Related papers: Operator learning regularization for macroscopic p…

We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hilbert space. We model the intrinsically non-linear structure…

This paper addresses supervised deep metric learning for open-set image retrieval, focusing on three key aspects: the loss function, mixup regularization, and model initialization. In deep metric learning, optimizing the retrieval…

Multiple kernel learning (MKL), structured sparsity, and multi-task learning have recently received considerable attention. In this paper, we show how different MKL algorithms can be understood as applications of either regularization on…

Focus of this work is solving a non-smooth constraint minimization problem by a primal-dual splitting algorithm involving proximity operators. The problem is penalized by the Bregman divergence associated with the non-smooth total variation…

The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…

The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of…

Machine learning-based weather forecasting models now surpass state-of-the-art numerical weather prediction systems, but training and operating these models at high spatial resolution remains computationally expensive. We present a modular…

We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage…

Robotic cloth folding is a challenging task, particularly when considering dynamic folding tasks, which aim at folding cloth by fast motions that leverage its dynamics. When subject to such fast motions, the complexity of cloth dynamics…

While the authors of Batch Normalization (BN) identify and address an important problem involved in training deep networks-- \textit{Internal Covariate Shift}-- the current solution has certain drawbacks. For instance, BN depends on batch…

A data-driven surrogate framework to accelerate particle-resolved modelling of quasi-dilute suspensions of rigid, non-spherical particles in Stokes flow is introduced. A regularized-Stokeslet boundary element method (BEM) is implemented to…

Neural networks have shown tremendous potential for reconstructing high-resolution images in inverse problems. The non-convex and opaque nature of neural networks, however, hinders their utility in sensitive applications such as medical…

We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…

Neural networks can be used to learn the solution of partial differential equations (PDEs) on arbitrary domains without requiring a computational mesh. Common approaches integrate differential operators in training neural networks using a…

Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively…

Lagrangian data assimilation exploits the trajectories of moving tracers as observations to recover the underlying flow field. One major challenge in Lagrangian data assimilation is the intrinsic nonlinearity that impedes using exact…

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…

This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear…

While reinforcement learning (RL) holds great potential for decision making in the real world, it suffers from a number of unique difficulties which often need specific consideration. In particular: it is highly non-stationary; suffers from…

An autoencoder is used to compress and then reconstruct three-dimensional stratified turbulence data in order to better understand fluid dynamics by studying the errors in the reconstruction. The original single data set is resolved on…