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Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address…
This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction-diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be…
Diffusion-based posterior samplers use pretrained diffusion priors to sample from measurement- or reward-conditioned posteriors, and are widely used for inverse problems. Yet their theoretical behavior remains poorly understood: even with…
Target tracking plays a crucial role in real-world scenarios, particularly in drug-trafficking interdiction, where the knowledge of an adversarial target's location is often limited. Improving autonomous tracking systems will enable…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
A microscopic, driven lattice gas model is proposed for the dynamics and spatio-temporal fluctuations of the precursor film observed in spreading experiments. Matter is transported both by holes and particles, and the distribution of each…
In this work we are concerned with the inverse problem of the estimation of modeling parameters for a reactive bimolecular transport based on experimental data that is non-uniformly distributed along the interval where the process takes…
Infrared imaging technology has gained significant attention for its reliable sensing ability in low visibility conditions, prompting many studies to convert the abundant RGB images to infrared images. However, most existing image…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
In a preliminary attempt to address the problem of data scarcity in physics-based machine learning, we introduce a novel methodology for data generation in physics-based simulations. Our motivation is to overcome the limitations posed by…
We analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes in the medium. We investigate the…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…
Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical…
Many steady-state transport problems in condensed matter physics can be reduced to a set of coupled diffusion equations. This is true in particular when relaxation processes are sufficiently fast that the system is in the diffusive…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
This paper proposes a two-stage framework named ST-PAD for spatio-temporal fluid dynamics modeling in the field of earth sciences, aiming to achieve high-precision simulation and prediction of fluid dynamics through spatio-temporal physics…
Wildfires represent a problem for ecosystems, human activities, and economies, driven by the climate crisis and land-use changes. Predicting wildfire propagation through mathematical modelling is essential for damage mitigation and risk…
The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of…
A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…
Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a…