mlsanityData to 7 Oct 2026

Weak neural variational inference for solving Bayesian inverse problems without forward models: applications in elastography

arXiv 2407.20697 ↗First posted 30 Jul 2024stat.ML cs.LGcited by 5

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Abstract (arXiv)

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).

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 25 of its 80 references that are in the map. First posted on arXiv 30 Jul 2024.

Builds on

25 of 80 references.

References · 25

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 1.

5 papers.

  1. 2025DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modelingcited by 5
  2. 2025A unified physics-informed generative operator framework for general inverse problemscited by 1
  3. 2025The Illusion of Fit: Spatially Resolved Assessment of Constitutive Model Validity in Elastography and Physics-Based Inverse Problemscited by 0
  4. 2025Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Datacited by 0
  5. 2026GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Mediacited by 0