Application of neural network collocation method to data assimilation

• Published in: Computer physics communications 2001-12, Vol.141 (3), p.350-364
• Main Authors: Liaqat, Ali, Fukuhara, Makoto, Takeda, Tatsuoki
• Format: Article
• Language: English
• Subjects: Classical chaos; Collocation methods; Computational techniques; Computers in experimental physics; Data assimilation; Differential equations; Exact sciences and technology; Feed-forward multi-layer neural network; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Inverse problem; Lorenz model; Mathematical methods in physics; Neural networks, fuzzy logic, artificial intelligence; Nonlinear dynamics and nonlinear dynamical systems; Numerical simulations of chaotic models; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Weak constraint formulation
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/S0010-4655(01)00431-3

In this paper we propose a new data assimilation method by using a neural network. In the method we make use of the flexibility of a neural network for constructing an arbitrary mapping function. We train a neural network by optimizing an object function composed of squared residuals of differential equations at collocation points and squared deviations of the observation data from the computed values. The method we propose is, therefore, data assimilation with weak constraints. In this way we can solve an assimilation problem even if the model differential equations do not express the observed phenomena exactly. As an example we applied the new method to a data assimilation problem where the model is the well-known Lorenz model. Though the practically applicable data assimilation method should be able to solve four-dimensional problems (one temporal and three spatial dimensions) and the Lorenz model is one-dimensional, this model is still useful for a benchmark test of the data assimilation methods due to its strong nonlinearity and chaotic nature. We have examined the new method for the above mentioned problem under various conditions and obtained satisfactory results.