Particles to partial differential equations parsimoniously
نویسندگان
چکیده
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential (PDEs), can explain system evolution much coarser, meso- or macroscopic length scales. Discovering those coarse-grained effective PDEs lead to considerable savings computation-intensive tasks like prediction control. We propose a framework combining artificial neural networks with multiscale computation, equation-free numerics, for efficient discovery such macro-scale directly from simulations. Gathering sufficient data training be computationally prohibitive; numerics enable more parsimonious collection by only operating sparse subset space-time domain. also using data-driven approach, based on manifold learning and unnormalized optimal transport distributions, identify dependent variable(s) suitable said PDEs. This approach corroborate physically motivated candidate variables, introduce new terms which PDE formulated. illustrate our extracting equations particle-based simulations priori unknown variable(s), while significantly reducing requisite computational effort.
منابع مشابه
Partial Differential Equations applied to Medical Image Segmentation
This paper presents an application of partial differential equations(PDEs) for the segmentation of abdominal and thoracic aortic in CTA datasets. An important challenge in reliably detecting aortic is the need to overcome problems associated with intensity inhomogeneities. Level sets are part of an important class of methods that utilize partial differential equations (PDEs) and have been exte...
متن کاملglobal results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Partial Differential Equations Midterm
1), find the explicit fundamental solution to the heat equation ∆u + b · ∇u − u t = 0 in R n × (0, ∞). (1) Letting G be what you find, show u 0 (x) = lim t→0 + R n G(x, t; y, 0)u 0 (y) dy, (2) when u 0 is bounded and continuous on R n. Taking the Fourier transform (with respect to x) of the equation gives −|ξ| 2 ˆ u + ib · ξ ˆ u − ˆ u t = 0 − |ξ| 2 + ib · ξ ˆ u = ˆ u t =⇒û = ce −(|ξ| 2 +ib·ξ)t ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Chaos
سال: 2021
ISSN: ['1527-2443', '1089-7682', '1054-1500']
DOI: https://doi.org/10.1063/5.0037837