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

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…

In this paper, we study the diffusability (learnability) of variational autoencoders (VAE) in latent diffusion. First, we show that pixel-space diffusion trained with an MSE objective is inherently biased toward learning low and mid spatial…

The variational autoencoder (VAE) is a popular deep latent variable model used to analyse high-dimensional datasets by learning a low-dimensional latent representation of the data. It simultaneously learns a generative model and an…

Among likelihood-based approaches for deep generative modelling, variational autoencoders (VAEs) offer scalable amortized posterior inference and fast sampling. However, VAEs are also more and more outperformed by competing models such as…

While unsupervised variational autoencoders (VAE) have become a powerful tool in neuroimage analysis, their application to supervised learning is under-explored. We aim to close this gap by proposing a unified probabilistic model for…

Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…

This paper introduces the Descriptive Variational Autoencoder (DVAE), an unsupervised and end-to-end trainable neural network for predicting vehicle trajectories that provides partial interpretability. The novel approach is based on the…

In the task of predicting spatio-temporal fields in environmental science using statistical methods, introducing statistical models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest.…

Learning representations of underlying environmental dynamics from partial observations is a critical challenge in machine learning. In the context of Partially Observable Markov Decision Processes (POMDPs), state representations are often…

We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…

Developing fast surrogates for Partial Differential Equations (PDEs) will accelerate design and optimization in almost all scientific and engineering applications. Neural networks have been receiving ever-increasing attention and…

By capturing the anisotropic water diffusion in tissue, diffusion magnetic resonance imaging (dMRI) provides a unique tool for noninvasively probing the tissue microstructure and orientation in the human brain. The diffusion profile can be…

Data-driven methods for computer simulations are blooming in many scientific areas. The traditional approach to simulating physical behaviors relies on solving partial differential equations (PDE). Since calculating these iterative…

Discrete latent variables are considered important for real world data, which has motivated research on Variational Autoencoders (VAEs) with discrete latents. However, standard VAE training is not possible in this case, which has motivated…

We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…

We present a simple neural rendering architecture that helps variational autoencoders (VAEs) learn disentangled representations. Instead of the deconvolutional network typically used in the decoder of VAEs, we tile (broadcast) the latent…

Time series data is ubiquitous, with forecasting applications spanning from finance to healthcare. Beyond popular deterministic methods, generative models are gaining attention due to advancements in areas like image synthesis and video…

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…

Purpose: Handling heterogeneous and mixed data types has become increasingly critical with the exponential growth in real-world databases. While deep generative models attempt to merge diverse data views into a common latent space, they…