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Micro-CT scanning of rocks significantly enhances our understanding of pore-scale physics in porous media. With advancements in pore-scale simulation methods, such as pore network models, it is now possible to accurately simulate multiphase…

Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a…

The rapid development of deep learning has significant implications for the advancement of Computational Fluid Dynamics (CFD). Currently, most pixel-grid-based deep learning methods for flow field prediction exhibit significantly reduced…

In this work, we propose a simple kernel ridge regression (KRR) framework with a dynamic-aware validation strategy for long-term prediction of complex dynamical systems. By employing a data-driven kernel derived from diffusion maps, the…

Quantitative structure-property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure…

Permeability is a central concept in the macroscopic description of flow through porous media, with applications spanning from oil recovery to hydrology. Traditional methods for determining the permeability tensor involving flow simulations…

Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…

Approximate Bayesian computation has emerged as a standard computational tool when dealing with the increasingly common scenario of completely intractable likelihood functions in Bayesian inference. We show that many common Markov chain…

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…

We propose a new method for approximating active learning acquisition strategies that are based on retraining with hypothetically-labeled candidate data points. Although this is usually infeasible with deep networks, we use the neural…

Prediction of a molecule's 3D conformer ensemble from the molecular graph holds a key role in areas of cheminformatics and drug discovery. Existing generative models have several drawbacks including lack of modeling important molecular…

We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an approach based on supervised learning of a greedy…

Shape priors have been widely utilized in medical image segmentation to improve segmentation accuracy and robustness. A major way to encode such a prior shape model is to use a mesh representation, which is prone to causing…

In this paper, we present an efficient adaptive multigrid strategy for the geometry optimization of large-scale three dimensional molecular mechanics. The resulting method can achieve significantly reduced complexity by exploiting the…

Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy…

We show the potential of greedy recovery strategies for the sparse approximation of multivariate functions from a small dataset of pointwise evaluations by considering an extension of the orthogonal matching pursuit to the setting of…

Large kernel convolutions offer a scalable alternative to vision transformers for high-resolution 3D volumetric analysis, yet naively increasing kernel size often leads to optimization instability. Motivated by the spatial bias inherent in…

Orthogonal greedy learning (OGL) is a stepwise learning scheme that starts with selecting a new atom from a specified dictionary via the steepest gradient descent (SGD) and then builds the estimator through orthogonal projection. In this…

Finding efficient tensor contraction paths is essential for a wide range of problems, including model counting, quantum circuits, graph problems, and language models. There exist several approaches to find efficient paths, such as the…

Diffusion-based voxel prior modelling is challenging for the reconstruction of large-scale 3D porous microstructures. Due to the demanding requirements for simultaneously modelling both the continuous pore morphology and the discrete…