Related papers: Bridging Sequential Deep Operator Network and Vide…

The solution of partial differential equations (PDEs) plays a central role in numerous applications in science and engineering, particularly those involving multiphase flow in porous media. Complex, nonlinear systems govern these problems…

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…

We introduce FLEX (FLow EXpert), a backbone architecture for generative modeling of spatio-temporal physical systems using diffusion models. FLEX operates in the residual space rather than on raw data, a modeling choice that we motivate…

Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data…

Due to storage and bandwidth limitations, videos transmitted over the Internet often exhibit low quality, characterized by low-resolution and compression artifacts. Although video super-resolution (VSR) is an efficient video enhancing…

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…

Diffusion models have emerged as powerful generative priors for solving PDE-constrained inverse problems. Compared to end-to-end approaches relying on massive paired datasets, explicitly decoupling the prior distribution of physical…

Reference-based super-resolution (RefSR) has the potential to build bridges across spatial and temporal resolutions of remote sensing images. However, existing RefSR methods are limited by the faithfulness of content reconstruction and the…

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…

Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…

Deep-learning video super-resolution has progressed rapidly, but climate applications typically super-resolve (increase resolution) either space or time, and joint spatiotemporal models are often designed for a single pair of…

Predicting stress fields in hyperelastic materials with complex microstructures remains challenging for traditional deep learning surrogates, which struggle to capture both sharp stress concentrations and the wide dynamic range of stress…

We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space $\mathbb{R}_2$ [1] to position-orientation space $\mathbb{M}_2 \cong \mathbb{R}^2 \times S^1$. This has numerous advantages, e.g. making it possible to enhance and…

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…

Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In…

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these…

Diffusion models demonstrate remarkable capabilities in capturing complex data distributions and have achieved compelling results in many generative tasks. While they have recently been extended to dense prediction tasks such as depth…

Designing urban spaces that provide pedestrian wind comfort and safety requires time-resolved Computational Fluid Dynamics (CFD) simulations, but their current computational cost makes extensive design exploration impractical. We introduce…

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained…

We present a combined numerical and data-driven workflow for efficient prediction of nonlinear, instationary convection-diffusion-reaction dynamics on a two-dimensional phenotypic domain, motivated by macroscopic modeling of cancer cell…