Related papers: Unsupervised Solution Operator Learning for Mean-F…

We present a new semi-supervised domain adaptation framework that combines a novel auto-encoder-based domain adaptation model with a simultaneous learning scheme providing stable improvements over state-of-the-art domain adaptation models.…

We propose a new method for learning with multi-field categorical data. Multi-field categorical data are usually collected over many heterogeneous groups. These groups can reflect in the categories under a field. The existing methods try to…

The intelligent fault diagnosis of rotating mechanical equipment usually requires a large amount of labeled sample data. However, in practical industrial applications, acquiring enough data is both challenging and expensive in terms of time…

We propose a novel sampling-based federated learning framework for statistical inference on M-estimators with non-smooth objective functions, which frequently arise in modern statistical applications such as quantile regression and AUC…

Deep reinforcement learning (RL) can acquire complex behaviors from low-level inputs, such as images. However, real-world applications of such methods require generalizing to the vast variability of the real world. Deep networks are known…

We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. the control. Existence, uniqueness, and stability of solutions are studied from the point…

Multiple operator learning concerns learning operator families $\{G[\alpha]:U\to V\}_{\alpha\in W}$ indexed by an operator descriptor $\alpha$. Training data are collected hierarchically by sampling operator instances $\alpha$, then input…

Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving exact operators and…

The integration of machine learning models in various real-world applications is becoming more prevalent to assist humans in their daily decision-making tasks as a result of recent advancements in this field. However, it has been discovered…

Effective implementations of sampling-based probabilistic inference often require manually constructed, model-specific proposals. Inspired by recent progresses in meta-learning for training learning agents that can generalize to unseen…

Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for traditional solvers. Although operator learning has shown…

Meshfree simulation methods are emerging as compelling alternatives to conventional mesh-based approaches, particularly in the fields of Computational Fluid Dynamics (CFD) and continuum mechanics. In this publication, we provide a…

Neural network-based methods are effective for solving equilibria in Mean-Field Games (MFGs), particularly in high-dimensional settings. However, solving the coupled partial differential equations (PDEs) in MFGs limits their applicability…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

Supervised matrix factorization (SMF) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. Our goal is to use SMF to learn…

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…

We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The objective function is traditionally defined by…

We extend the methods from Nurbekyan, Saude "Fourier approximation methods for first-order nonlocal mean-field games" [Port. Math. 75 (2018), no. 3-4] and Liu, Jacobs, Li, Nurbekyan, Osher "Computational methods for nonlocal mean field…

In supervised learning, it is known that overparameterized neural networks with one hidden layer provably and efficiently learn and generalize, when trained using stochastic gradient descent with a sufficiently small learning rate and…

We develop a framework for the analysis of deep neural networks and neural ODE models that are trained with stochastic gradient algorithms. We do that by identifying the connections between control theory, deep learning and theory of…