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Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
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A physics-informed neural network based on mixed data sampling for solving modified diffusion equations.

Qian Fang1, Xuankang Mou1, Shiben Li2

  • 1Department of Physics, Wenzhou University, Wenzhou, 325035, Zhejiang, China.

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|February 13, 2023
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We developed an efficient physics-informed neural network solver for modified diffusion equations. This novel approach accurately solves both forward and backward problems, offering a versatile tool for complex differential equations.

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Area of Science:

  • Computational Mathematics
  • Numerical Analysis
  • Machine Learning

Background:

  • Modified diffusion equations are crucial in various scientific fields.
  • Solving these equations, especially for forward and backward problems, presents significant computational challenges.
  • Existing numerical methods may face limitations in accuracy and efficiency.

Purpose of the Study:

  • To develop and validate a novel physics-informed neural network (PINN) solver.
  • To address both forward and backward modified diffusion equations efficiently.
  • To demonstrate the solver's accuracy and generalizability.

Main Methods:

  • A hybrid sampling strategy combining Cartesian grid and Latin hypercube sampling was employed.
  • Neural network parameters and sampling coefficients were optimized.
  • The solver was tested on a specific modified diffusion equation, comparing results against numerical solutions.

Main Results:

  • The PINN solver demonstrated high accuracy in solving both forward and backward modified diffusion equations.
  • Observed good agreement between neural network predictions and established numerical solutions.
  • The optimization of network parameters and sampling methods proved effective.

Conclusions:

  • The developed PINN solver offers an efficient and accurate method for modified diffusion equations.
  • The approach shows promise for generalization to a wider range of partial differential equations.
  • This work highlights the potential of PINNs in computational science and engineering.