Omer San

• PhD
• Professor (Assistant) at Oklahoma State University

Reduced-order models (ROMs) have achieved a lot of success in reducing the computational cost of traditional numerical methods across many disciplines. In fluid dynamics, ROMs have been successful in providing efficient and relatively accurate solutions for the numerical simulation of laminar flows. For convection-dominated (e.g., turbulent) flows,...

This paper presents an advanced methodology for enhancing the accuracy of trajectory prediction of atmospheric entry vehicles by combining experimental and numerically simulated data. The study utilizes sparse oscillation observation from the ballistic range during the deceleration phase of entry vehicles. It aims to enhance the accuracy of predict...

A blunt body entering through the atmosphere is subjected to strong forces and moments, which can lead to strong oscillations in the trajectory. Therefore, it is important to identify these oscillations and analyze the dynamic motion of the vehicle for a safe entry and descent. However, this challenging event includes complex interactions of the ve...

Atmospheric entry and descent is one of the most important stages of a space mission. After a successful entry, the vehicle decelerates with the aerodynamic forces exerted on the body. As the vehicle decelerates, it starts to oscillate due to the aerodynamic nature of the blunt bodies. However, a safe landing often requires parachute deployment whi...

The importance of energy conservation has greatly increased to promote the decarbonization of buildings. This has resulted in significant interest in variable-speed heat pumping systems with improved efficiency. This paper formulates and evaluates a variable heat pump system model compatible with Building Energy Modeling (BEM) software like EnergyP...

This paper presents a gray-box model developed for unitary air conditioning equipment. The proposed gray-box component-based model uses lumped heat exchanger models with a new formulation for UA of each heat exchanger in terms of the system model inputs which are outdoor and indoor temperatures along with indoor supply air flowrate. Key input param...

Reduced order models (ROMs) have achieved a lot of success in reducing the computational cost of traditional numerical methods across many disciplines. For convection-dominated (e.g., turbulent) flows, however, standard ROMs generally yield inaccurate results, usually affected by spurious oscillations. Thus, ROMs are usually equipped with numerical...

The evolution of a turbulent flow to a statistically steady state can be cast as a multiscale problem involving energy redistribution processes that take place on the long, large eddy turnover timescale and chaotic processes that take place on the much shorter timescale of the turbulence fluctuations. But the absence of a way to perform super-resol...

This paper presents an ansatz-informed approach to modeling the dynamics of blunt-body entry vehicles by combining physics-based modeling with machine-learning techniques. The main focus is developing an augmented physics-informed neural network (PINN) to simulate the vehicle's behavior during atmospheric entry. The proposed PINN architecture is ca...

In this article, we introduce a decentralized digital twin (DDT) modeling framework and its potential applications in computational science and engineering. The DDT methodology is based on the idea of federated learning, a subfield of machine learning that promotes knowledge exchange without disclosing actual data. Clients can learn an aggregated m...

The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse in forecasting centres for over three decades. While this method provides a computationally efficient framework for dynamic data assimilation, it is largely silent on the important question concerning...

Super-Resolution (SR) techniques aim to enhance data resolution, enabling the retrieval of finer details, and improving the overall quality and fidelity of the data representation. There is growing interest in applying SR methods to complex spatiotemporal systems within the Scientific Machine Learning (SciML) community, with the hope of acceleratin...

Differential equations are the foundation of mathematical models representing the universe’s physics. Hence, it is significant to solve partial and ordinary differential equations, such as Navier–Stokes, heat transfer, convection–diffusion, and wave equations, to model, calculate and simulate the underlying complex physical processes. However, it i...

The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse of forecasting centers for over three decades. While this method provides a computationally efficient framework for dynamic data assimilation, it is largely silent on the important question concerning...

This article presents a comprehensive overview of the digital twin technology and its capability levels, with a specific focus on its applications in the wind energy industry. It consolidates the definitions of digital twin and its capability levels on a scale from 0-5; 0-standalone, 1-descriptive, 2-diagnostic, 3-predictive, 4-prescriptive, 5-auto...

