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Henrik Pedersen

Publications and source records attributed to Henrik Pedersen.

6 recordsLinked to original sources
arXiv2026

Modelling Gas-Phase Reaction Kinetics with Guided Particle Diffusion Sampling

Physics-guided sampling with diffusion priors has recently shown strong performance in solving complex systems of partial differential equations (PDEs) from sparse observations. However, these methods are typically evaluated on benchmark problems that do not fully demonstrate their ability to generate temporally consistent solutions of time-dependent PDEs, often focusing instead on reconstructing a single snapshot. In this work, we apply these methods to gas-phase reaction kinetics problems governed by the advection-reaction-diffusion (ARD) equation, providing a setting that more closely reflects realistic laboratory experiments. We demonstrate that guided sampling can be used to reconstruct full spatiotemporal trajectories, rather than isolated states. Furthermore, we show that these methods generalise to previously unseen parameter regimes, highlighting their potential for real-world applications.

physics.comp-ph↗
arXiv2026

Particle-Guided Diffusion for Gas-Phase Reaction Kinetics

Physics-guided sampling with diffusion model priors has shown promise for solving partial differential equation (PDE) governed problems, but applications to chemically meaningful reaction-transport systems remain limited. We apply diffusion-based guided sampling to gas-phase chemical reactions by training on solutions of the advection-reaction-diffusion (ARD) equation across varying parameters. The method generates physically consistent concentration fields and accurately predicts outlet concentrations, including at unseen parameter values, demonstrating the potential of diffusion models for inference in reactive transport.

physics.chem-ph↗
arXiv2020

DeepMorph: A System for Hiding Bitstrings in Morphable Vector Drawings

We introduce DeepMorph, an information embedding technique for vector drawings. Provided a vector drawing, such as a Scalable Vector Graphics (SVG) file, our method embeds bitstrings in the image by perturbing the drawing primitives (lines, circles, etc.). This results in a morphed image that can be decoded to recover the original bitstring. The use-case is similar to that of the well-known QR code, but our solution provides creatives with artistic freedom to transfer digital information via drawings of their own design. The method comprises two neural networks, which are trained jointly: an encoder network that transforms a bitstring into a perturbation of the drawing primitives, and a decoder network that recovers the bitstring from an image of the morphed drawing. To enable end-to-end training via back propagation, we introduce a soft rasterizer, which is differentiable with respect to perturbations of the drawing primitives. In order to add robustness towards real-world image capture conditions, image corruptions are injected between the soft rasterizer and the decoder. Further, the addition of an object detection and camera pose estimation system enables decoding of drawings in complex scenes as well as use of the drawings as markers for use in augmented reality applications. We demonstrate that our method reliably recovers bitstrings from real-world photos of printed drawings, thereby providing a novel solution for creatives to transfer digital information via artistic imagery.

cs.CV↗
arXiv2006

Deformations of hypercomplex structures related to Heisenberg groups

Let $X$ be a compact quotient of the product of the real Heisenberg group $H_{4m+1}$ of dimension $4m+1$ and the 3-dimensional real Euclidean space $\bR^3$. A left invariant hypercomplex structure on $H_{4m+1}\times \bR^3$ descends onto the compact quotient $X$. The space $X$ is a hyperholomorphic fibration of 4-tori over a $4m$-torus. We calculate the parameter space and obstructions to deformations of this hypercomplex structure on $X$. Using our calculations we show that all small deformations generate invariant hypercomplex structures on $X$ but not all of them arise from deformations of the lattice. This is in contrast to the deformations on the $4m$-torus.

math.DG↗
arXiv2001

Selfdual Einstein metrics with torus symmetry

It is well known that any 4-dimensional hyperkahler metric with two commuting Killing fields may be obtained explicitly, via the Gibbons-Hawking Ansatz, from a harmonic function invariant under a Killing field on R^3. In this paper, we find all selfdual Einstein metrics of nonzero scalar curvature with two commuting Killing fields. They are given explicitly in terms of a local eigenfunction of the Laplacian on the hyperbolic plane. We discuss the relation of this construction to a class of selfdual spaces found by Joyce, and some Einstein-Weyl spaces found by Ward, and then show that certain `multipole' hyperbolic eigenfunctions yield explicit formulae for the quaternion-kahler quotients of HP(m-1) by an (m-2)-torus first studied by Galicki and Lawson. As a consequence we are able to place the well-known cohomogeneity one metrics, the quaternion-kahler quotients of HP(2) (and noncompact analogues), and the more recently studied selfdual Einstein hermitian metrics in a unified framework, and give new complete examples.

math.DG↗