相关论文: DeepSPoC: A Deep Learning-Based PDE Solver Governe…

This paper introduces an approach for learning to solve continuous constraint satisfaction problems (CCSP) in robotic reasoning and planning. Previous methods primarily rely on hand-engineering or learning generators for specific constraint…

Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at…

Incorporating probabilistic terms in mathematical models is crucial for capturing and quantifying uncertainties in real-world systems, especially when the solution is not unique or exhibits sudden qualitative changes as parameters vary.…

In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations,…

We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly…

The invariant distribution, which is characterized by the stationary Fokker-Planck equation, is an important object in the study of randomly perturbed dynamical systems. Traditional numerical methods for computing the invariant distribution…

A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of…

Coupled partial differential equation (PDE) systems, which often represent multi-physics models, are naturally suited for modular numerical solution methods. However, several challenges yet remain in extending the benefits of modularization…

Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…

The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…

McKean-Vlasov SDEs describe systems where the dynamics depend on the law of the process. The corresponding Fokker-Planck equation is a nonlinear, nonlocal PDE for the corresponding measure flow. In the presence of common noise and…

Stochastic differential equations play an important role in various applications when modeling systems that have either random perturbations or chaotic dynamics at faster time scales. The time evolution of the probability distribution of a…

We consider a class of sequential decision-making problems under uncertainty that can encompass various types of supervised learning concepts. These problems have a completely observed state process and a partially observed modulation…

Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success,…

Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…

In this paper, we study the stochastic collocation (SC) methods for uncertainty quantification (UQ) in hyperbolic systems of nonlinear partial differential equations (PDEs). In these methods, the underlying PDEs are numerically solved at a…

Sequential Monte Carlo (SMC) is an inference algorithm for state space models that approximates the posterior by sampling from a sequence of target distributions. The target distributions are often chosen to be the filtering distributions,…

Considering generating samples with high rewards, we focus on optimizing deep neural networks parameterized stochastic differential equations (SDEs), the advanced generative models with high expressiveness, with policy gradient, the leading…

Sparse coding (SC) is attracting more and more attention due to its comprehensive theoretical studies and its excellent performance in many signal processing applications. However, most existing sparse coding algorithms are nonconvex and…

Deep Equilibrium Models (DEQs) have emerged as a powerful paradigm in deep learning, offering the ability to model infinite-depth networks with constant memory usage. However, DEQs incur significant inference latency due to the iterative…