Henrik Pedersen

Andrew Millard, Zheng Zhao, Henrik Pedersen

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.

Andrew Millard, Henrik Pedersen

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.

Søren Rasmussen, Karsten Østergaard Noe, Oliver Gyldenberg Hjermitslev et al.

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.