Related papers: Pattern formation with pde2path -- a tutorial
The production of high-quality 2D animation is highly labor-intensive process, as animators are currently required to draw and color a large number of frames by hand. We present SketchColour, the first sketch-to-colour pipeline for 2D…
We exhibit a set of edges (moves) and 2-cells (relations) making the complex of pant decompositions on a surface a simply connected complex. Our construction, unlike the previous ones, keeps the arguments concerning the structural…
We develop a generalization of the Schwinger boson and Holstein-Primakoff transformations that is applicable to ensembles of $N$ spin $1/2$'s with weak permutational symmetry. These generalized mappings are constructed by introducing two…
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)…
The effects of a surfactant on two-dimensional pattern formation in epitaxial growth are explored theoretically using a simple model, in which an adatom becomes immobile only after overcoming a large energy barrier as it exchanges positions…
Since the PointNet was proposed, deep learning on point cloud has been the concentration of intense 3D research. However, existing point-based methods usually are not adequate to extract the local features and the spatial pattern of a point…
We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through…
We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced…
In this paper, we present a novel deep method to reconstruct a point cloud of an object from a single still image. Prior arts in the field struggle to reconstruct an accurate and scalable 3D model due to either the inefficient and expensive…
Diffusion models generate structure by progressively transforming noise into data, yet the mechanisms underlying this transition remain poorly understood. In this work, we show that pattern formation in trained diffusion models can be…
If a curve in R^3 is closed, then the curvature and the torsion are periodic functions satisfying some additional constraints. We show that these constraints can be naturally formulated in terms of the spectral problem for a 2x2 matrix…
A key problem in the modern study of AI is predicting and understanding emergent capabilities in models during training. Inspired by methods for studying reactions in quantum chemistry, we present the ``2-datapoint reduced density matrix".…
This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends prior works that…
Phase separation can drive spatial organization of multicomponent mixtures. For instance in developing animal embryos, effective phase separation descriptions have been used to account for the spatial organization of different tissue types.…
Functions with jumps and kinks typically arising from parameter dependent or stochastic hyperbolic PDEs are notoriously difficult to approximate. If the jump location in physical space is parameter dependent or random, standard…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic…
Deformation band patterning in single crystals is investigated using a finite strain crystal viscoplasticity model based on the evolution of dislocation densities. In the presence of strong latent hardening and weak rate dependence, the…
Control over the physical properties of materials is ubiquitously required in many fields. One means by which this can be achieved is controlling the internal structure of multi-component materials with an eye to enhancing mechanical…
In this work, we address the problem of 4D facial expressions generation. This is usually addressed by animating a neutral 3D face to reach an expression peak, and then get back to the neutral state. In the real world though, people show…