Related papers: Ultra Fast PDE Solving via Physics Guided Few-step…
Recent advances in generative modeling -- particularly diffusion models and flow matching -- have achieved remarkable success in synthesizing discrete data such as images and videos. However, adapting these models to physical applications…
Diffusion Models have emerged as a leading class of generative models, yet their iterative sampling process remains computationally expensive. Timestep distillation is a promising technique to accelerate generation, but it often requires…
Score-based distillation methods (e.g., variational score distillation) train one-step diffusion models by first pre-training a teacher score model and then distilling it into a one-step student model. However, the gradient estimator in the…
Diffusion models excel in image generation but are computational and resource-intensive due to their reliance on iterative Markov chain processes, leading to error accumulation and limiting the effectiveness of naive compression techniques.…
Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…
Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…
Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…
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…
In scientific and engineering domains, modeling high-dimensional complex systems governed by partial differential equations (PDEs) remains challenging in terms of physical consistency and numerical stability. However, existing approaches,…
Fluid mechanics is a fundamental field in engineering and science. Solving the Navier-Stokes equation (NSE) is critical for understanding the behavior of fluids. However, the NSE is a complex partial differential equation that is difficult…
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…
We develop a robust physics-guided diffusion framework for full-waveform inversion that combines a score-based generative prior with likelihood guidance computed through wave-equation simulations. We adopt a transport-based data-consistency…
We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…
We propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled advection-dispersion and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the…
Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across diverse equation families. However, existing multi-operator…
Diffusion-based image compression has demonstrated impressive perceptual performance. However, it suffers from two critical drawbacks: (1) excessive decoding latency due to multi-step sampling, and (2) poor fidelity resulting from…
Diffusion-based text-to-image generation models trained on extensive text-image pairs have demonstrated the ability to produce photorealistic images aligned with textual descriptions. However, a significant limitation of these models is…
Diffusion- and flow-based models have advanced Real-world Image Super-Resolution (Real-ISR), but their multi-step sampling makes inference slow and hard to deploy. One-step distillation alleviates the cost, yet often degrades restoration…
As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…
The integral equation approach to partial differential equations (PDEs) provides significant advantages in the numerical solution of the incompressible Navier-Stokes equations. In particular, the divergence-free condition and boundary…