  Physics-informed neural networks (PINNs) have proven a suitable mathematical
scaffold for solving inverse ordinary (ODE) and partial differential equations
(PDE). Typical inverse PINNs are formulated as soft-constrained multi-objective
optimization problems with several hyperparameters. In this work, we
demonstrate that inverse PINNs can be framed in terms of maximum-likelihood
estimators (MLE) to allow explicit error propagation from interpolation to the
physical model space through Taylor expansion, without the need of
hyperparameter tuning. We explore its application to high-dimensional coupled
ODEs constrained by differential algebraic equations that are common in
transient chemical and biological kinetics. Furthermore, we show that
singular-value decomposition (SVD) of the ODE coupling matrices (reaction
stoichiometry matrix) provides reduced uncorrelated subspaces in which PINNs
solutions can be represented and over which residuals can be projected.
Finally, SVD bases serve as preconditioners for the inversion of covariance
matrices in this hyperparameter-free robust application of MLE to
``kinetics-informed neural networks''.