Model reduction by projection-based approaches is often associated with losing some of the important features that contribute towards the dynamics of the retained scales. As a result, a mismatch occurs between the predicted trajectories of the original system and the truncated one. We put forth a framework to apply a continuous time control signal...

One outcome of rapid digital transformation is the emergence of technologies like reduced order models. This growth has resulted in a major challenge in many scientific applications. It is computationally demanding to train an end-to-end data-driven machine learning model that can be trustworthily used in future predictions. To address this challen...

In this paper, we formulate three nonintrusive methods and systematically explore their performance in terms of the ability to reconstruct the quantities of interest and their predictive capabilities. The methods include deterministic dynamic mode decomposition, randomised dynamic mode decomposition and nonlinear proper orthogonal decomposition (NL...

Recent developments in diagnostic and computing technologies offer to leverage numerous forms of nonintrusive modelling approaches from data where machine learning can be used to build computationally cheap and accurate surrogate models. To this end, we present a nonlinear proper orthogonal decomposition (POD) framework, denoted as NLPOD, to forge...

A digital twin is a powerful tool that can help monitor and optimize physical assets in real-time. Simply put, it is a virtual representation of a physical asset, enabled through data and simulators, that can be used for a variety of purposes such as prediction, monitoring, and decision-making. However, the concept of digital twin can be vague and...

This article presents a comprehensive overview of the digital twin technology and its capability levels, with a specific focus on its applications in the wind energy industry. It consolidates the definitions of digital twin and its capability levels on a scale from 0-5; 0-standalone, 1-descriptive, 2-diagnostic, 3-predictive, 4-prescriptive, 5-auto...

A digital twin is defined as a virtual representation of a physical asset enabled through data and simulators for real-time prediction, optimization, monitoring, controlling, and improved decision-making. Unfortunately, the term remains vague and says little about its capability. Recently, the concept of capability level has been introduced to addr...

Recent developments in diagnostic and computing technologies offer to leverage numerous forms of nonintrusive modeling approaches from data where machine learning can be used to build computationally cheap and accurate surrogate models. To this end, we present a nonlinear proper orthogonal decomposition (POD) framework, denoted as NLPOD, to forge a...

In this paper, we propose a novel reduced order model (ROM) lengthscale that is constructed by using energy distribution arguments. The new energy-based ROM lengthscale is fundamentally different from the current ROM lengthscales, which are built by using dimensional arguments. To assess the novel, energy-based ROM lengthscale, we compare it with a...

There is a growing interest in developing data‐driven reduced‐order models for atmospheric and oceanic flows that are trained on data obtained either from high‐resolution simulations or satellite observations. The data‐driven models are non‐intrusive in nature and offer significant computational savings compared to large‐scale numerical models. The...

In this study, we present a parametric, non-intrusive reduced order modeling (NIROM) framework as a potential digital-twin enabler for fluid flow around an aerofoil. A wind turbine blade has its basic foundation in the aerofoil shape. A faster way of understanding dynamic flow changes around the aerofoil-shaped blade can help make quick decisions r...

Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models for subgrid scale (SGS) processes using physical insights and mathematical approximations, they remain imperf...

A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to...

Engineering wake models that accurately predict wake in a computationally efficient manner are very important for tasks such as layout optimization and control of wind farms. In this paper, we explore an application of deep learning (DL) to learn the wake model from hierarchies of physics-based approaches ranging from analytical models to an approx...

Physics-based models have been mainstream in fluid dynamics for developing predictive models. In recent years, machine learning has offered a renaissance to the fluid community due to the rapid developments in data science, processing units, neural network based technologies, and sensor adaptations. So far in many applications in fluid dynamics, ma...

Physics-based models have been mainstream in fluid dynamics for developing predictive models. In recent years, machine learning has offered a renaissance to the fluid community due to the rapid developments in data science, processing units, neural network based technologies, and sensor adaptations. So far in many applications in fluid dynamics, ma...

