基于生物信息神经网络的方程学习中的超参数选择
Hyperparameter selection for equation learning with biologically-informed neural networks
- Uppsala University（乌普萨拉大学）
- The College of New Jersey（新泽西学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对生物信息神经网络在方程学习中的超参数选择难题，提出一种基于三个诊断问题的结构化工作流程，并在合成系统上验证其有效性，提供实用经验法则和起始值建议。
AI中文摘要：
生物信息神经网络（BINNs）作为物理信息神经网络（PINNs）的一个灵活子类，已出现用于从数据中学习偏微分方程中的项。BINNs特别适用于生物系统，其中控制方程高度非线性且先验仅部分已知，并且数据观测通常稀疏、有噪声且不完整。然而，在实践中有效应用BINNs关键依赖于超参数选择，这仍然是方程学习框架中的核心挑战。超参数通常启发式地选择，并且仅粗略地记录，这限制了结果的可重复性和方法的可迁移性。我们提出了一种用于超参数选择的诊断工作流程，可在真实方程未知时使用。该工作流程由三个主要问题引导：（1）更大网络容量的好处是否值得付出代价？（2）更多的训练轮次是否持续降低验证损失？（3）随着网络容量和训练增加，学习到的项是否停止变化？我们将我们的工作流程应用于具有已知真实方程的不同复杂度的合成系统，涵盖扩散和增长右手边项，数据范围从1D+t到2D+t。我们证明了验证损失通常遵循学习项中的真实误差，并提炼出用于在BINN架构中选择超参数的实用经验法则。通过提供结构化的工作流程、实用指南和建议的超参数选择起始值，这项工作降低了基于BINN的方程学习的门槛。
英文摘要：
Biologically-informed neural networks (BINNs) have emerged as a flexible subclass of physics-informed neural networks (PINNs) for learning terms in partial differential equations from data. BINNs are particularly suited for biological systems, where the governing equations are highly nonlinear and only partially known a priori, and where data observations are often sparse, noisy, and incomplete. However, applying BINNs effectively in practice depends critically on hyperparameter selection, which remains a central challenge in equation-learning frameworks. Hyperparameters are often chosen heuristically and only cursorily documented, which limits the reproducibility of results and the transferability of methods. We present a diagnostic workflow for hyperparameter selection that can be used when the ground-truth equations are not known. The workflow is guided by three main questions: (1) Are the benefits of greater network capacity worth the cost? (2) Do more training epochs keep reducing the validation loss? (3) Do the learned terms stop changing as network capacity and training increase? We apply our workflow to synthetic systems of varying complexity with known ground truth, spanning diffusion and growth right-hand side terms and data ranging from 1D+t to 2D+t. We demonstrate that the validation loss generally follows the true error in the learned terms and distil practical rules of thumb for selecting hyperparameters in the BINN architecture. By providing a structured workflow, practical guidelines, and suggested starting values for hyperparameter selection, this work lowers the barrier to BINN-based equation learning.
