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Diffusion Policy (DP) enables robots to learn complex behaviors by imitating expert demonstrations through action diffusion. However, in practical applications, hardware limitations often degrade data quality, while real-time constraints…

The problem of a spatially discontinuous diffusion coefficient ($D(\boldsymbol x)$) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow…

Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often…

Generalist robot policies built upon 2D visual representations excel at semantic reasoning but inherently lack the explicit 3D spatial awareness required for high-precision tasks. Existing 3D integration methods struggle to bridge this gap…

Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent…

Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several…

The Dynamic Pickup and Delivery Problem (DPDP) is aimed at dynamically scheduling vehicles among multiple sites in order to minimize the cost when delivery orders are not known a priori. Although DPDP plays an important role in modern…

In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under the diffusive scaling. We extend to the present case the bi-fidelity stochastic collocation method…

Recent advances in generative deep learning have transformed small molecule design, but most methods lack biological systems context, focusing narrowly on specific protein pockets. We introduce a non-differentiable diffusion guidance method…

Clustering is one of the most widely used procedures in the analysis of microarray data, for example with the goal of discovering cancer subtypes based on observed heterogeneity of genetic marks between different tissues. It is well-known…

Molecular representation learning has shown great success in advancing AI-based drug discovery. The core of many recent works is based on the fact that the 3D geometric structure of molecules provides essential information about their…

Transport maps have become a popular mechanic to express complicated probability densities using sample propagation through an optimized push-forward. Beside their broad applicability and well-known success, transport maps suffer from…

Currently, deep learning (DL) has achieved the automatic prediction of dose distribution in radiotherapy planning, enhancing its efficiency and quality. However, existing methods suffer from the over-smoothing problem for their commonly…

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical…

This paper presents a minimum flow approach applicable to a wide range of doubly nonlinear diffusion problems. We introduce a minimum flow steepest descent algorithm that seeks an optimal traffic flow by minimizing an internal energy…

We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in…

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…

Safe trajectory planning in complex environments must balance stringent collision avoidance with real-time efficiency, which is a long-standing challenge in robotics. In this work, we present a diffusion-based trajectory planning framework…

We present a generative learning framework for probabilistic sampling based on an extension of the Probabilistic Learning on Manifolds (PLoM) approach, which is designed to generate statistically consistent realizations of a random vector…

Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…