Works (46)
Updated: July 15th, 2024 05:25
2024 article
Enforcing conserved quantities in Galerkin truncation and finite volume discretization
Hilliard, Z. T., & Farazmand, M. (2024, June 24). NONLINEAR DYNAMICS, Vol. 6.
author keywords: Galerkin truncation; Finite volume method; Model order reduction; Partial differential equations
Sources: ORCID, Web Of Science, NC State University Libraries
Added: July 8, 2024
2024 journal article
Modeling correlated uncertainties in stochastic compartmental models
MATHEMATICAL BIOSCIENCES, 374.
author keywords: Epidemiology; Compartmental models; Uncertainty quantification; Correlated noise; Noise-induced transitions; COVID-19
open access via arxiv.org (repository)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: July 1, 2024
2023 journal article
Fast and scalable computation of shape-morphing nonlinear solutions with application to evolutional neural networks
JOURNAL OF COMPUTATIONAL PHYSICS, 498.
author keywords: Partial different i a l equations; Reduced-order modeling; Spectral methods; Neural networks
TL;DR:
Three separate methods are developed to address computational bottlenecks in reduced-order nonlinear solutions (RONS) by making it possible to use RONS for accurate numerical solution of linear and nonlinear PDEs.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: January 2, 2024
2023 journal article
Fisher information and shape-morphing modes for solving the Fokker-Planck equation in higher dimensions
APPLIED MATHEMATICS AND COMPUTATION, 467.
author keywords: Partial differential equations; Stochastic differential equations; Fokker-Planck equation; Neural networks; Information theory
Sources: Web Of Science, NC State University Libraries, ORCID
Added: January 16, 2024
2023 journal article
Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties
author keywords: COVID-19; compartmental models; epidemiology; uncertainty quantification; correlated noise; noise-induced transitions
TL;DR:
It is proved that the correlated Ornstein–Uhlenbeck (OU) process is the appropriate tool for modelling uncertainties in the infectivity rate of the COVID-19 pandemic and an exact closed-form solution for the final distribution of infected individuals is derived.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science; OpenAlex)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: April 17, 2023
2023 journal article
Tensor-based flow reconstruction from optimally located sensor measurements
JOURNAL OF FLUID MECHANICS, 962.
author keywords: low-dimensional models; big data; computational methods
TL;DR:
This work introduces a tensor-based sensor placement and flow reconstruction method which retains and exploits the inherent multidimensionality of the flow and is significantly more accurate than similar vectorized methods.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water
(OpenAlex)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 7, 2023
2022 journal article
EVOLUTION OF NONLINEAR REDUCED-ORDER SOLUTIONS FOR PDEs WITH CONSERVED QUANTITIES
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 44(1), A176–A197.
author keywords: model order reduction; partial differential equations; conservation laws; Galerkin projection
Sources: ORCID, Web Of Science, NC State University Libraries
Added: February 15, 2022
2022 journal article
Model-assisted deep learning of rare extreme events from partial observations
CHAOS, 32(4).
MeSH headings : Computer Simulation; Deep Learning; Memory, Long-Term; Neural Networks, Computer; Reproducibility of Results
TL;DR:
Long short-term memory networks are found to be most robust to noise and to yield relatively accurate predictions, while requiring minimal fine-tuning of the hyperparameters.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: May 16, 2022
2022 journal article
Quantifying rare events in spotting: How far do wildfires spread?
FIRE SAFETY JOURNAL, 132.
author keywords: Firebrand transport; Spotting; Monte Carlo method; Rare event simulation; Large deviation theory
UN Sustainable Development Goal Categories
13. Climate Action
(Web of Science)
15. Life on Land
(Web of Science)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: July 23, 2022
2022 article
Shape-morphing reduced-order models for nonlinear Schrodinger equations
Anderson, W., & Farazmand, M. (2022, April 25). NONLINEAR DYNAMICS, Vol. 4.
author keywords: Model order reduction; Partial differential equations; Nonlinear Schrodinger equation; Variational methods
Sources: Web Of Science, NC State University Libraries, ORCID
Added: May 10, 2022
2021 journal article
Data-driven prediction of multistable systems from sparse measurements
CHAOS, 31(6).
