1. On the Structure of Stationary Solutions to McKean-Vlasov Equations with Applications to Noisy Transformers
   2025/10/23 by Krishnakumar Balasubramanian, Balasubramanian, Krishnakumar, Sayan Banerjee +3 · 3 citations
   Engineering · Environmental Science · Physics and Astronomy · #34K18 #35B27 #35Q70 #35Q83 #60H50 #82C22 #Analysis of PDEs (math.AP) #Artificial Intelligence (cs.AI) #Ecosystem dynamics and resilience #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probability (math.PR) #Statistical Mechanics and Entropy #Thermoelastic and Magnetoelastic Phenomena
2. Long-Time Asymptotics of Passive Scalar Transport in Periodically Modulated Channels
   2025/04/20 by Ding, Lingyun · 1 citation
   #35B27 #35B40 #35C20 #35Q35 #76F25 #76M45 #76R50 #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
3. Learning Memory and Material Dependent Constitutive Laws
   2025/02/08 by Bhattacharya, Kaushik, Cao, Lianghao, Stepaniants, George +2 · 1 citation
   #35B27 #65M60 #68T07 #74D05 #74D10 #74Q10 #74Q15 #FOS: Computer and information sciences #FOS: Mathematics #G.1.8 #I.6 #J.2 #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
4. Homogenisation for the Robin eigenvalue problem on manifolds and flexibility of optimal Schrödinger potentials
   2024/11/03 by Lo, Chia-Chun · 1 citation
   #35B27 #35P15 #47A75 (Secondary) #58C40 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)
5. Effective interface laws for fluid flow and solute transport through thin reactive porous layers
   2024/09/24 by Gahn, Markus, Neuss-Radu, Maria · 3 citations
   #35B27 #35K57 #35K61 #76M50 #Analysis of PDEs (math.AP) #FOS: Mathematics
6. Asymptotics for Random Quadratic Transportation Costs
   2024/09/13 by Martin Huesmann, Michaël Goldman, Huesmann, Martin +3 · 3 citations
   Computer Science · Mathematics · #35B27 #49Q22 #60D05 #60L99 #90C05 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Point processes and geometric inequalities #Probability (math.PR) #Statistics Theory (math.ST)
7. Finite element approximation of stationary Fokker--Planck--Kolmogorov equations with application to periodic numerical homogenization
   2024/09/11 by Sprekeler, Timo, Süli, Endre, Zhang, Zhiwen · 2 citations
   #35B27 #35J15 #65N12 #65N15 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)
8. New unexpected limit operators for homogenizing optimal control parabolic problems with dynamic reaction flow on the boundary of critically scaled particles
   2024/06/26 by Diaz, Jesus Ildefonso, Podolskiy, Alexander V., Shaposhnikova, Tatiana A. · 1 citation
   #35B27 #35K20 #49K20 #93C20 #Analysis of PDEs (math.AP) #FOS: Mathematics
9. Homogenization of non-local energies on disconnected sets
   2024/05/15 by Braides, Andrea, Scalabrino, Sergio, Trifone, Chiara · 1 citation
   #26A33 #35B27 #49J45 #74A70 #74Q05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)
10. Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications
    2024/05/02 by Yuxi Han, Han, Yuxi, Wenjia Jing +5 · 3 citations
    Computer Science · Engineering · #35B10 #35B27 #35B40 #35F21 #49L25 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Control and Stability of Dynamical Systems #FOS: Mathematics
11. Quantitative homogenization and hydrodynamic limit of non-gradient exclusion process
    2024/04/18 by Tadahisa Funaki, Chenlin Gu, Funaki, Tadahisa +3 · 4 citations
    Computer Science · Mathematics · Physics and Astronomy · #35B27 #60K35 #82C22 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
12. Thermo-Elasticity Problems with Evolving Microstructures
    2024/04/15 by Michael Eden, Adrian Muntean, Eden, Michael +1 · 1 citation
    Computer Science · Engineering · #35B27 #35K55 #35R37 #80A22 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics
13. Tensor Neural Network Based Machine Learning Method for Elliptic Multiscale Problems
    2024/03/25 by Zhongshuo Lin, Lin, Zhongshuo, Haochen Liu +3 · 1 citation
    Computer Science · Earth and Planetary Sciences · Engineering · #35B27 #65L15 #65M05 #68T07 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geological Modeling and Analysis #Numerical Analysis (math.NA)
14. A Darcy law with memory by homogenisation for evolving microstructure
    2024/03/13 by Wiedemann, David, Peter, Malte A. · 2 citations
    #35B27 #35R37 #76D07 #76M50 #76S05 #Analysis of PDEs (math.AP) #FOS: Mathematics
15. Tiny fluctuations of the averaging process around its degenerate steady state
    2024/03/04 by Sau, Federico · 1 citation
    #35B27 #60K35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
