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<p>Approximate solutions to certain partial differential equations can be expressed in a finite form using basic operations, such as sums, products, and compositions of elementary functions. To obtain adequate expressions that also fit observational data, it is necessary to estimate parameters. For this purpose, well established optimization techniques can be employed with modifications and adaptations that may be applied to a broad family of problems. In this paper, we consider the equations governing the flux of natural channels and propose a closed-form expression with parameters whose estimation requires adapting and modifying box-constraint minimization methods. Numerical results are reported and discussed.</p>

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Optimization tools for PDE-Informed regression in river model training

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • José Mario Martínez

摘要

Approximate solutions to certain partial differential equations can be expressed in a finite form using basic operations, such as sums, products, and compositions of elementary functions. To obtain adequate expressions that also fit observational data, it is necessary to estimate parameters. For this purpose, well established optimization techniques can be employed with modifications and adaptations that may be applied to a broad family of problems. In this paper, we consider the equations governing the flux of natural channels and propose a closed-form expression with parameters whose estimation requires adapting and modifying box-constraint minimization methods. Numerical results are reported and discussed.