Related papers: Single-shot prediction of parametric partial diffe…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

Data-driven flow-field reconstruction typically relies on autoencoder architectures that compress high-dimensional states into low-dimensional latent representations. However, classical approaches such as variational autoencoders (VAEs)…

Large, multi-dimensional spatio-temporal datasets are omnipresent in modern science and engineering. An effective framework for handling such data are Gaussian process deep generative models (GP-DGMs), which employ GP priors over the latent…

Variational autoencoders (VAE) are a powerful and widely-used class of models to learn complex data distributions in an unsupervised fashion. One important limitation of VAEs is the prior assumption that latent sample representations are…

Variational Autoencoders (VAEs) are powerful generative models widely used for learning interpretable latent spaces, quantifying uncertainty, and compressing data for downstream generative tasks. VAEs typically rely on diagonal Gaussian…

We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the…

Time-dependent partial differential equations (PDEs) for classic physical systems are established based on the conservation of mass, momentum, and energy, which are ubiquitous in scientific and engineering applications. These PDEs are…

Disentangled representation learning aims to represent the underlying generative factors of a dataset in a latent representation independently of one another. In our work, we propose a discrete variational autoencoder (VAE) based model…

Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our…

Fast and robust dynamic state estimation (DSE) is essential for accurately capturing the internal dynamic processes of power systems, and it serves as the foundation for reliably implementing real-time dynamic modeling, monitoring, and…

We propose a predictor-corrector adaptive method for the simulation of hyperbolic partial differential equations (PDEs) on networks under general uncertainty in parameters, initial conditions, or boundary conditions. The approach is based…

Variational Auto-Encoder (VAE) has been widely applied as a fundamental generative model in machine learning. For complex samples like imagery objects or scenes, however, VAE suffers from the dimensional dilemma between reconstruction…

The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator…

We consider propagating, spatially localised waves in a class of equations that contain variational and non-variational terms. The dynamics of the waves is analysed through a collective coordinate approach. Motivated by the variational…

Recently there has been an increased interest in unsupervised learning of disentangled representations using the Variational Autoencoder (VAE) framework. Most of the existing work has focused largely on modifying the variational cost…

Diffusion models are widely recognized for their ability to generate high-fidelity images. Despite the excellent performance and scalability of the Diffusion Transformer (DiT) architecture, it applies fixed compression across different…

Computational Fluid Dynamics (CFD) plays a pivotal role in fluid mechanics, enabling precise simulations of fluid behavior through partial differential equations (PDEs). However, traditional CFD methods are resource-intensive, particularly…

The Variational Autoencoder (VAE) is a seminal approach in deep generative modeling with latent variables. Interpreting its reconstruction process as a nonlinear transformation of samples from the latent posterior distribution, we apply the…