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In light of the widespread success of generative models, a significant amount of research has gone into speeding up their sampling time. However, generative models are often sampled multiple times to obtain a diverse set incurring a cost…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under…
The primary goal of this paper is to characterize solutions to coupled reaction-diffusion systems. Indeed, we use operators theory to show that under suitable assumptions, then the solutions to the reaction-diffusion equations exist. As…
Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…
In many scientific settings, acquiring complete observations of PDE coefficients and solutions can be expensive, hazardous, or impossible. Recent diffusion-based methods can reconstruct fields given partial observations, but require…
The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-range time memory and spatial interactions, such as the…
Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…
Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
This paper presents a hybrid optimization methodology for parameter estimation of reactive transport systems. Using reduced-order advection-diffusion-reaction (ADR) models, the computational requirements of global optimization with dynamic…
Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple,…
This work presents a physics-conditioned latent diffusion model tailored for dynamical downscaling of atmospheric data, with a focus on reconstructing high-resolution 2-m temperature fields. Building upon a pre-existing diffusion…
Guided diffusion is a technique for conditioning the output of a diffusion model at sampling time without retraining the network for each specific task. One drawback of diffusion models, however, is their slow sampling process. Recent…
In this work I show how a diffusion-advection equation in three space-dimensions may have its advection term weakly limited to a velocity field localized to a moving curve. This is rigorously accomplished through the technique of…
We present a first numerical study of transport phenomena involving chemically reactive species, modeled by advection-diffusion-reaction systems with flow fields governed by Darcy's law. Among the various discretisation approaches, we…
Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…
A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural…