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We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow-field data useful for flow analysis, reduced-order modeling, and flow control.…

We propose a non-intrusive, Autoencoder-based framework for reduced-order modeling in continuum mechanics. Our method integrates three stages: (i) an unsupervised Autoencoder compresses high-dimensional finite element solutions into a…

In recent years, there have been a surge in applications of neural networks (NNs) in physical sciences. Although various algorithmic advances have been proposed, there are, thus far, limited number of studies that assess the…

This interdisciplinary study, which combines machine learning, statistical methodologies, high-fidelity simulations, and flow physics, demonstrates a new process for building an efficient surrogate model for predicting spatiotemporally…

In recent years, there has been significant progress in the development of fully data-driven global numerical weather prediction models. These machine learning weather prediction models have their strength, notably accuracy and low…

Overparameterized models have recently challenged conventional learning theory by exhibiting improved generalization beyond the interpolation limit, a phenomenon known as benign overfitting. This work introduces Adaptive Benign Overfitting…

The use of model order reduction techniques in combination with ensemble-based methods for estimating the state of systems described by nonlinear partial differential equations has been of great interest in recent years in the data…

How an agent can act optimally in stochastic, partially observable domains is a challenge problem, the standard approach to address this issue is to learn the domain model firstly and then based on the learned model to find the (near)…

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…

In recent years, both online and offline deep learning models have been developed for time series forecasting. However, offline deep forecasting models fail to adapt effectively to changes in time-series data, while online deep forecasting…

We present a novel reduced-order pressure stabilization strategy based on continuous data assimilation(CDA) for two-dimensional incompressible Navier-Stokes equations. A feedback control term is incorporated into pressure-correction…

We present Online3R, a new sequential reconstruction framework that is capable of adapting to new scenes through online learning, effectively resolving inconsistency issues. Specifically, we introduce a set of learnable lightweight visual…

Reservoir computing (RC) is an innovative paradigm in neuromorphic computing that leverages fixed, randomized, internal connections to address the challenge of overfitting. RC has shown remarkable effectiveness in signal processing and…

In this work, we consider the task of improving the accuracy of dynamic models for model predictive control (MPC) in an online setting. Although prediction models can be learned and applied to model-based controllers, these models are often…

This paper presents a model based on an hybrid system to numerically simulate the climbing phase of an aircraft. This model is then used within a trajectory prediction tool. Finally, the Covariance Matrix Adaptation Evolution Strategy…

The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at…

We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…

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 study presents an artificial neural network and proper orthogonal decomposition (POD)-based reduced-order model (ROM) of turbulent flow around a finite wall-mounted square cylinder. The proposed model is suitable for turbulent wake…

In this book, I introduce the basic concepts of Online Learning through the modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order…