- On the inadequacy of nudging data assimilation algorithms for non-dissipative systems
2024/11/13 by Edriss S. Titi, Collin Victor, Titi, Edriss S. +1 · 1 citation
Earth and Planetary Sciences · Engineering · #34D06 #35Q53 #35Q93 #37N35 #93C20 #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Geophysics and Gravity Measurements #Mathematical Physics (math-ph) #Meteorological Phenomena and Simulations #Optimization and Control (math.OC)
- Emergence of meta-stable clustering in mean-field transformer models
2024/10/30 by Bruno, Giuseppe, Pasqualotto, Federico, Agazzi, Andrea · 11 citations
#34D05 #34D06 #35Q83 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG)
- An Assessment of Ensemble Kalman Filter and Azouani-Olson-Titi Algorithms for Data Assimilation: A Comparative Study
2024/07/24 by Ning, Ning, Victor, Collin · 1 citation
#34D06 #35Q93 #37N10 #62F15 #93C20 #93E11 #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)
- Application of Continuous Data Assimilation in High-Resolution Ocean Modeling
2023/08/04 by Larios, Adam, Petersen, Mark R., Victor, Collin · 1 citation
#34D06 #35Q86 #35Q93 #37N10 #86A05 #93C20 #Analysis of PDEs (math.AP) #Atmospheric and Oceanic Physics (physics.ao-ph) #FOS: Mathematics #FOS: Physical sciences #Geophysics (physics.geo-ph)
- Super-exponential convergence rate of a nonlinear continuous data assimilation algorithm: The 2D Navier-Stokes equations paradigm
2023/04/03 by Elizabeth Carlson, Carlson, Elizabeth, Adam Larios +3 · 4 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #34D06 #35K61 #35Q93 #93C20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Stochastic processes and financial applications
- Stable Synchronous Propagation of Signals by Feedforward Networks
2023/02/08 by Stewart, Ian, Wood, David · 1 citation
#05C20 #34A34 #34C15 #34C25 #34D06 #34D20 #37C27 #37C75 #37C80 #37N25 #92B25 #92C20 #92C42 #Dynamical Systems (math.DS) #FOS: Mathematics
- Global well-posedness of a three-dimensional Brinkman-Forchheimer-Bénard convection model in porous media
2022/04/07 by Titi, Edriss S., Trabelsi, Saber · 1 citation
#34D06 #35Q30 #35Q35 #37C50 #76B03 #76B75 #86A10 #93C20 #Analysis of PDEs (math.AP) #FOS: Mathematics
- Collective behaviors of second-order nonlinear consensus models with a bonding force
2021/12/30 by Hyunjin Ahn, Junhyeok Byeon, Ahn, Hyunjin +5 · 1 citation
Computer Science · Materials Science · Physics and Astronomy · #34D06 #70F10 #70G60 #92D25 #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Mathematics #Material Dynamics and Properties #Nonlinear Dynamics and Pattern Formation
- Dynamically learning the parameters of a chaotic system using partial observations
2021/08/18 by Elizabeth Carlson, Carlson, Elizabeth, Joshua Hudson +9 · 5 citations
Computer Science · Physics and Astronomy · #34A55 #34D06 #34H10 #35B30 #37C50 #60H10 #Chaos control and synchronization #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Model Reduction and Neural Networks #Neural Networks and Applications #Optimization and Control (math.OC)
- Continuous Data Assimilation For the 3D Ladyzhenskaya Model: Analysis and Computations
2021/08/07 by Cao, Yu, Giorgini, Andrea, Jolly, Michael +1 · 5 citations
#34D06 #76A05 #76D03 #Analysis of PDEs (math.AP) #Computational Physics (physics.comp-ph) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
- Data Assimilation with Higher Order Finite Element Interpolants
2021/08/08 by Jolly, Michael S., Pakzad, Ali · 1 citation
#34D06 #35Q93 #76B75 #Computational Physics (physics.comp-ph) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Numerical Analysis (math.NA) #Primary 35Q30 #Secondary 35Q35
- Data assimilation for the Navier-Stokes equations using local observables
2020/08/16 by Biswas, Animikh, Bradshaw, Zachary, Jolly, Michael S. · 1 citation
#34D06 #35Q93 #76B75 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35Q30 #Secondary 35Q35
- Continuous Data Assimilation with a Moving Cluster of Data Points for a\n Reaction Diffusion Equation: A Computational Study
2018/12/04 by Adam Larios, Collin Victor, Larios, Adam +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #34D06 #35K40 #35K57 #35K61 #35Q93 #37C50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Number Theory (math.NT) #Optimization and Control (math.OC) #Stochastic processes and financial applications
- A detectability criterion and data assimilation for non-linear differential equations
2017/11/14 by Frank, Jason, Zhuk, Sergiy · 1 citation
#34D06 #37C50 #37M25 #62M20 #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Geophysics (physics.geo-ph) #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
- A data assimilation algorithm for the subcritical surface quasi-geostrophic equation
2016/07/28 by Jolly, Michael S., Martinez, Vincent R., Titi, Edriss S. · 3 citations
#34D06 #35Q35 #35Q86 #37C50 #76B75 #93C20 #Analysis of PDEs (math.AP) #FOS: Mathematics
- Data Assimilation algorithm for 3D Bénard convection in porous media employing only temperature measurements
2015/06/29 by Farhat, Aseel, Lunasin, Evelyn, Titi, Edriss S. · 4 citations
#34D06 #35Q30 #37C50 #76B75 #93C20 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Geophysics (physics.geo-ph)