Learning partial differential equations via data discovery and sparse optimization

Solving partial differential equations via sparse SDP

To solve a partial differential equation (PDE) numerically, we formulate it as a polynomial optimization problem (POP) by discretizing it via a finite difference approximation. The resulting POP satisfies a structured sparsity, which we can exploit to apply the sparse SDP relaxation of Waki, Kim, Kojima and Muramatsu [20] to the POP to obtain a roughly approximate solution of the PDE. To comput...

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Data-driven discovery of partial differential equations

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large ...

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Solving partial differential equations via sparse SDP relaxations

To solve a partial differential equation (PDE) numerically, we formulate it as a polynomial optimization problem (POP) by discretizing it via a finite difference approximation. The resulting POP satisfies a structured sparsity, which we can exploit to apply the sparse SDP relaxation of Waki, Kim, Kojima and Muramatsu [20] to the POP to obtain a roughly approximate solution of the PDE. To comput...

متن کامل

1342 - 2804 Solving partial differential equations via sparse SDP

To solve a partial differential equation (PDE) numerically, we formulate it as a polynomial optimization problem (POP) by discretizing it via a finite difference approximation. The resulting POP satisfies a structured sparsity, which we can exploit to apply the sparse SDP relaxation of Waki, Kim, Kojima and Muramatsu [20] to the POP to obtain a roughly approximate solution of the PDE. To comput...

متن کامل

global 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...

Learning partial differential equations via data discovery and sparse optimization

نویسندگان

چکیده

منابع مشابه

Solving partial differential equations via sparse SDP

Data-driven discovery of partial differential equations

Solving partial differential equations via sparse SDP relaxations

1342 - 2804 Solving partial differential equations via sparse SDP

global results on some nonlinear partial differential equations for direct and inverse problems

ژورنال