In this paper, we present a brief tutorial on reduced order model (ROM) closures. First, we carefully motivate the need for ROM closure modeling in under-resolved simulations. Then, we construct step by step the ROM closure model by extending the classical Galerkin framework to the spaces of resolved and unresolved scales. Finally, we develop the d...

Upcoming technologies like digital twins, autonomous, and artificial intelligent systems involving safety-critical applications require accurate, interpretable, computationally efficient, and generalizable models. Unfortunately, the two most commonly used modeling approaches, physics-based modeling (PBM) and data-driven modeling (DDM) struggle to s...

In this paper, we introduce a decentralized digital twin (DDT) framework for dynamical systems and discuss the prospects of the DDT modeling paradigm in computational science and engineering applications. The DDT approach is built on a federated learning concept, a branch of machine learning that encourages knowledge sharing without sharing the act...

A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to...

The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However, it is difficult to train these models on complex dynamical systems from data alone due to their low data effici...

A digital twin is a surrogate model that has the main feature to mirror the original process behavior. Associating the dynamical process with a digital twin model of reduced complexity has the significant advantage to map the dynamics with high accuracy and reduced costs in CPU time and hardware to timescales over which that suffers significantly c...

Upcoming technologies like digital twins, autonomous, and artificial intelligent systems involving safety-critical applications require models which are accurate, interpretable, computationally efficient, and generalizable. Unfortunately, the two most commonly used modeling approaches, physics-based modeling (PBM) and data-driven modeling (DDM) fai...

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these data sets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and e...

There is a growing interest in developing data-driven reduced-order models for atmospheric and oceanic flows that are trained on data obtained either from high-resolution simulations or satellite observations. The data-driven models are non-intrusive in nature and offer significant computational savings compared to large-scale numerical models. The...

We propose a new physics guided machine learning (PGML) paradigm that leverages the variational multiscale (VMS) framework and available data to dramatically increase the accuracy of reduced order models (ROMs) at a modest computational cost. The hierarchical structure of the ROM basis and the VMS framework enable a natural separation of the resolv...

The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However, it is difficult to train these models on complex dynamical systems from data alone due to their low data effici...

Autonomous systems are becoming ubiquitous and gaining momentum within the marine sector. Since the electrification of transport is happening simultaneously, autonomous marine vessels can reduce environmental impact, lower costs, and increase efficiency. Although close monitoring is still required to ensure safety, the ultimate goal is full autonom...

In this paper, we present a brief tutorial on reduced order model (ROM) closures. First, we carefully motivate the need for ROM closure modeling in under-resolved simulations. Then, we construct step by step the ROM closure model by extending the classical Galerkin framework to the spaces of resolved and unresolved scales. Finally, we develop the d...

Dynamic mode decomposition (DMD) is an emerging methodology that has recently attracted computational scientists working on nonintrusive reduced order modeling. One of the major strengths that DMD possesses is having ground theoretical roots from the Koopman approximation theory. Indeed, DMD may be viewed as the data-driven realization of the famou...

Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models for subgrid scale (SGS) processes using physical insights and mathematical approximations, they remain imperf...

The computational models for geophysical flows are computationally very expensive to employ in multi-query tasks such as data assimilation, uncertainty quantification, and hence surrogate models sought to alleviate the computational burden associated with these full order models. Researchers have started applying machine learning algorithms, partic...

View Video Presentation: https://doi.org/10.2514/6.2022-0459.vid The computational models for geophysical flows are computationally very expensive to employ in multi-query tasks such as data assimilation, uncertainty quantification, and hence surrogate models sought to alleviate the computational burden associated with these full order models. Rese...

View Video Presentation: https://doi.org/10.2514/6.2022-2325.vid Dynamic mode decomposition (DMD) is an emerging methodology that has recently attracted computational scientists working on nonintrusive reduced order modeling. One of the major strengths that DMD possesses is having ground theoretical roots from the Koopman approximation theory. Inde...

