Related papers: DeepSPoC: A Deep Learning-Based PDE Solver Governe…

Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions,…

In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements.…

Distributed Constraint Satisfaction (DCSP) has long been considered an important problem in multi-agent systems research. This is because many real-world problems can be represented as constraint satisfaction and these problems often…

Stochastic dynamical systems provide essential mathematical frameworks for modeling complex real-world phenomena. The Fokker-Planck-Kolmogorov (FPK) equation governs the evolution of probability density functions associated with stochastic…

This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…

Deep neural networks have become invaluable tools for supervised machine learning, e.g., classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in…

In this paper, we introduce a new method called SPSC (Simulation, Partitioning, Selection, Cloning) to estimate efficiently the probability of possible solutions in stochastic simulations. This method can be applied to any type of…

In this paper, we investigate the limiting behavior of a continuous-time counterpart of the Stochastic Gradient Descent (SGD) algorithm applied to two-layer overparameterized neural networks, as the number or neurons (ie, the size of the…

We develop a complete and rigorous mathematical framework for the analysis of stochastic neural field equations under the influence of spatially extended additive noise. By comparing a solution to a fixed deterministic front profile it is…

While large language models (LLMs) have demonstrated remarkable success on a broad range of tasks, math reasoning remains a challenging one. One of the approaches for improving math reasoning is self-correction, which designs self-improving…

Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple strategies for evaluating PCE coefficients. In contrast,…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

We systematically develop a learning-based treatment of stochastic optimal control (SOC), relying on direct optimization of parametric control policies. We propose a derivation of adjoint sensitivity results for stochastic differential…

Deep learning approaches are nowadays ubiquitously used to tackle computer vision tasks such as semantic segmentation, requiring large datasets and substantial computational power. Continual learning for semantic segmentation (CSS) is an…

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…

For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality…

Reducing communication complexity is critical for efficient decentralized optimization. The proximal decentralized optimization (PDO) framework is particularly appealing, as methods within this framework can exploit functional similarity…

Topic models provide a useful tool to organize and understand the structure of large corpora of text documents, in particular, to discover hidden thematic structure. Clustering documents from big unstructured corpora into topics is an…

This article is devoted to providing a review of mathematical formulations in which Polynomial Chaos Theory (PCT) has been incorporated into stochastic model predictive control (SMPC). In the past decade, PCT has been shown to provide a…