开源工具包让微分方程求解器支持梯度计算，便于集成到深度学习模型中。
Open source Differentiable ODE Solving Infrastructure
- 将多种可微分的微分方程求解器集成进DeepChem框架
- 在多个系统上实现10⁻⁴至10⁻⁶的高精度，支持最多100个组分的大规模求解
- 适合需要可微分建模的科研人员，如生物动力学、药代动力学研究
常微分方程（ODE）广泛用于物理、化学和生物学中对动态系统建模，包括反应动力学、种群动态和生物过程。本文将支持多种数值方法的GPU加速可微分ODE求解器集成到开源DeepChem框架中，使这些工具更易获取。求解器完全可微，可无缝嵌入复杂可微程序。我们通过洛特卡-沃尔泰拉捕食者-猎物模型、药代动力学隔室模型、神经微分方程以及基于反应-扩散方程的偏微分方程求解实验展示了其能力。结果表明，求解器在各类任务中均达到高精度，平均平方误差介于10⁻⁴至10⁻⁶之间，并能有效扩展至包含最多100个隔室的大型系统。
原文摘要 · Abstract (English)
Ordinary Differential Equations (ODEs) are widely used in physics, chemistry, and biology to model dynamic systems, including reaction kinetics, population dynamics, and biological processes. In this work, we integrate GPU-accelerated ODE solvers into the open-source DeepChem framework, making these tools easily accessible. These solvers support multiple numerical methods and are fully differentiable, enabling easy integration into more complex differentiable programs. We demonstrate the capabilities of our implementation through experiments on Lotka-Volterra predator-prey dynamics, pharmacokinetic compartment models, neural ODEs, and solving PDEs using reaction-diffusion equations. Our solvers achieved high accuracy with mean squared errors ranging from $10^{-4}$ to $10^{-6}$ and showed scalability in solving large systems with up to 100 compartments.
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