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Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

Normalizing flows are deep generative models that enable efficient likelihood estimation and sampling through invertible transformations. A key challenge is to design linear layers that enhance expressiveness while maintaining efficient…

A recent paper by Gatys et al. describes a method for rendering an image in the style of another image. First, they use convolutional neural network features to build a statistical model for the style of an image. Then they create a new…

Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity…

Flows in networks (or graphs) play a significant role in numerous computer vision tasks. The scalar-valued edges in these graphs often lead to a loss of information and thereby to limitations in terms of expressiveness. For example,…

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…

A normalizing flow is an invertible mapping between an arbitrary probability distribution and a standard normal distribution; it can be used for density estimation and statistical inference. Computing the flow follows the change of…

Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. The central challenge is to simulate turbulent flows in complex geometries, a compute-power intensive task due to the large…

The lateral-line system that has evolved in many aquatic animals enables them to navigate murky fluid environments, locate and discriminate obstacles. Here, we present a data-driven model that uses artificial neural networks to process flow…

Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…

Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data…

We present a framework to use recently introduced Capsule Networks for solving the problem of Optical Flow, one of the fundamental computer vision tasks. Most of the existing state of the art deep architectures either uses a correlation…

Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…

We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an…

Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…

For intelligent transportation systems and autonomous vehicles to operate safely and efficiently, they must reliably predict the future motion and trajectory of surrounding agents within complex traffic environments. At the same time, the…

This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called {\it the flow of finite type}, are in one-to-one correspondence with discrete structures such as…

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly…

Neural Ordinary Differential Equations model dynamical systems with ODEs learned by neural networks. However, ODEs are fundamentally inadequate to model systems with long-range dependencies or discontinuities, which are common in…

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…