially observed signals that jointly influence the generated values. However, existing methods face…
Accurately modeling time-continuous stochastic processes from irregular observations remains a significant challenge. In this paper, we leverage ideas from generative modeling of image data to push the boundary of time series generation.…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
This paper introduces a novel, robust, and computationally efficient framework for high-quality quadrilateral mesh generation on general two-dimensional domains. The core of the proposed approach is a novel method for computing cross fields…
Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, rather than the…
Modern generative models can be understood as probability transport from a simple base distribution to a target data distribution. Deterministic transport models offer tractable velocity-field parameterizations, whereas stochastic…
A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step.…
Domain decomposition (DD) methods for solving time-dependent problems can be classified by (i) the method of domain decomposition used, (ii) the choice of decomposition operators (exchange of boundary conditions), and (iii) the splitting…
Accurate forecasting of spatiotemporal data remains challenging due to complex spatial dependencies and temporal dynamics. The inherent uncertainty and variability in such data often render deterministic models insufficient, prompting a…
Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems,…
This paper describes a novel method of generating hex-dominant meshes using pre-computed optimal subdivisions of the unit cube in a grid-based approach. Our method addresses geometries that are standard in mechanical engineering and often…
Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or…
Masked generative models have become a strong paradigm for text-to-motion synthesis, but they still treat motion frames too uniformly during masking, attention, and decoding. This is a poor match for motion, where local dynamic complexity…