TL;DR:
A data-driven method, based on semi-supervised classification, to predict the asymptotic state of multistable systems when only sparse spatial measurements of the system are feasible, and proves that the proposed SPML optimization is convex, its minimizer is non-degenerate, and it is equivariant with respect to the scaling of the constraints.
(via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: September 11, 2021
2021 journal article
Evolution of nonlinear reduced-order solutions for PDEs with conserved quantities
SIAM J. on Scientific Computing, In Press. https://arxiv.org/abs/2104.13515
Source: ORCID
Added: November 28, 2021
2021 journal article
Investigating climate tipping points under various emission reduction and carbon capture scenarios with a stochastic climate model
author keywords: climate transition; tipping points; transient growth; bifurcation; stochastic differential equations
UN Sustainable Development Goal Categories
2. Zero Hunger
(Web of Science)
13. Climate Action
(Web of Science; OpenAlex)
15. Life on Land
(Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: January 3, 2022
2021 journal article
Mitigation of rare events in multistable systems driven by correlated noise
PHYSICAL REVIEW E, 104(3).
TL;DR:
It is shown that undesirable transitions can be mitigated by a simple time-delay feedback control if the control parameters are judiciously chosen, and a parsimonious method for selecting the optimal control parameters is devised, without requiring any Monte Carlo simulations of the system.
(via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: September 11, 2021
2020 journal article
MULTISCALE ANALYSIS OF ACCELERATED GRADIENT METHODS
SIAM JOURNAL ON OPTIMIZATION, 30(3), 2337–2354.
author keywords: convex optimization; accelerated gradient methods; invariant manifolds; singular perturbation theory
TL;DR:
It is shown that, under certain conditions, the accelerated gradient flow possesses an attracting invariant slow manifold to which the trajectories of the flow converge asymptotically, and a general explicit expression in the form of functional series expansions that approximates theslow manifold to any arbitrary order of accuracy is obtained.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: October 26, 2020
2020 journal article
Mitigation of tipping point transitions by time-delay feedback control
CHAOS, 30(1).
TL;DR:
These results eliminate the need for any Monte Carlo simulations of the stochastic differential equations and, therefore, significantly reduce the computational cost of determining the suitable control parameters.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
2. Zero Hunger
(Web of Science)
13. Climate Action
(Web of Science; OpenAlex)
15. Life on Land
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: June 29, 2020
2020 journal article
Vortex boundaries as barriers to diffusive vorticity transport in two-dimensional flows
PHYSICAL REVIEW FLUIDS, 5(2).
UN Sustainable Development Goal Categories
13. Climate Action
(Web of Science)
14. Life Below Water
(Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: March 10, 2020
2019 journal article
Are extreme dissipation events predictable in turbulent fluid flows?
Physical Review Fluids.
Source: ORCID
Added: December 2, 2019
2019 journal article
Closed-loop adaptive control of extreme events in a turbulent flow
PHYSICAL REVIEW E, 100(3).
TL;DR:
This work introduces a control strategy for mitigating extreme events in a turbulent shear flow that combines a probabilistic prediction of the extreme events with a deterministic actuator and proposes that such adaptive low-dimensional controllers should be used to mitigateextreme events in general chaotic dynamical systems, beyond the shear flowed here.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: October 7, 2019
2019 journal article
Closure to “Discussion of ‘Extreme Events: Mechanisms and Prediction’” (Grigoriu, M. D., and Uy, W. I. T., ASME Appl. Mech. Rev., 2019, 71(5), p. 055501)
Applied Mechanics Reviews.
Source: ORCID
Added: December 2, 2019
2019 journal article
Mitigation of tipping point transitions by time-delay feedback control
ArXiv Preprint ArXiv:1911.05292.
Source: ORCID
Added: December 2, 2019
2019 journal article
Surface Waves Enhance Particle Dispersion
Fluids.
author keywords: turbulent dispersion; waves; stokes drift
Source: ORCID
Added: December 2, 2019
2018 journal article
Extreme Events: Mechanisms and Prediction
Applied Mechanics Reviews, 71(5).
