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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2411.19882 |
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| _version_ | 1866915040638009344 |
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| author | Singh, Rakshit Kr. Menezes, Aaron Rock Irfan, Rida Ramsundar, Bharath |
| author_facet | Singh, Rakshit Kr. Menezes, Aaron Rock Irfan, Rida Ramsundar, Bharath |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Open source Differentiable ODE Solving Infrastructure Singh, Rakshit Kr. Menezes, Aaron Rock Irfan, Rida Ramsundar, Bharath Machine Learning 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. |
| title | Open source Differentiable ODE Solving Infrastructure |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2411.19882 |