Related papers: Physics-Informed Generator-Encoder Adversarial Net…

Generative Adversarial Networks (GAN) are trained to generate sample images of interest distribution. To this end, generator network of GAN learns implicit distribution of real data set from the classification with candidate generated…

Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimension of data can be much lower than the ambient dimension. We argue that this discrepancy may contribute to the…

We present an algorithm to directly solve numerous image restoration problems (e.g., image deblurring, image dehazing, image deraining, etc.). These problems are highly ill-posed, and the common assumptions for existing methods are usually…

Recent advances in artificial intelligence have propelled the development of innovative computational materials modeling and design techniques. Generative deep learning models have been used for molecular representation, discovery, and…

Among the major remaining challenges for generative adversarial networks (GANs) is the capacity to synthesize globally and locally coherent images with object shapes and textures indistinguishable from real images. To target this issue we…

Generative adversarial networks (GANs) transform latent vectors into visually plausible images. It is generally thought that the original GAN formulation gives no out-of-the-box method to reverse the mapping, projecting images back into…

Combining Generative Adversarial Networks (GANs) with encoders that learn to encode data points has shown promising results in learning data representations in an unsupervised way. We propose a framework that combines an encoder and a…

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…

Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…

The numerical approximation of solutions to the compressible Euler and Navier-Stokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been…

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part…

Current Generative Adversarial Network (GAN)-based approaches for time series generation face challenges such as suboptimal convergence, information loss in embedding spaces, and instability. To overcome these challenges, we introduce an…

In many computational problems in engineering and science, function or model differentiation is essential, but also integration is needed. An important class of computational problems include so-called integro-differential equations which…

Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss…

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

Generative adversarial networks (GANs) are capable of producing high quality image samples. However, unlike variational autoencoders (VAEs), GANs lack encoders that provide the inverse mapping for the generators, i.e., encode images back to…

We present an encoder-powered generative adversarial network (EncGAN) that is able to learn both the multi-manifold structure and the abstract features of data. Unlike the conventional decoder-based GANs, EncGAN uses an encoder to model the…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

Generative adversarial networks (GANs) can synthesize high-quality (HQ) images, and GAN inversion is a technique that discovers how to invert given images back to latent space. While existing methods perform on StyleGAN inversion, they have…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…