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.

翻译：常微分方程（ODEs）在物理学、化学和生物学中被广泛用于建模动态系统，包括反应动力学、种群动态和生物过程。在本工作中，我们将GPU加速的ODE求解器集成到开源DeepChem框架中，使这些工具易于获取。这些求解器支持多种数值方法，并且完全可微分，便于集成到更复杂的可微分程序中。我们通过对Lotka-Volterra捕食者-猎物动力学、药代动力学房室模型、神经ODE以及使用反应-扩散方程求解PDE的实验，展示了我们实现的性能。我们的求解器实现了高精度，均方误差范围在$10^{-4}$至$10^{-6}$之间，并在求解多达100个房室的大型系统中展现了良好的可扩展性。