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

We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…

We study a class of McKean--Vlasov Stochastic Differential Equations (MV-SDEs) with drifts and diffusions having super-linear growth in measure and space -- the maps have general polynomial form but also satisfy a certain monotonicity…

Recent deep reinforcement learning methods have achieved remarkable success in solving multi-objective combinatorial optimization problems (MOCOPs) by decomposing them into multiple subproblems, each associated with a specific weight…

This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling…

The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…

Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be…

This paper develops a parametric Koopman operator framework for Stochastic Model Predictive Control (SMPC), where the Koopman operator is parametrized by Polynomial Chaos Expansions (PCEs). The model is learned from data using the Extended…

Spatial confounding between the spatial random effects and fixed effects covariates has been recently discovered and showed that it may bring misleading interpretation to the model results. Solutions to alleviate this problem are based on…

The field of deep clustering combines deep learning and clustering to learn representations that improve both the learned representation and the performance of the considered clustering method. Most existing deep clustering methods are…

Parallel Continual Learning (PCL) tasks investigate the training methods for continual learning with multi-source input, where data from different tasks are learned as they arrive. PCL offers high training efficiency and is well-suited for…

This paper presents a new supervised representation learning framework, namely structured probabilistic coding (SPC), to learn compact and informative representations from input related to the target task. SPC is an encoder-only…

Leveraging planning during learning and decision-making is central to the long-term development of intelligent agents. Recent works have successfully combined tree-based search methods and self-play learning mechanisms to this end. However,…

Recent deep models for solving routing problems always assume a single distribution of nodes for training, which severely impairs their cross-distribution generalization ability. In this paper, we exploit group distributionally robust…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…

Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling, due to their state-of-the art performance in many generation tasks while relying on mathematical foundations such as stochastic…

The flow-driven spectral chaos (FSC) is a recently developed method for tracking and quantifying uncertainties in the long-time response of stochastic dynamical systems using the spectral approach. The method uses a novel concept called…

In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…

In this paper, we consider the density estimation problem associated with the stationary measure of ergodic It\^o diffusions from a discrete-time series that approximate the solutions of the stochastic differential equations. To take an…

Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…