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposit...

Autonomous systems are becoming ubiquitous and gaining momentum within the marine sector. Since the electrification of transport is happening simultaneously, autonomous marine vessels can reduce environmental impact, lower costs, and increase efficiency. Although close monitoring is still required to ensure safety, the ultimate goal is full autonom...

In this work, we introduce, justify and demonstrate the Corrective Source Term Approach (CoSTA) – a novel approach to Hybrid Analysis and Modeling (HAM). The objective of HAM is to combine physics-based modeling (PBM) and data-driven modeling (DDM) to create generalizable, trustworthy, accurate, computationally efficient and self-evolving models. C...

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this letter, we put forth a nonlinear proper orthogonal decomposit...

Recently, computational modeling has shifted towards the use of deep learning, and other data-driven modeling frameworks. Although this shift in modeling holds promise in many applications like design optimization and real-time control by lowering the computational burden, training deep learning models needs a huge amount of data. This big data is...

This work presents a hybrid modeling approach to data-driven learning and representation of unknown physical processes and closure parameterizations. These hybrid models are suitable for situations where the mechanistic description of dynamics of some variables is unknown, but reasonably accurate observational data can be obtained for the evolution...

The physics-based modeling has been the workhorse for many decades in many scientific and engineering applications ranging from wind power, weather forecasting, and aircraft design. Recently, data-driven models are increasingly becoming popular in many branches of science and engineering due to their non-intrusive nature (i.e., they are equation-fr...

In this study, we present a parametric non-intrusive reduced order modeling framework as a potential digital twin enabler for fluid flow related applications. The case study considered here involves building-induced flows and turbulence with inlet turbulence value as a parameter. The framework proposed employs a Grassmann manifold interpolation app...

For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr–Sommerfeld stability equation and numerous vortex models, of which the von Kármán vortex street is one of the most prominent. Subsequent ROMs typically relied on first principl...

In this paper, we propose a novel reduced order model (ROM) lengthscale definition that is based on energy distribution arguments. This novel ROM lengthscale is fundamentally different from the current ROM lengthscales, which are generally based on dimensional arguments. As a first step in the assessment of the new, energy based ROM lengthscale, we...

The FitzHugh–Nagumo (FHN) model, from computational neuroscience, has attracted attention in nonlinear dynamics studies as it describes the behavior of excitable systems and exhibits interesting bifurcation properties. The accurate estimation of the model parameters is vital to understand how the solution trajectory evolves in time. To this end, we...

For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr-Sommerfeld stability equation (1907) and numerous vortex models, of which the von K\'arm\'an vortex street (1911) is one of the most prominent. Subsequent ROMs typically relied...

The unprecedented amount of data generated from experiments, field observations, and large-scale numerical simulations at a wide range of spatiotemporal scales has enabled the rapid advancement of data-driven and especially deep learning models in the field of fluid mechanics. Although these methods are proven successful for many applications, ther...

Most modeling approaches lie in either of the two categories: physics-based or data-driven. Recently, a third approach which is a combination of these deterministic and statistical models is emerging for scientific applications. To leverage these developments, our aim in this perspective paper is centered around exploring numerous principle concept...

Hybrid Analysis and Modeling (HAM) is an emerging modeling paradigm which aims to combine physics-based modeling (PBM) and data-driven modeling (DDM) to create generalizable, trustworthy, accurate, computationally efficient and self-evolving models. Here, we introduce, justify and demonstrate a novel approach to HAM -- the Corrective Source Term Ap...

A uniform mathematical framework based on probabilistic graphical models drives the digital twin technologies towards dynamical control with real-time data.

In the past couple of years, there has been a proliferation in the use of machine learning approaches to represent subgrid-scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical simulations of these flows. Despite its success for different types of flow, the online deployment of a data-dri...

Digital twins are meant to bridge the gap between real-world physical systems and virtual representations. Both stand-alone and descriptive digital twins incorporate 3D geometric models, which are the physical representations of objects in the digital replica. Digital twin applications are required to rapidly update internal parameters with the evo...

