Related papers: Parametric Probabilistic Manifold Decomposition fo…
Data-driven machine learning models often require extensive datasets, which can be costly or inaccessible, and their predictions may fail to comply with established physical laws. Current approaches for incorporating physical priors…
In this paper, we present efficient solutions for the nonlinear program (NLP) associated with nonlinear model predictive control (NMPC) by leveraging the linear parameter-varying (LPV) embedding of nonlinear models and sequential quadratic…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
This paper focuses on the problem of 3D human reconstruction from 2D evidence. Although this is an inherently ambiguous problem, the majority of recent works avoid the uncertainty modeling and typically regress a single estimate for a given…
In this paper, we combine deep learning concepts and some proper orthogonal decomposition (POD) model reduction methods for predicting flow in heterogeneous porous media. Nonlinear flow dynamics is studied, where the dynamics is regarded as…
We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…
During the last decades, many studies have been dedicated to improving the performance of neural networks, for example, the network architectures, initialization, and activation. However, investigating the importance and effects of…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…
In this work, we present a method which determines optimal multi-step dynamic mode decomposition (DMD) models via entropic regression, which is a nonlinear information flow detection algorithm. Motivated by the higher-order DMD (HODMD)…
Probabilistic modeling enables combining domain knowledge with learning from data, thereby supporting learning from fewer training instances than purely data-driven methods. However, learning probabilistic models is difficult and has not…
Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…
We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…
We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean…
Semiparametric forecasting and filtering are introduced as a method of addressing model errors arising from unresolved physical phenomena. While traditional parametric models are able to learn high-dimensional systems from small data sets,…
Dynamic Mode Decomposition (DMD) has received increasing research attention due to its capability to analyze and model complex dynamical systems. However, it faces challenges in computational efficiency, noise sensitivity, and difficulty…
This review article revisits and outlines the perfectly matched layer (PML) method and its various formulations developed over the past 25 years for the numerical modeling and simulation of wave propagation in unbounded media. Based on the…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…