Discrete Spatial Diffusion: Intensity-Preserving Diffusion Modeling

Generative diffusion models have achieved remarkable success in producing high-quality images. However, because these models typically operate in continuous intensity spaces - diffusing independently per pixel and color channel - they are fundamentally ill-suited for applications where quantities such as particle counts or material units are inherently discrete and governed by strict conservation laws such as mass preservation, limiting their applicability in scientific workflows. To address this limitation, we propose Discrete Spatial Diffusion (DSD), a framework based on a continuous-time, discrete-state jump stochastic process that operates directly in discrete spatial domains while strictly preserving mass in both forward and reverse diffusion processes. By using spatial diffusion to achieve mass preservation, we introduce stochasticity naturally through a discrete formulation. We demonstrate the expressive flexibility of DSD by performing image synthesis, class conditioning, and image inpainting across widely-used image benchmarks, with the ability to condition on image intensity. Additionally, we highlight its applicability to domain-specific scientific data for materials microstructure, bridging the gap between diffusion models and mass-conditioned scientific applications.

Machine learned reconstruction of tsunami dynamics from sparse observations

We investigate the use of the Senseiver, a transformer neural network designed for sparse sensing applications, to estimate full-field surface height measurements of tsunami waves from sparse observations. The model is trained on a large ensemble of simulated data generated via a shallow water equations solver, which we show to be a faithful reproduction for the underlying dynamics by comparison to historical events. We train the model on a dataset consisting of 8 tsunami simulations whose epicenters correspond to historical USGS earthquake records, and where the model inputs are restricted to measurements obtained at actively deployed buoy locations. We test the Senseiver on a dataset consisting of 8 simulations not included in training, demonstrating its capability for extrapolation. The results show remarkable resolution of fine scale phase and amplitude features from the true field, provided that at least a few of the sensors have obtained a non-zero signal. Throughout, we discuss which forecasting techniques can be improved by this method, and suggest ways in which the flexibility of the architecture can be leveraged to incorporate arbitrary remote sensing data (eg. HF Radar and satellite measurements) as well as investigate optimal sensor placements.

Reconstruction of Fields from Sparse Sensing: Differentiable Sensor Placement Enhances Generalization

Recreating complex, high-dimensional global fields from limited data points is a grand challenge across various scientific and industrial domains. Given the prohibitive costs of specialized sensors and the frequent inaccessibility of certain regions of the domain, achieving full field coverage is typically not feasible. Therefore, the development of algorithms that intelligently improve sensor placement is of significant value. In this study, we introduce a general approach that employs differentiable programming to exploit sensor placement within the training of a neural network model in order to improve field reconstruction. We evaluated our method using two distinct datasets; the results show that our approach improved test scores. Ultimately, our method of differentiable placement strategies has the potential to significantly increase data collection efficiency, enable more thorough area coverage, and reduce redundancy in sensor deployment.