用神经微分方程动态建模肿瘤生长，提升有限数据下的预测精度。
Adaptive tumor growth forecasting via neural & universal ODEs
- 用神经网络替代经典模型中的固定项，实现自适应建模。
- 在数据有限条件下仍能准确预测肿瘤生长趋势。
- 可将学习到的动态转化为显式数学表达式，适合临床应用。
肿瘤生长预测对优化治疗至关重要。经典增长模型如戈培茨和贝塔兰菲方程虽能描述一般肿瘤动态，但在面对患者个体差异时可能表现不佳，尤其在数据稀缺情况下。本研究利用神经微分方程（Neural ODEs）与通用微分方程（UDEs）——科学机器学习的两大支柱——构建可从实验数据中学习的自适应肿瘤生长模型。以戈培茨模型为基线，我们用自适应神经网络替换其中刚性项，通过 Julia 编程语言实现鲁棒建模，捕捉隐藏动力学。在数据受限条件下进行预测，并完成符号恢复，将学习到的动力学转换为显式数学表达式。该方法有望提升预测准确性，支持动态、高效的治疗策略，改善临床结局。
原文摘要 · Abstract (English)
Forecasting tumor growth is critical for optimizing treatment. Classical growth models such as the Gompertz and Bertalanffy equations capture general tumor dynamics but may fail to adapt to patient-specific variability, particularly with limited data available. In this study, we leverage Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs), two pillars of Scientific Machine Learning (SciML), to construct adaptive tumor growth models capable of learning from experimental data. Using the Gompertz model as a baseline, we replace rigid terms with adaptive neural networks to capture hidden dynamics through robust modeling in the Julia programming language. We use our models to perform forecasting under data constraints and symbolic recovery to transform the learned dynamics into explicit mathematical expressions. Our approach has the potential to improve predictive accuracy, guiding dynamic and effective treatment strategies for improved clinical outcomes.
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