发表机构
Mathematical Institute, University of Oxford（牛津大学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究生物信息神经网络用于机械算子恢复时网络架构、优化策略等因素对其的影响，通过对典型偏微分方程模型实证研究，发现成功推理依赖平衡目标，给出架构、参数设置建议及失败模式诊断方法，为生物模型发现提供指导。
AI 中文摘要
许多生物过程受复杂动力学机制支配，尽管实验数据增多仍未完全理解。生物信息神经网络（BINNs）通过将机械微分方程嵌入神经网络训练来应对这一挑战，以从稀疏且有噪声的观测中直接恢复可解释的本构算子。然而，可靠的算子恢复敏感地依赖于网络架构、优化策略和数据信息性。本文对这些因素如何影响应用于典型一维平流 - 扩散 - 反应偏微分方程模型的BINNs的机械推理进行了系统实证研究。在一系列基准问题中，研究了网络表达能力、学习率、损失加权和批量大小对优化行为和算子恢复的影响。结果表明成功的机械推理依赖于平衡相互竞争的目标，而非最大化模型或优化的任何单一方面。适度表达的架构优于过于复杂的网络，中等学习率提高优化稳定性，平衡的数据和偏微分方程损失对准确的算子恢复至关重要，中等批量大小在计算效率和可重复性之间提供了最佳折衷。还确定了识别常见失败模式的实用诊断方法。这些发现为将BINNs用作生物模型发现的可靠工具提供了基于证据的指导方针。
英文摘要
Many biological processes are governed by complex dynamical mechanisms that remain incompletely understood despite increasing volumes of experimental data. Biologically-informed neural networks (BINNs) seek to address this challenge by embedding differential equations into neural network training, enabling constitutive operators to be recovered directly from sparse and noisy observations. However, the extent to which operator recovery depends on architectural design, optimisation strategy and the information within the data is not yet well understood. We present an empirical study of how these factors influence mechanistic inference using BINNs applied to one-dimensional advection-diffusion-reaction partial differential equations. Across a suite of problems, we investigate how network expressivity, learning rate, loss weighting and batch size influence optimisation behaviour, reconstruction accuracy and operator recovery. We show that mechanistic inference is governed by balancing competing objectives rather than maximising any single aspect. Moderately expressive architectures outperform complex networks, intermediate learning rates balance efficient exploration with optimisation stability, accurate operator recovery requires a balance between data-fitting and PDE residual losses and intermediate batch sizes provide the best compromise between efficient parameter space exploration, computational efficiency and reproducibility. We further identify practical diagnostics for recognising common failure modes, including over-fitting, unstable optimisation and poor mechanistic recovery. These findings establish guidelines for deploying BINNs as credible tools for biological model discovery and demonstrate that reliable mechanistic inference is achieved by appropriately balancing model expressivity, optimisation, physical consistency and data informativeness.
Comments64 pages, 27 figures
