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Deraining is a significant and fundamental computer vision task, aiming to remove the rain streaks and accumulations in an image or video captured under a rainy day. Existing deraining methods usually make heuristic assumptions of the rain…

The multi-step denoising process in diffusion and Flow Matching models causes major efficiency issues, which motivates research on few-step generation. We present Solution Flow Models (SoFlow), a framework for one-step generation from…

The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically…

Many optimization problems require balancing multiple conflicting objectives. As gradient descent is limited to single-objective optimization, we introduce its direct generalization: Jacobian descent (JD). This algorithm iteratively updates…

Hydroelectric power generation is a critical component of the global energy matrix, particularly in countries like Brazil, where it represents the majority of the energy supply. However, its strong dependence on river discharges, which are…

Turbulent flows are chaotic and unsteady, but their statistical distribution converges to a statistical steady state. Engineering quantities of interest typically take the form of time-average statistics such as $ \frac{1}{t} \int_0^t f (…

We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but…

The scalability of continuous normalizing flows (CNFs) for unbiased Boltzmann sampling remains limited in high-dimensional systems due to the cost of Jacobian-determinant evaluation, which requires $D$ backpropagation passes through the…

Understanding the geometric properties of gradient descent dynamics is a key ingredient in deciphering the recent success of very large machine learning models. A striking observation is that trained over-parameterized models retain some…

Evaporation is gaining increasing attention as a calibration and evaluation variable in hydrologic studies that seek to improve the physical realism of hydrologic models and go beyond the long-established streamflow-only calibration.…

Implementing effective control mechanisms to ensure the proper functioning and security of deployed NLP models, from translation to chatbots, is essential. A key ingredient to ensure safe system behaviour is Out-Of-Distribution (OOD)…

Accurate polyp segmentation remains challenging due to irregular lesion morphologies, ambiguous boundaries, and heterogeneous imaging conditions. While U-Net variants excel at local feature fusion, they often lack explicit mechanisms to…

In geophysics, inverse modelling can be applied to a wide range of goals, including, for instance, mapping the distribution of rock physical parameters in applied geophysics and calibrating models to forecast the behaviour of natural…

Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…

We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…

Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE…

In the domain of computer vision, optical flow stands as a cornerstone for unraveling dynamic visual scenes. However, the challenge of accurately estimating optical flow under conditions of large nonlinear motion patterns remains an open…

The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…

We propose RainyScape, an unsupervised framework for reconstructing clean scenes from a collection of multi-view rainy images. RainyScape consists of two main modules: a neural rendering module and a rain-prediction module that incorporates…

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…