Simulate, solve and visualize nonlinear differential equations utilizing probabilistic models that are optimized via maximum marginal likelihood.
- The class ODE_Analysis enables the simulation of coupled ODEs with additional observation uncertainties. The goal is to describe Lotka Volterra sequences with an ODE-solver and a probabilistic model. In addition, we want to analyze and visualize results.
- A domain-driven time integration approach is applied to model our coupled set of ODEs. The ODE-solver is combined with a probabilistic model. The residuum of the pure ODE-solver and probabilistically boosted model is depicted here:
- The parameters of our probabilistically boosted model are optimized by tuning the maximum marginal likelihood. Time series behavior of the optimized system model is plotted with associated noisy observations:
- A trajectory plot with samples from the optimized system model is shown:
- Modelling techniques are applied, utilizing Neural Ordinary Differential Equations (Neural ODEs):
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- https://www.tensorflow.org/probability
- https://github.com/scipy/scipy-cookbook
- https://github.com/smkalami
- https://en.wikipedia.org/wiki/Marginal_likelihood
- https://chrisrackauckas.com/research.html
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