相关论文: Learning Surrogate Potential Mean Field Games via …

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…

A key challenge with controlling complex dynamical systems is to accurately model them. However, this requirement is very hard to satisfy in practice. Data-driven approaches such as Gaussian processes (GPs) have proved quite effective by…

Learning by experience in Multi-Agent Systems (MAS) is a difficult and exciting task, due to the lack of stationarity of the environment, whose dynamics evolves as the population learns. In order to design scalable algorithms for systems…

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

Mean Field Games (MFG) provide a theoretical frame to model socio-economic systems. In this letter, we study a particular class of MFG which shows strong analogies with the {\em non-linear Schr\"odinger and Gross-Pitaevski equations}…

Gaussian processes (GPs) are ubiquitously used in sciences and engineering as metamodels. Standard GPs, however, can only handle numerical or quantitative variables. In this paper, we introduce latent map Gaussian processes (LMGPs) that…

Existing deep learning methods for solving mean-field games (MFGs) with common noise fix the sampling common noise paths and then solve the corresponding MFGs. This leads to a nested-loop structure with millions of simulations of common…

With the digitalization of power grids, physical equations become insufficient to describe the network's behavior, and realistic but time-consuming simulators must be used. Numerical experiments, such as safety validation, that involve…

Deep Gaussian Processes (DGPs) are powerful surrogate models known for their flexibility and ability to capture complex functions. However, extending them to multi-output settings remains challenging due to the need for efficient dependency…

Multi-output Gaussian Processes provide principled uncertainty-aware learning of vector-valued fields but are difficult to deploy in large-scale, distributed, and streaming settings due to their computational and centralized nature. This…

In this paper, we consider a mean field game (MFG) model perturbed by small common noise. Our goal is to give an approximation of the Nash equilibrium strategy of this game using a solution from the original no common noise MFG whose…

A Coefficient Inverse Problem (CIP) of the determination of a coefficient of the Mean Field Games System (MFGS) of the second order is considered. The input data are generated by a single measurement event. Lateral Cauchy data, i.e.…

In this paper, we propose an initial value fomulation of the discrete mean field games on finite graphs (Graph MFG), and design a neural network based approach to solve it. Graph MFG describes infinite, non-cooperative and interactive…

In this paper, we explore the application of Gaussian Processes (GPs) for predicting mean-reverting time series with an underlying structure, using relatively unexplored functional and augmented data structures. While many conventional…

We develop the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces with common noise modeled by an infinite-dimensional Wiener process that affects the dynamics of all agents. In the presence of common noise, the…

While the topic of mean-field games (MFGs) has a relatively long history, heretofore there has been limited work concerning algorithms for the computation of equilibrium control policies. In this paper, we develop a computable policy…

In complex large-scale systems such as climate, important effects are caused by a combination of confounding processes that are not fully observable. The identification of sources from observations of system state is vital for attribution…

Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper we refer to this task as "semi-described…

Deep-learning has achieved good performance and shown great potential for solving forward and inverse problems. In this work, two categories of innovative deep-learning based inverse modeling methods are proposed and compared. The first…

Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when…