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Interpretable representation learning is a central challenge in modern machine learning, particularly in high-dimensional settings such as neuroimaging, genomics, and text analysis. Current methods often struggle to balance the competing…

Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete…

Inverse modeling for computing a high-dimensional spatially-varying property field from indirect sparse and noisy observations is a challenging problem. This is due to the complex physical system of interest often expressed in the form of…

High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…

Modeling the evolution of high-dimensional systems from limited snapshot observations at irregular time points poses a significant challenge in quantitative biology and related fields. Traditional approaches often rely on dimensionality…

The probability prediction of multivariate time series is a notoriously challenging but practical task. On the one hand, the challenge is how to effectively capture the cross-series correlations between interacting time series, to achieve…

An adaptive model for the description of flows in highly heterogeneous porous media is developed in~\cite{FP21,FP23}. There, depending on the magnitude of the fluid's velocity, the constitutive law linking velocity and pressure gradient is…

We present Functional Mean Flow (FMF) as a one-step generative model defined in infinite-dimensional Hilbert space. FMF extends the one-step Mean Flow framework to functional domains by providing a theoretical formulation for Functional…

Motion prediction has been studied in different contexts with models trained on narrow distributions and applied to downstream tasks in human motion prediction and robotics. Simultaneously, recent efforts in scaling video prediction have…

There are many situations when modelling environmental phenomena for which it is not appropriate to assume a stationary dependence structure. \cite{sampson1992} proposed an approach to allowing nonstationarity in dependence based on a…

Computational fluid dynamics (CFD) provides high-fidelity simulations of fluid flows but remains computationally expensive for many-query applications. In recent years deep learning (DL) has been used to construct data-driven fluid-dynamic…

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…

We introduce a novel neural representation for maps between 3D shapes based on flow-matching models, which is computationally efficient and supports cross-representation shape matching without large-scale training or data-driven procedures.…

Neural radiance fields (NeRFs) have achieved impressive view synthesis results by learning an implicit volumetric representation from multi-view images. To project the implicit representation into an image, NeRF employs volume rendering…

We introduce Hyper-Conditioned Neural Autoregressive Flow (HCNAF); a powerful universal distribution approximator designed to model arbitrarily complex conditional probability density functions. HCNAF consists of a neural-net based…

We present a new method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform…

We propose a framework for surrogate modelling of spiking systems. These systems are often described by stiff differential equations with high-amplitude oscillations and multi-timescale dynamics, making surrogate models an attractive tool…

Dense granular flows exhibit nonlocal effects due to stress transmission in microplastic events, especially in quasi-static or slowly sheared regions. Hence, traditional local rheological models fail to capture spatial cooperativity effects…

Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…

Gaussian process state-space models (GPSSMs) offer a principled framework for learning and inference in nonlinear dynamical systems with uncertainty quantification. However, existing GPSSMs are limited by the use of multiple independent…