Stable methods improve estimation of unknown forces in dynamic systems
Stable and Calibrated Latent Force ODE Filters
Machine Learning
Summary
When machines or natural systems change over time, we often want to guess hidden forces affecting them. The authors study a way to combine known system rules with observed data to estimate these hidden forces more reliably. They found that how the method handles uncertainty strongly affects its stability and accuracy. Using this insight, they made a better version of the method that gives more stable and trustworthy estimates, tested on simulated examples.
What this means in practice
- •For control engineers: Estimate unknown forces acting on mechanical systems by integrating observational data with known system dynamics for improved control decisions.
- •For environmental modelers: Integrate observational data into process-based models to better estimate unobserved environmental forces affecting system states.
Tested on simulated data.
Authors
Paul Fischer, Jonathan Schmidt, Philipp Hennig
Abstract
Estimating unobserved forces in mechanistic systems is a central task of scientific machine learning. Approximate Gaussian filtering methods that synthesize mechanistic and empirical information have shown remarkable capacity in jointly identifying latent processes together with the system state in a single forward-backward pass. The resulting latent force ODE filter framework channels information from observational data specifically into the unknown parts of the system. This work addresses open questions about calibration and stability of the method. We show that the joint posterior over state and force is the reweighted conventional latent force posterior. This uncovers a crucial dependence of the stability of the method on the prior variance of the system state, which effectively controls the flow of information from observations to the latent force through the mechanistic system. From this insight, we construct an improved algorithm that provides stable and calibrated plug-and-play inference. We demonstrate the improved framework on several simulated experimental settings.