Report
chebgreen: Learning and Interpolating Continuous Empirical Green's Functions from Data
| العنوان: | chebgreen: Learning and Interpolating Continuous Empirical Green's Functions from Data |
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| المؤلفون: | Praveen, Harshwardhan, Brown, Jacob, Earls, Christopher |
| سنة النشر: | 2025 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Mathematics - Numerical Analysis |
| الوصف: | In this work, we present a mesh-independent, data-driven library, chebgreen, to mathematically model one-dimensional systems, possessing an associated control parameter, and whose governing partial differential equation is unknown. The proposed method learns an Empirical Green's Function for the associated, but hidden, boundary value problem, in the form of a Rational Neural Network from which we subsequently construct a bivariate representation in a Chebyshev basis. We uncover the Green's function, at an unseen control parameter value, by interpolating the left and right singular functions within a suitable library, expressed as points on a manifold of Quasimatrices, while the associated singular values are interpolated with Lagrange polynomials. Comment: Code is available at https://github.com/hsharsh/chebgreen |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2501.18715 |
| رقم الانضمام: | edsarx.2501.18715 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |