Weak neural variational inference for solving Bayesian inverse problems without forward models: Applications in elastography
Year: 2024
Type: article
Abstract: In this paper, we introduce a novel, data-driven approach for solving high-dimensional Bayesian inverse problems based on partial differential equations (PDEs), called Weak Neural Variational Inference (WNVI). The method complements real measurements with virtual observations derived from the physical model. In particular, weighted residuals are employed as probes to the governing PDE in order to formulate and solve a Bayesian inverse problem without ever formulating nor solving a forward model. The formulation treats the state variables of the physical model as latent variables, inferred using Stochastic Variational Inference (SVI), along with the usual unknowns. The approximate posterior employed uses neural networks to approximate the inverse mapping from state variables to the unknowns. We illustrate the proposed method in a biomedical setting where we infer spatially-varying, material properties from noisy, tissue deformation data. We demonstrate that WNVI is not only as accurate and more efficient than traditional methods that rely on repeatedly solving the (non)linear forward problem as a black-box, but it can also handle ill-posed forward problems (e.g., with insufficient boundary conditions). • Novel Bayesian method using ML and physics to solve model-based, inverse problems. • Uses weighted residuals as virtual observables, avoiding a classical forward model. • Solving inverse problems for ill-posed (insufficient bound. cond.) forward problems. • Demonstrations in elastography and comparison to traditional inference methods.
Institution: Technical University of Munich
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,660
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4404131141