I am interested in probabilistic modeling for the physical sciences, particularly the integration of statistical inference and machine learning with physics-based models. My research has focused on developing new data assimilation algorithms that incorporate machine learning within physically grounded inference frameworks.
State estimation for nonlinear state space models is a challenging task. Existing assimilation methodologies predominantly assume Gaussian posteriors on physical space, where true posteriors become inevitably non-Gaussian. We propose Deep Bayesian Filtering (DBF) for data assimilation on nonlinear state space models (SSMs). DBF constructs new latent variables ht on a new latent (“fancy”) space and assimilates observations ot. By (i) constraining the state transition on fancy space to be linear and (ii) learning a Gaussian inverse observation operator q(ht|ot), posteriors always remain Gaussian for DBF. Quite distinctively, the structured design of posteriors provides an analytic formula for the recursive computation of posteriors without accumulating Monte-Carlo sampling errors over time steps. DBF seeks the Gaussian inverse observation operators q(ht|ot) and other latent SSM parameters (e.g., dynamics matrix) by maximizing the evidence lower bound. Experiments show that DBF outperforms model-based approaches and latent assimilation methods in various tasks and conditions.
In Dual-polarization radar observations, we can utilize radar observables, namely differential reflectivity (Zdr) and differential phase shift (PhiDP), that allow us to infer the size of raindrops through their deformations. In particular, the specific differential phase shift (kDP), the derivative of the differential phase shift PhiDP, is unaffected by rain attenuation and is a moment with an exponent close to the precipitation rate (approximately the 4.78th power), allowing for better estimation than the Z-R relationship. However, observations of PhiDP are noisy in general. A stable estimation of the true kDP already poses a challenge.
Here, we propose to build a state space model that takes raindrop size distribution (DSD) parameters as the latent variables ht and radar observables as the observation variables ot. This formulation allows us to use different relations between observables and the rain rate, thanks to the degrees of freedom in DSD parameters. We prepare a test distribution q(h1:T|o1:T), where the means and standard deviations of the distribution are yielded by neural networks (NN). The NN is trained by maximizing the evidence lower bound. In this talk, I will present the methodology and the results of the DSD parameters obtained.
This is an ongoing work.