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A RANDOM-FOREST-GUIDED COUPLED SELECTION OF DECOMPOSITION ORDER AND PADÉ DEGREE FOR PADÉ-RESUMMED ADOMIAN SERIES: THE FISHER–KPP TRAVELING WAVE | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 آبان 1405 اصل مقاله (1.34 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.73558.3762 | ||
| نویسندگان | ||
| Sathish Marakonda* ؛ Y. Rajashekhar Reddy | ||
| Department of Mathematics, Jawaharlal Nehru Technological University Hyderabad, Telangana, India. | ||
| چکیده | ||
| A truncated Adomian series for the Fisher-KPP traveling wave stops improving after a handful of terms; replacing the truncated sum with a rational Padé approximant is a known remedy, but the two quantities that govern its accuracy - how many series terms to generate and what Padé degree to fit through them - are ordinarily chosen by hand for each new problem. We formulate this choice as a constrained search: find the cheapest Padé degree pair (L,N) whose approximant meets a prescribed accuracy tolerance, then train a random forest regressor to predict that pair directly from three problem parameters (reaction rate, wave-front location, and evaluation time), so that the search need not be repeated for every new configuration. The underlying series is generated symbolically from a rescaled autonomous recursion, evaluated on 45 sampled configurations, and used to train the regressor with a 75/25 holdout split. Across the sampled range, the Padé route meets a tolerance of 0.001 on 42 of 45 configurations against 34 of 45 for size-matched plain truncation. Four configurations withheld entirely from training were then tested: the regressor reproduced the cost-optimal degree pair exactly in three instances and rounded to a configuration one cost unit short of optimal in the fourth. Held-out prediction of the combined cost was strong (R-squared = 0.934); the numerator degree alone was harder to predict in isolation (R-squared = 0.384). | ||
| کلیدواژهها | ||
| Adomian decomposition؛ Pad\'e approximation؛ Fisher--KPP equation؛ random forest regression؛ traveling wave | ||
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