Related papers: Structured inverse modeling in parabolic diffusion…

Point-based representations have consistently played a vital role in geometric data structures. Most point cloud learning and processing methods typically leverage the unordered and unconstrained nature to represent the underlying geometry…

We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant…

Various substances in the liquid state tend to form droplets. In this paper the shape of such droplets is investigated within the spherical model of a lattice gas. We show that in this case the droplet boundary is always diffusive, as…

Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…

We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…

The surrounding world surprises us by the beauty and variety of complex shapes that emerge from nanometric to macroscopic scales. Natural or manufactured materials (sandstones, sedimentary rocks and cement), colloidal solutions (proteins…

A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…

Synthesizing realistic microstructure images conditioned on processing parameters is crucial for understanding process-structure relationships in materials design. However, this task remains challenging due to limited training micrographs…

Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…

Probabilistic denoising diffusion models (DDMs) have set a new standard for 2D image generation. Extending DDMs for 3D content creation is an active field of research. Here, we propose TetraDiffusion, a diffusion model that operates on a…

Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion…

We present a robust method to find region-level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the…

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…

Seismic full-waveform inversion is a core technology for obtaining high-resolution subsurface model parameters. However, its highly nonlinear characteristics and strong dependence on the initial model often lead to the inversion process…

The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from…

We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…

The design of aerodynamic shapes, such as airfoils, has traditionally required significant computational resources and relied on predefined design parameters, which limit the potential for novel shape synthesis. In this work, we introduce a…

Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of…

In materials science, microstructures and their associated extrinsic properties are critical for engineering advanced structural and functional materials, yet their robust reconstruction and generation remain significant challenges. In this…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…