Related papers: PDE+: Enhancing Generalization via PDE with Adapti…
We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…
Deep neural networks are susceptible to human imperceptible adversarial perturbations. One of the strongest defense mechanisms is \emph{Adversarial Training} (AT). In this paper, we aim to address two predominant problems in AT. First,…
As overparameterized models become increasingly prevalent, training loss alone offers limited insight into generalization performance. While smoothness has been linked to improved generalization across various settings, directly enforcing…
Pretraining for partial differential equation (PDE) modeling has recently shown promise in scaling neural operators across datasets to improve generalizability and performance. Despite these advances, our understanding of how pretraining…
Species transport models typically combine partial differential equations (PDEs) with relations from hindered transport theory to quantify electromigrative, convective, and diffusive transport through complex nanoporous systems; however,…
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…
We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…
Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…
We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…
Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
In this paper, we propose Diffusion Domain Expansion (DDE), a method that efficiently extends pre-trained diffusion models to generate larger objects and handle more complex conditioning beyond their original capabilities. Our method…
Diffusion models are a new class of generative models that have shown outstanding performance in image generation literature. As a consequence, studies have attempted to apply diffusion models to other tasks, such as speech enhancement. A…
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…
Solving parametric partial differential equations (PDEs) presents significant challenges for data-driven methods due to the sensitivity of spatio-temporal dynamics to variations in PDE parameters. Machine learning approaches often struggle…
When models, e.g., for semantic segmentation, are applied to images that are vastly different from training data, the performance will drop significantly. Domain adaptation methods try to overcome this issue, but need samples from the…
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…
Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…