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We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic…

We propose a novel framework, Continuous_Time Attention, which infuses partial differential equations (PDEs) into the Transformer's attention mechanism to address the challenges of extremely long input sequences. Instead of relying solely…

In this paper we focus on learning optimized partial differential equation (PDE) models for image filtering. In this approach, the grey-scaled images are represented by a vector field of two real-valued functions and the image restoration…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and…

We obtain a fast diffusion equation (FDE) as scaling limit of a sequence of zero-range process with symmetric unit rate. Fast diffusion effect comes from the fact that the diffusion coefficient goes to infinity as the density goes to zero.…

Geological parameterization entails the representation of a geomodel using a small set of latent variables and a mapping from these variables to grid-block properties such as porosity and permeability. Parameterization is useful for data…

This study investigates the application of deep-learning diffusion models for the super-resolution of weather data, a novel approach aimed at enhancing the spatial resolution and detail of meteorological variables. Leveraging the…

The state of the art for physical hazard prediction from weather and climate requires expensive km-scale numerical simulations driven by coarser resolution global inputs. Here, a generative diffusion architecture is explored for downscaling…

Downscaling, or super-resolution, provides decision-makers with detailed, high-resolution information about the potential risks and impacts of climate change, based on climate model output. Machine learning algorithms are proving themselves…

We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…

This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…

This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations. Within this framework, we establish identifiability conditions for general disentangled latent variable models,…

In recent years, partial differential equation (PDE) systems have been successfully applied to the binarization of text images, achieving promising results. Inspired by the DH model and incorporating a novel image modeling approach, this…

Lie group methods are applied to the time-dependent, monoenergetic neutron diffusion equation in materials with spatial and time dependence. To accomplish this objective, the underlying 2nd order partial differential equation (PDE) is…

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…

In this study, a new coupled Partial Differential Equation (CPDE) based image denoising model incorporating space-time regularization into non-linear diffusion is proposed. This proposed model is fitted with additive Gaussian noise which…

We present our deep learning framework to solve and accelerate the Time-Dependent partial differential equation's solution of one and two spatial dimensions. We demonstrate DiffusionNet solver by solving the 2D transient heat conduction…

A partial differential equation (PDE) was developed to describe time-dependent ligand-receptor interactions for applications in biosensing using field effect transistors (FET). The model describes biochemical interactions at the sensor…

We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…