相关论文: Data-driven reduced order modeling for parametric …

Gaussian processes (GPs) are non-parametric Bayesian models that are widely used for diverse prediction tasks. Previous work in adding strong privacy protection to GPs via differential privacy (DP) has been limited to protecting only the…

Data-driven Model Predictive Control (MPC), where the system model is learned from data with machine learning, has recently gained increasing interests in the control community. Gaussian Processes (GP), as a type of statistical models, are…

We propose a new method in which a generative network (GN) integrate into a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and…

Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…

Projection-based reduced order models rely on offline-online model decomposition, where the data-based energetic spatial basis is used in the expensive offline stage to obtain equations of reduced states that evolve in time during the…

This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…

This paper deals with the problem of adaptive output regulation for multivariable nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. The approach builds on the recently proposed adaptive internal…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

In this work we introduce a reduced-rank algorithm for Gaussian process regression. Our numerical scheme converts a Gaussian process on a user-specified interval to its Karhunen-Lo\`eve expansion, the $L^2$-optimal reduced-rank…

This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…

Gaussian processes (GPs) based methods for solving partial differential equations (PDEs) demonstrate great promise by bridging the gap between the theoretical rigor of traditional numerical algorithms and the flexible design of machine…

Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset.…

In this paper, we propose a subspace method based on neural networks for eigenvalue problems with high accuracy and low cost. We first construct a neural network-based orthogonal basis by some deep learning method and dimensionality…

In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such…

We consider the estimation of parameter-dependent statistics of functional outputs of elliptic boundary value problems (BVPs) with parametrized random and deterministic inputs. For a given value of the deterministic paremeter, a stochastic…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian…

Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…

Retinal prostheses restore vision by electrically stimulating surviving neurons, but calibrating perceptual thresholds (i.e., the minimum stimulus intensity required for perception) remains a time-intensive challenge, especially for…

Directed energy deposition (DED) is a promising metal additive manufacturing technology capable of 3D printing metal parts with complex geometries at lower cost compared to traditional manufacturing. The technology is most effective when…