The unprecedented amount of data generated from experiments, field observations, and large-scale numerical simulations at a wide range of spatio-temporal scales have enabled the rapid advancement of data-driven and especially deep learning models in the field of fluid mechanics. Although these methods are proven successful for many applications, th...

This work presents a hybrid analysis and modeling approach to the data-driven learning and representation of unknown physical processes and closure parameterizations. These hybrid models are suitable for situations where the mechanistic description of dynamics of some variables is unknown, but reasonably accurate observational data can be obtained...

Most modeling approaches lie in either of the two categories: physics-based or data-driven. Recently, a third approach which is a combination of these deterministic and statistical models is emerging for scientific applications. To leverage these developments, our aim in this perspective paper is centered around exploring numerous principle concept...

Digital twins are meant to bridge the gap between real-world physical systems and virtual representations. Both stand-alone and descriptive digital twins incorporate 3D geometric models, which are the physical representations of objects in the digital replica. Digital twin applications are required to rapidly update internal parameters with the evo...

We put forth a long short-term memory (LSTM) nudging framework for the enhancement of reduced order models (ROMs) of fluid flows utilizing noisy measurements for air traffic improvements. Toward emerging applications of digital twins in aviation, the proposed approach allows for constructing a realtime predictive tool for wake-vortex transport and...

With the rise of focus on man made changes to our planet and wildlife therein, more and more emphasis is put on sustainable and responsible gathering of resources. In an effort to preserve maritime wildlife the Norwegian government decided to create an overview of the presence and abundance of various species of marine lives in the Norwegian fjords...

Hybrid physics-machine learning models are increasingly being used in simulations of transport processes. Many complex multiphysics systems relevant to scientific and engineering applications include multiple spatiotemporal scales and comprise a multifidelity problem sharing an interface between various formulations or heterogeneous computational e...

The FitzHugh-Nagumo (FHN) model, from computational neuroscience, has attracted attention in nonlinear dynamics studies as it describes the behavior of excitable systems and exhibits interesting bifurcation properties. The accurate estimation of the model parameters is vital to understand how the solution trajectory evolves in time. To this end, we...

Control theory provides engineers with a multitude of tools to design controllers that manipulate the closed-loop behavior and stability of dynamical systems. These methods rely heavily on insights into the mathematical model governing the physical system. However, in complex systems, such as autonomous underwater vehicles performing the dual objec...

The physics-based modeling has been the workhorse for many decades in many scientific and engineering applications ranging from wind power, weather forecasting, and aircraft design. Recently, data-driven models are increasingly becoming popular in many branches of science and engineering due to their non-intrusive nature and online learning capabil...

The Kuramoto-Sivashinsky equation is a nonlinear partial differential equation and is used as a low-dimensional prototype for complex flows due to its chaotic behavior. In this work, we investigate two sequential data assimilation algorithms, namely the stochastic Ensemble Kalman filter and the deterministic Ensemble Kalman filter for capturing the...

Closure modeling offers a feasible method to perform efficient and effective numerical simulations of fluid flows of practical significance using coarse resolutions while including the effects of truncated scales on the flow dynamics. Usually, the unresolved scales correspond to the smaller scales, responsible for energy dissipation (e.g., in turbu...

Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences. In this Letter, we introduce a modular physics guided machine learning framework to improve the accuracy of such data-driven predictive engines. The chief idea in our a...

We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost. The VMS methodology is a natural fit for the hierarchical structure of the ROM basis: In the first step, we use...

Lung sounds refer to the sound generated by air moving through the respiratory system. These sounds, as most biomedical signals, are non-linear and non-stationary. A vital part of using the lung sound for disease detection is discrimination between normal lung sound and abnormal lung sound. In this paper, several approaches for classifying between...

Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences. In this letter, we introduce a modular physics guided machine learning framework to improve the accuracy of such data-driven predictive engines. The chief idea in our a...