Related papers: Generative Reduced Basis Method

We propose Generative Probabilistic Image Colorization, a diffusion-based generative process that trains a sequence of probabilistic models to reverse each step of noise corruption. Given a line-drawing image as input, our method suggests…

With the rise of large radio interferometric telescopes, particularly the SKA, there is a growing demand for computationally efficient image reconstruction techniques. Existing reconstruction methods, such as the CLEAN algorithm or proximal…

Recent advances in data collection technologies have led to the emergence of massive spatial datasets, with measurements obtained at millions of spatial locations. Geostatistical models typically employ Gaussian processes (GPs) to capture…

Novel architectures have recently improved generative image synthesis leading to excellent visual quality in various tasks. Much of this success is due to the scalability of these architectures and hence caused by a dramatic increase in…

We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in…

In this paper, we present a unified framework for reduced basis approximations of parametrized partial differential equations defined on parameter-dependent domains. Our approach combines unfitted finite element methods with both classical…

The reconstruction of X-rays CT images from sparse or limited-angle geometries is a highly challenging task. The lack of data typically results in artifacts in the reconstructed image and may even lead to object distortions. For this…

We present a partitioned Model Order Reduction method for multiphysics problems, that is based on a semi-implicit treatment of the coupling conditions, and on a projection scheme. The proposed Reduced Order Method is based on the Proper…

The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parametrized partial differential equations. We consider a quantity of interest, which is a linear…

Addressing the challenges of climate change requires accurate and high-resolution mapping of geospatial data, especially climate and weather variables. However, many existing geospatial datasets, such as the gridded outputs of the…

We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…

We develop an approach to training generative models based on unrolling a variational auto-encoder into a Markov chain, and shaping the chain's trajectories using a technique inspired by recent work in Approximate Bayesian computation. We…

Sampling-based path planning is a popular methodology for robot path planning. With a uniform sampling strategy to explore the state space, a feasible path can be found without the complex geometric modeling of the configuration space.…

This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…

In this paper, we present how high-order accurate solutions to elliptic partial differential equations can be achieved in arbitrary spatial domains using radial basis function-generated finite differences (RBF-FD) on unfitted node sets…

Reduced-order modeling lies at the interface of numerical analysis and data-driven scientific computing, providing principled ways to compress high-fidelity simulations in science and engineering. We propose a training framework that…

In the recent years, there has been a significant improvement in the quality of samples produced by (deep) generative models such as variational auto-encoders and generative adversarial networks. However, the representation capabilities of…

This paper presents a novel paradigm in simulation-based engineering sciences by introducing a new framework called Generative Parametric Design (GPD). The GPD framework enables the generation of new designs along with their corresponding…