Machine Learning of Linear Differential Equations using Gaussian Processes
This addresses the challenge of parameter inference in linear differential equations for researchers in scientific computing and machine learning, but appears incremental as it builds on existing probabilistic methods.
The paper tackles the problem of discovering conservation laws expressed by parametric linear equations from scarce and noisy observations, using Gaussian process priors modified according to the operators to infer parameters, but does not provide concrete numerical results.
This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential, integro-differential, and fractional order operators. Here, Gaussian process priors are modified according to the particular form of such operators and are employed to infer parameters of the linear equations from scarce and possibly noisy observations. Such observations may come from experiments or "black-box" computer simulations.