16. The Neumann sieve problem revisited
    2024/02/26 by Khrabustovskyi, Andrii · 1 citation
    #35B27 #35B40 #35P05 #47A55 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)
17. Lagrangian, Game Theoretic and PDE Methods for Averaging G-equations in Turbulent Combustion: Existence and Beyond
    2024/01/26 by Jack Xin, Yifeng Yu, Xin, Jack +3 · 2 citations
    Engineering · Environmental Science · Mathematics · #35B27 #35B40 #35F21 #35Q-XX #Analysis of PDEs (math.AP) #Atmospheric and Environmental Gas Dynamics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical methods for differential equations
18. Quantitative equilibrium fluctuations for interacting particle systems
    2024/01/18 by Gu, Chenlin, Mourrat, Jean-Christophe, Nitzschner, Maximilian · 1 citation
    #35B27 #60K35 #82C22 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)
19. Solving High-dimensional Parametric Elliptic Equation Using Tensor Neural Network
    2024/01/15 by Chen, Hongtao, Fu, Rui, Wang, Yifan +1 · 1 citation
    #35B27 #60H15 #60H35 #68T07 #FOS: Mathematics #Numerical Analysis (math.NA)
20. Effective models for generalized Newtonian fluids through a thin porous medium following the Carreau law
    2023/12/04 by María Anguiano, Matthieu Bonnivard, Anguiano, Maria +3 · 4 citations
    Chemical Engineering · Computer Science · Engineering · #35B27 #35Q35 #76A05 #76A20 #76M50 #76S05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Rheology and Fluid Dynamics Studies
21. Homogenized lattice Boltzmann methods for fluid flow through porous media -- part I: kinetic model derivation
    2023/10/23 by Simonis, Stephan, Hafen, Nicolas, Jeßberger, Julius +3 · 1 citation
    #35B27 #35Q20 #35Q30 #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)
22. Homogenization of a nonlinear elliptic problem with imperfect rough interface
    2023/10/19 by Monsurrò, S., Perugia, C., Raimondi, F. · 1 citation
    #35B27 #35J60 #35J66 #35Q92 #Analysis of PDEs (math.AP) #FOS: Mathematics
23. Homogenisation of nonlinear Dirichlet problems in randomly perforated domains under minimal assumptions on the size of perforations
    2023/07/21 by Lucia Scardia, Konstantinos Zemas, Scardia, Lucia +3 · 2 citations
    Computer Science · Mathematics · #35B27 #49J45 #49J55 #60F15 #60G10 #60G55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Probability (math.PR)
24. Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. II
    2023/07/03 by Cherednichenko, Kirill, Kiselev, Alexander, Velčić, Igor +1 · 3 citations
    #35B27 #47A10 #47N50 #81U30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 35Q99 #Secondary 47F05
25. Another look at elliptic homogenization
    2023/06/21 by Braides, Andrea, Brusca, Giuseppe Cosma, Donati, Davide · 3 citations
    #35B27 #35R11 #49J45 #Analysis of PDEs (math.AP) #FOS: Mathematics
26. Learning Homogenization for Elliptic Operators
    2023/06/21 by Kaushik Bhattacharya, Nikola Kovachki, Bhattacharya, Kaushik +7 · 2 citations
    Computer Science · Engineering · #35B27 #35J47 #74H15 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Composite Material Mechanics #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
27. Anomalous diffusion by fractal homogenization
    2023/05/08 by Scott A. Armstrong, Armstrong, Scott, Vlad Vicol +1 · 4 citations
    Computer Science · Mathematics · Physics and Astronomy · #35B27 #35Q35 #76F25 #76F30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Theoretical and Computational Physics
28. Bifurcation of homogenization and nonhomogenization of the curvature G-equation with shear flows
    2023/03/28 by Hiroyoshi Mitake, Mitake, Hiroyoshi, Connor Mooney +7 · 2 citations
    Computer Science · Mathematics · #35B10 #35B27 #35J93 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows
29. Rate of Convergence in Periodic Homogenization for Convex Hamilton-Jacobi Equations with Multiscales
    2023/03/10 by Yuxi Han, Han, Yuxi, Ji-Woong Jang +1 · 3 citations
    Computer Science · Mathematics · #35B27 #35F21 #41A25 #49L25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations
30. A continuous dependence estimate for viscous Hamilton-Jacobi equations on networks with applications
    2023/03/08 by Fabio Camilli, Camilli, Fabio, Claudio Marchi +1 · 1 citation
    Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #35B27 #35R02 #49N70 #91A16 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Optimization and Control (math.OC)

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