arXiv：cs.LG· Rebecca M. Crossley, Yuan Yin, Sarah L. Waters, Ruth E. Baker·· 5 小时前AI 评分32
生物信息神经网络（BINNs）如何可靠恢复机制算子：架构与优化设计原则
Reliable mechanistic operator recovery with biologically-informed neural networks: principles for architecture and optimisation design
AI 导读
一项针对一维对流-扩散-反应 PDE 的实证研究显示，生物信息神经网络（BINNs）的机制推断取决于多目标平衡而非单一指标最大化。中等表达力架构优于复杂网络，中间学习率兼顾探索效率与优化稳定性，算子恢复需平衡数据拟合与 PDE 残差损失，中等 batch size 在参数空间探索、计算效率与可复现性间取得最佳折中。研究还给出识别过拟合、优化不稳定与机制恢复不佳等常见失败模式的实用诊断方法。
正文
Abstract: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.
| Comments: | 64 pages, 27 figures |
| Subjects: | Quantitative Methods (q-bio.QM); Machine Learning (cs.LG) |
| Cite as: | arXiv:2607.07425 [q-bio.QM] |
| (or arXiv:2607.07425v2 [q-bio.QM] for this version) | |
| https://doi.org/10.48550/arXiv.2607.07425 arXiv-issued DOI via DataCite |
Submission history
From: Rebecca Crossley [view email]
[v1]
Wed, 8 Jul 2026 13:52:50 UTC (12,867 KB)
[v2]
Fri, 2 Oct 2026 13:39:47 UTC (16,275 KB)
来源：arXiv：cs.LG · arxiv.org