TL;DR:
Several aspects of extreme events in phenomena described by high-dimensional, chaotic dynamical systems are reviewed, focusing on two pressing aspects of the problem: Mechanisms underlying the formation ofextreme events and real-time prediction of extremeEvents.
(via Semantic Scholar)
Source: ORCID
Added: December 2, 2019
2018 journal article
Physics-based probing and prediction of extreme events
SIAM News, 51(1), 1, 3. https://www.researchgate.net/profile/Mohammad_Farazmand/publication/323245041_Physics-based_probing_and_prediction_of_extreme_events/links/5a887e4daca272017e5f5bef/Physics-based-probing-and-prediction-of-extreme-events.pdf
Source: NC State University Libraries
Added: November 8, 2020
2017 journal article
A critical comparison of Lagrangian methods for coherent structure detection
Chaos: An Interdisciplinary Journal of Nonlinear Science.
Source: ORCID
Added: December 2, 2019
2017 journal article
A variational approach to probing extreme events in turbulent dynamical systems
Science Advances, 3(9), e1701533.
TL;DR:
It is found that the intermittent bursts of the energy dissipation are independent of the external forcing and are instead caused by the spontaneous transfer of energy from large scales to the mean flow via nonlinear triad interactions.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
13. Climate Action
(OpenAlex)
Source: ORCID
Added: December 2, 2019
2017 journal article
Optimal initial condition of passive tracers for their maximal mixing in finite time
Physical Review Fluids.
Source: ORCID
Added: December 2, 2019
2017 journal article
Reduced-order description of transient instabilities and computation of finite-time Lyapunov exponents
Chaos: An Interdisciplinary Journal of Nonlinear Science.
TL;DR:
It is proved that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy-Green tensor associated with the most intense finite-time instabilities.
(via Semantic Scholar)
Source: ORCID
Added: December 2, 2019
2017 journal article
Reduced-order prediction of rogue waves in two-dimensional deep-water waves
Journal of Computational Physics.
author keywords: Prediction of rogue waves; Extreme rare events; Modulation instability and focusing; Random waves; Reduced-order stochastic prediction
TL;DR:
This work considers the problem of large wave prediction in two-dimensional water waves and proposes a robust and parsimonious reduced-order prediction scheme for large waves based on the decomposition of the wave field into a discrete set of localized wave groups with optimal length scales and amplitudes.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water
(OpenAlex)
Source: ORCID
Added: December 2, 2019
2017 journal article
Relative periodic orbits form the backbone of turbulent pipe flow
Journal of Fluid Mechanics.
author keywords: nonlinear dynamical systems; turbulence modelling; turbulent flows
Source: ORCID
Added: December 2, 2019
2016 journal article
An adjoint-based approach for finding invariant solutions of Navier–Stokes equations
Journal of Fluid Mechanics.
author keywords: chaos; intermittency; transition to turbulence
Source: ORCID
Added: December 2, 2019
2016 journal article
Defining coherent vortices objectively from the vorticity
Journal of Fluid Mechanics, 795, 136–173.
author keywords: nonlinear dynamical systems; topological fluid dynamics; vortex dynamics
Sources: Crossref, NC State University Libraries
Added: December 9, 2019
2016 journal article
Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems
Physical Review E.
TL;DR:
This work proposes indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates and uses Bayesian statistics to quantify the predictive power of the proposed indicators.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation
(OpenAlex)
Source: ORCID
Added: December 2, 2019
2016 journal article
Kinematics of fluid particles on the sea surface: Hamiltonian theory
Journal of Fluid Mechanics, 801, 260–288.
author keywords: general fluid mechanics; Hamiltonian theory; waves/free-surface flows
UN Sustainable Development Goal Categories
14. Life Below Water
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: December 9, 2019
2015 journal article
Asymptotic Dynamics of Inertial Particles with Memory
Journal of Nonlinear Science, 25(6), 1225–1255.
author keywords: Inertial particles; Fractional calculus; Integro-differential equations; Maxey-Riley equation; Solid-fluid interaction
Sources: Crossref, NC State University Libraries
Added: December 9, 2019
2015 journal article
Attraction-based computation of hyperbolic Lagrangian coherent structures
Journal of Computational Dynamics, 2(1), 83–93.
