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Multistage stochastic programming deals with operational and planning problems that involve a sequence of decisions over time while responding to realizations that are uncertain. Algorithms designed to address multistage stochastic linear…
We consider solving a convex, possibly stochastic optimization problem over a randomly time-varying multi-agent network. Each agent has access to some local objective function, and it only has unbiased estimates of the gradients of the…
Recent works leveraging Graph Neural Networks to approach graph matching tasks have shown promising results. Recent progress in learning discrete distributions poses new opportunities for learning graph matching models. In this work, we…
This article proposes a novel computational modeling approach for short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations, and gives a detailed overview how it fits into the framework of existing…
The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit…
The emergence of diffusion models has significantly advanced generative AI, improving the quality, realism, and creativity of image and video generation. Among them, Stable Diffusion (StableDiff) stands out as a key model for text-to-image…
In this paper, we consider solving the distributed optimization problem over a multi-agent network under the communication restricted setting. We study a compressed decentralized stochastic gradient method, termed ``compressed exact…
We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The…
Stein Variational Gradient Descent (SVGD) is a popular variational inference algorithm which simulates an interacting particle system to approximately sample from a target distribution, with impressive empirical performance across various…
We present an effective stochastic advection-diffusion-reaction (SADR) model that explains incomplete mixing typically observed in transport with bimolecular reactions. Unlike traditional advection-dispersion-reaction models, the SADR model…
Stochastic Gradient Descent (SGD) is one of the most widely used techniques for online optimization in machine learning. In this work, we accelerate SGD by adaptively learning how to sample the most useful training examples at each time…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
We introduce relative and absolute position matching (RAPM), a diffusion distillation method resulting in high quality generation that can be trained efficiently on a single GPU. Recent diffusion distillation research has achieved excellent…
The interplay between stochastic chemical reactions and diffusion can generate rich spatiotemporal patterns. While the timescale for individual reaction or diffusion events may be very fast, the timescales for organization can be much…
In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion…
In this paper, we present a Scale-adaptive method for Anti-aliasing Gaussian Splatting (SA-GS). While the state-of-the-art method Mip-Splatting needs modifying the training procedure of Gaussian splatting, our method functions at test-time…
We introduce a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations. The proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems in…
Stochastic Gradient Descent (SGD) has been the method of choice for learning large-scale non-convex models. While a general analysis of when SGD works has been elusive, there has been a lot of recent progress in understanding the…
Modeling transformations between arbitrary data distributions is a fundamental scientific challenge, arising in applications like drug discovery and evolutionary simulation. While flow matching offers a natural framework for this task, its…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…