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Time-dependent partial differential equations (PDEs) often develop sharp fronts, localized peaks, and other moving structures that occupy only a small portion of the space--time domain but dominate the approximation error. This makes fixed…

The goal of a generative model is to capture the distribution underlying the data, typically through latent variables. After training, these variables are often used as a new representation, more effective than the original features in a…

Neural operators have emerged as powerful data-driven frameworks for solving Partial Differential Equations (PDEs), offering significant speedups over numerical methods. However, existing neural operators struggle with scalability in…

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…

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…

Latent dynamics models have emerged as powerful tools for modeling and interpreting neural population activity. Recently, there has been a focus on incorporating simultaneously measured behaviour into these models to further disentangle…

A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural networks are used, with the goal of predicting the future state…

Deep learning paradigms, such as PINNs and neural operators, have significantly advanced the solving of PDEs. However, they often struggle to capture the continuous integral nature of physical systems, relying either on pointwise residuals…

Reliable training of generative adversarial networks (GANs) typically require massive datasets in order to model complicated distributions. However, in several applications, training samples obey invariances that are \textit{a priori}…

Data driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data driven techniques face the dilemma of balancing search space with…

Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics of observed sequence data. They are often trained by maximising the evidence lower bound. However, as we show, this does not ensure the model…

Masked Autoencoders (MAEs) learn generalizable representations for image, text, audio, video, etc., by reconstructing masked input data from tokens of the visible data. Current MAE approaches for videos rely on random patch, tube, or…

The Analog Ensemble (AnEn) method tries to estimate the probability distribution of the future state of the atmosphere with a set of past observations that correspond to the best analogs of a deterministic Numerical Weather Prediction…

The field of neural generative models is dominated by the highly successful Generative Adversarial Networks (GANs) despite their challenges, such as training instability and mode collapse. Auto-Encoders (AE) with regularized latent space…

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…

Accurately quantifying uncertainty in predictions and projections arising from irreducible internal climate variability is critical for informed decision making. Such uncertainty is typically assessed using ensembles produced with physics…

Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original…

Learning to represent and simulate the dynamics of physical systems is a crucial yet challenging task. Existing equivariant Graph Neural Network (GNN) based methods have encapsulated the symmetry of physics, \emph{e.g.}, translations,…

The scarcity of annotated data in LiDAR point cloud understanding hinders effective representation learning. Consequently, scholars have been actively investigating efficacious self-supervised pre-training paradigms. Nevertheless, temporal…

The usage of deep generative models for image compression has led to impressive performance gains over classical codecs while neural video compression is still in its infancy. Here, we propose an end-to-end, deep generative modeling…