TL;DR:
This work develops a new approach to compute arbitrary positions of hyperbolic LCS in a numerically robust fashion, which only involves the advection of attracting material surfaces, thereby providing accurate LCS tracking at low computational cost.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: December 9, 2019
2015 journal article
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(8), 087412.
TL;DR:
It is obtained that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic incoherent Lagrangians attract ( repel) positively (negatively) buoyancy-based particles.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: December 9, 2019
2015 journal article
Polar rotation angle identifies elliptic islands in unsteady dynamical systems
Physica D: Nonlinear Phenomena, 315, 1–12.
author keywords: Non-autonomous dynamical systems; Invariant tori; Coherent structures; Turbulence; Polar decomposition
UN Sustainable Development Goal Categories
14. Life Below Water
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: December 9, 2019
2014 journal article
How coherent are the vortices of two-dimensional turbulence?
ArXiv Preprint ArXiv:1402.4835.
Source: ORCID
Added: December 2, 2019
2014 journal article
Shearless transport barriers in unsteady two-dimensional flows and maps
Physica D, 278-279, 44–57.
author keywords: Dynamical systems; Shearless transport barriers; Invariant tori; Lagrangian coherent structures; Mixing
Source: ORCID
Added: December 2, 2019
2014 journal article
The Maxey-Riley Equation: Existence, Uniqueness and Regularity of Solutions
J. Nonliner Analysis-B.
author keywords: Inertial particles; Fractional-order differential equations; Integro-differential equations; Maxey-Riley equation
Source: ORCID
Added: December 2, 2019
2013 journal article
Attracting and repelling Lagrangian coherent structures from a single computation
Chaos, 15, 023101.
TL;DR:
This work shows how both repelling and attracting hyperbolic LCSs are computable at the same time instance from a single forward or a single backward run.
(via Semantic Scholar)
Source: ORCID
Added: December 2, 2019
2013 journal article
Detecting invariant manifolds, attractors, and generalized KAM tori in aperiodically forced mechanical systems
Nonlinear Dynamics, 73(1-2), 689–704.
author keywords: Stability of mechanical systems; Non-autonomous dynamical systems; Invariant manifolds; Coherent structures
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions
(OpenAlex)
Source: ORCID
Added: December 2, 2019
2012 journal article
Computing Lagrangian Coherent Structures from their variational theory
Chaos, 22, 013128.
MeSH headings : Algorithms; Computer Simulation; Nonlinear Dynamics; Oscillometry / methods; Rheology / methods
TL;DR:
A computational approach is introduced that renders attracting and repelling LCSs as smooth, parametrized curves in two-dimensional flows as trajectories of an autonomous ordinary differential equation for the tensor lines of the Cauchy-Green strain tensor.
(via Semantic Scholar)
Source: ORCID
Added: December 2, 2019
2011 journal article
Erratum and addendum to ``A variational theory of hyperbolic Lagrangian coherent structures, Physica D 240 (2011) 574-598''
Physica D, 241, 439–441.
Source: ORCID
Added: December 2, 2019
2010 journal article
Controlling the dual cascade of two-dimensional turbulence
J. Fluid Mech., 668, 202–222.
author keywords: turbulence control; turbulence simulation; turbulence theory
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy
(OpenAlex)
Source: ORCID
Added: December 2, 2019
Employment
Updated: August 29th, 2019 23:00
2019 - present
North Carolina State University Raleigh, NC, US
Assistant Professor
Mathematics
2015 - 2019
Massachusetts Institute of Technology Cambridge, MA, US
Postdoctoral Associate
2014 - 2015
Georgia Institute of Technology Atlanta, GA, US
Postdoc
Physics
Education
Updated: January 6th, 2017 16:00
ETH Zurich Zurich, CH
PhD
Mathematics
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