1,576 research outputs found
Parameter Inference in Differential Equation Models of Biopathways using Time Warped Gradient Matching
Parameter inference in mechanistic models of biopathways based on systems
of coupled differential equations is a topical yet computationally challenging problem,
due to the fact that each parameter adaptation involves a numerical integration of the
differential equations. Techniques based on gradient matching, which aim to minimize
the discrepancy between the slope of a data interpolant and the derivatives predicted
from the differential equations, offer a computationally appealing shortcut to the inference
problem. However, gradient matching critically hinges on the smoothing scheme
for function interpolation, with spurious wiggles in the interpolant having a dramatic
effect on the subsequent inference. The present article demonstrates that a time warping
approach aiming to homogenize intrinsic functional length scales can lead to a signifi-
cant improvement in parameter estimation accuracy. We demonstrate the effectiveness
of this scheme on noisy data from a dynamical system with periodic limit cycle and a
biopathway
On solving Ordinary Differential Equations using Gaussian Processes
We describe a set of Gaussian Process based approaches that can be used to
solve non-linear Ordinary Differential Equations. We suggest an explicit
probabilistic solver and two implicit methods, one analogous to Picard
iteration and the other to gradient matching. All methods have greater accuracy
than previously suggested Gaussian Process approaches. We also suggest a
general approach that can yield error estimates from any standard ODE solver
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