A Kalman–Bucy Informed Neural Network for Identification of Regime-Switching Diffusions, with an Application to Affine Term Structure Models

This paper constructs a Kalman–Bucy informed neural network for identifying diffusions modulated by a finite-state Markov chain and observed discretely in noise, which have no finite-dimensional filter. One network with an observation-phase input represents the filter path and its jumps at observations and is trained on a causal one-step quasi-likelihood at stop-gradient previous states, on residuals tying the states at observations to the collapsed Bayes posterior, and on residuals of the exact conditional-moment system in between. On a regime-switching affine term structure model, kept arbitrage-free, it reproduces the diffusion parameter, noise scale, and regime classification of an exact-moment filter where it converges. At coarse sampling the residuals cut the median bias of the frozen quasi-likelihood in the switching intensity fourfold at the default weight and budget. The correction comes from the parameter gradient of the residual along the optimization path: it vanishes when the parameters are detached, grows with the weight, and shrinks with the budget. Where the bias is small, it brings no gain over the ablation and only delays convergence. The terminal collapse residual flags, without the truth, fits short of a causal fixed point and selects the residual weight; a sensitivity analysis maps where neural estimators fail.