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Image denoising and image segmentation play essential roles in image processing. Partial differential equations (PDE)-based methods have proven to show reliable results when incorporated in both denoising and segmentation of images. In our…
We present a novel method to reconstruct 3D scenes from images by leveraging deep dense monocular SLAM and fast uncertainty propagation. The proposed approach is able to 3D reconstruct scenes densely, accurately, and in real-time while…
We introduce the Binless Multidimensional Thermodynamic Integration (BMTI) method for nonparametric, robust, and data-efficient density estimation. BMTI estimates the logarithm of the density by initially computing log-density differences…
Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and slow training times,…
Recent work on Path-Dependent Partial Differential Equations (PPDEs) has shown that PPDE solutions can be approximated by a probabilistic representation, implemented in the literature by the estimation of conditional expectations using…
This paper proposes a novel pixel interval down-sampling network (PID-Net) for dense tiny object (yeast cells) counting tasks with higher accuracy. The PID-Net is an end-to-end convolutional neural network (CNN) model with an…
The development of novel materials in recent years has been accelerated greatly by the use of computational modelling techniques aimed at elucidating the complex physics controlling microstructure formation in materials, the properties of…
This paper introduces a new modeling framework for optimization under uncertainty, called Probable Event Constrained Optimization (PECO). Unlike conventional chance-constrained formulations, which only limit the probability of constraint…
Even though the computation of local properties, such as densities or radial distribution functions, remains one of the most standard goals of molecular simulation, it still largely relies on straighforward histogram-based strategies. Here…
Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…
Survival analysis is a widely-used technique for analyzing time-to-event data in the presence of censoring. In recent years, numerous survival analysis methods have emerged which scale to large datasets and relax traditional assumptions…
Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the…
The Field Estimator for Arbitrary Spaces (FiEstAS) computes the continuous probability density field underlying a given discrete data sample in multiple, non-commensurate dimensions. The algorithm works by constructing a metric-independent…
We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…
Density ratio estimation (DRE) is a fundamental machine learning technique for comparing two probability distributions. However, existing methods struggle in high-dimensional settings, as it is difficult to accurately compare probability…
Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local…
Recent methods in quantile regression have adopted a classification perspective to handle challenges posed by heteroscedastic, multimodal, or skewed data by quantizing outputs into fixed bins. Although these regression-as-classification…
Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…
Machine learning models are increasingly used to predict material properties and accelerate atomistic simulations, but the reliability of their predictions depends on the representativeness of the training data. We present a scalable,…
Reaction-diffusion systems are used to represent many biological and physical phenomena. They model the random motion of particles (diffusion) and interactions between them (reactions). Such systems can be modelled at multiple scales with…