Related papers: Data-assisted reduced-order modeling of extreme ev…

Dynamical analysis of manufacturing and natural systems provides critical information about production of manufactured and natural resources respectively, thus playing an important role in assessing sustainability of these systems. However,…

The remarkable flexibility and adaptability of both deep learning models and ensemble methods have led to the proliferation for their application in understanding many physical phenomena. Traditionally, these two techniques have largely…

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…

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…

This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…

The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an…

Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…

We develop a deep convolutional neural network (DCNN) based framework for model-free prediction of the occurrence of extreme events both in time ("when") and in space ("where") in nonlinear physical systems of spatial dimension two. The…

Hybrid methods have been shown to outperform pure statistical and pure deep learning methods at both forecasting tasks, and at quantifying the uncertainty associated with those forecasts (prediction intervals). One example is Multivariate…

In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability…

Modern buildings encompass complex dynamics of multiple electrical, mechanical, and control systems. One of the biggest hurdles in applying conventional model-based optimization and control methods to building energy management is the huge…

Very often when studying non-equilibrium systems one is interested in analysing dynamical behaviour that occurs with very low probability, so called rare events. In practice, since rare events are by definition atypical, they are often…

Low-dimensional representations of underdamped systems often provide insightful grasps and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most…

In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…

In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…

Predicting the long-term behavior of chaotic systems remains a formidable challenge due to their extreme sensitivity to initial conditions and the inherent limitations of traditional data-driven modeling approaches. This paper introduces a…

Data-driven modeling and machine learning are widely used to model the behavior of dynamic systems. One application is the residual evaluation of technical systems where model predictions are compared with measurement data to create…