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Restoring real-world degraded images, such as old photographs or low-resolution images, presents a significant challenge due to the complex, mixed degradations they exhibit, such as scratches, color fading, and noise. Recent data-driven…

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,…

Snapshot compressive spectral imaging reconstruction aims to reconstruct three-dimensional spatial-spectral images from a single-shot two-dimensional compressed measurement. Existing state-of-the-art methods are mostly based on deep…

Diffusion-based models have demonstrated impressive accuracy and generalization in solving partial differential equations (PDEs). However, they still face significant limitations, such as high sampling costs and insufficient physical…

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…

Note: The final version of this article was published in Computers and Geosciences, Volume 206, January 2026, 106038. DOI: 10.1016/j.cageo.2025.106038. Readers should refer to the published version for the most up-to-date content.…

In science and engineering, machine learning techniques are increasingly successful in physical systems modeling (predicting future states of physical systems). Effectively integrating PDE loss as a constraint of system transition can…

Fine-grained air pollution forecasting is crucial for urban management and the development of healthy buildings. Deploying portable sensors on mobile platforms such as cars and buses offers a low-cost, easy-to-maintain, and wide-coverage…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Traditional elastic wavefield separation methods, while accurate, often demand substantial computational resources, especially for large geological models or 3D scenarios. Purely data-driven neural network approaches can be more efficient,…

Diffusion models achieve state-of-the-art image generation but remain computationally costly due to iterative denoising. Latent-space models like Stable Diffusion reduce overhead yet lose fine detail, while retrieval-augmented methods…

Machine learned partial differential equation (PDE) solvers trade the reliability of standard numerical methods for potential gains in accuracy and/or speed. The only way for a solver to guarantee that it outputs the exact solution is to…

Image restoration, which aims to recover high-quality images from their corrupted counterparts, often faces the challenge of being an ill-posed problem that allows multiple solutions for a single input. However, most deep learning based…

Current deep learning methods for low-light image enhancement (LLIE) typically rely on pixel-wise mapping learned from paired data. However, these methods often overlook the importance of considering degradation representations, which can…

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…

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,…

The ability to simulate the partial differential equations (PDE's) that govern multi-phase flow in porous media is essential for different applications such as geologic sequestration of CO2, groundwater flow monitoring and hydrocarbon…

This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based…

Efficient and stable solution of partial differential equations (PDEs) is central to scientific and engineering applications, yet existing numerical solvers rely heavily on matrix based discretizations, while learning based methods require…