Automatic Differentiation and AI Applied to Computational Physics

Team: 1003

School: Los Alamos High

Area of Science: Computational Physics

Proposal:
Rationale

    Automatic differentiation (AD) is the technique of carrying a value’s derivative with it throughout a calculation to have a derivative of the end result with respect to the input without needing to propagate backwards through the calculation. This is useful in the case of AI, where knowing the derivative of outputs is needed to train the AI. In computational physics, an approximate numerical solution to a set of differential equations is created to simulate the subject of the equations. Sometimes the terms in a differential equation are approximations or assumptions that are not perfectly aligned with reality. In this case, an AI could theoretically be put in place of the term and trained on the output of the model compared to real data, resulting in a more reality-fitting model. Automatic differentiation aids this process.

    Can automatic differentiation in combination with artificial intelligence be used in computational physics model to improve performance and increase alignment with reality?

    Automatic differentiation can be implemented in computational models to train an AI to imitate real world terms that can only be approximated in equation form, and will increase a model’s alignment with reality.

• Implement set of ordinary differential equations (ODEs) in Julia or Python
• Apply automatic differentiation libraries
• Implement artificial intelligence inside of model
• Train AI on data from the real world and model outputs
• Show improvement from past models not incorporating AD or AI

    I hope to achieve a functional implementation of AI in a computational physics model, enabling high accuracy predictions not possible without AD and AI.

• Learn about automatic differentiation libraries in Julia or Pytorch
• Create numerical equations solver utilizing automatic differentiation
• Implement AI in equation solver
• Train AI with data gained from AD
• Test accuracy and results of model against past models

    I will compare the outputs of my model to known results and observe the accuracy. I will see whether certain effects are taken into account in the model. I will compare the outputs of this model to other models and check for improvement in this model compared to others.

• Bezanson, Jeff, et al. “The Julia Language.” The Julia Language, https://julialang.org/blog/2019/01/fluxdiffeq.
• Christopher, et al. “A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions.” ArXiv.org, Cornell University, 5 Dec. 2018, https://arxiv.org/abs/1812.01892.
• Innes, Mike, et al. “∂P: A Differentiable Programming System to Bridge Machine Learning and Scientific Computing.” ArXiv, 18 July 2019, arxiv.org/pdf/1907.07587.pdf.
• Zhuang, Jiawei. “Solving ODE by artificial neural networks with Knet.jl and Optim.jl.” 2017. http://courses.csail.mit.edu/18.337/2017/projects/jiawei_zhuang/final_report_JiaweiZhuang.pdf.

Team Members:

  Robert Strauss

Sponsoring Teacher: NA

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