相关论文: Regression-based projection for learning Mori-Zwan…

Data-driven techniques have emerged as a promising alternative to traditional numerical methods for solving PDEs. For time-dependent PDEs, many approaches are Markovian -- the evolution of the trained system only depends on the current…

We develop rigorous estimates and provably convergent approximations for the memory integral in the Mori-Zwanzig (MZ) formulation. The new theory is built upon rigorous mathematical foundations and is presented for both state-space and…

Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the…

Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…

Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…

Modal regression, a widely used regression protocol, has been extensively investigated in statistical and machine learning communities due to its robustness to outliers and heavy-tailed noises. Understanding modal regression's theoretical…

We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique…

Machine learning models (mainly neural networks) are used more and more in real life. Users feed their data to the model for training. But these processes are often one-way. Once trained, the model remembers the data. Even when data is…

Built upon the hypoelliptic analysis of the effective Mori-Zwanzig (EMZ) equation for observables of stochastic dynamical systems, we show that the obtained semigroup estimates for the EMZ equation can be used to drive prior estimates of…

The Bellman equation and its continuous form, the Hamilton-Jacobi-Bellman equation, are ubiquitous in reinforcement learning and control theory. However, these equations become intractable for high-dimensional or nonlinear systems. This…

Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…

We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…

With the increasing penetration of renewable energy sources, growing demand variability, and evolving grid control strategies, accurate and efficient load modeling has become a critical yet challenging task. Traditional methods, such as…

We address the challenge of correlated predictors in high-dimensional GLMs, where regression coefficients range from sparse to dense, by proposing a data-driven random projection method. This is particularly relevant for applications where…

This paper introduces a method for data-driven control based on the Koopman operator model predictive control. Unlike exiting approaches, the method does not require a dictionary and incorporates a nonlinear input transformation, thereby…

Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in…

Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter extensive efforts have been made but…

Representation learning enables us to automatically extract generic feature representations from a dataset to solve another machine learning task. Recently, extracted feature representations by a representation learning algorithm and a…

We present a comparative study of two methods for the reduction of the dimensionality of a system of ordinary differential equations that exhibits time-scale separation. Both methods lead to a reduced system of stochastic differential…

The Koopman operator provides a powerful framework for data-driven analysis of dynamical systems. In the last few years, a wealth of numerical methods providing finite-dimensional approximations of the operator have been proposed (e.g.…