The Illusion of Fit: Spatially Resolved Assessment of Constitutive Model Validity in Elastography and Physics-Based Inverse Problems

[2502.07415] The Illusion of Fit: Spatially Resolved Assessment of Constitutive Model Validity in Elastography and Physics-Based Inverse Problems Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Machine Learning arXiv:2502.07415 (stat) [Submitted on 11 Feb 2025 ( v1 ), last revised 13 Apr 2026 (this version, v2)] Title: The Illusion of Fit: Spatially Resolved Assessment of Constitutive Model Validity in Elastography and Physics-Based Inverse Problems Authors: Vincent C. Scholz , P.S. Koutsourelakis View a PDF of the paper titled The Illusion of Fit: Spatially Resolved Assessment of Constitutive Model Validity in Elastography and Physics-Based Inverse Problems, by Vincent C. Scholz and P.S. Koutsourelakis View PDF HTML (experimental) Abstract: Inferring the mechanical properties of soft tissues from measured deformations is a fundamental challenge in elastography. A rarely examined assumption underlying existing approaches is that the assumed constitutive law correctly describes the imaged material. When it fails, inversion still yields plausible-looking estimates - an illusion of fit with no indication of local model invalidity, which can mislead clinical interpretation. We propose a probabilistic framework that transforms constitutive model validity from an implicit assumption into an explicit, spatially resolved inference target. The key is to treat the stress field as an independent latent variable rather than deriving it from the constitutive law. This enables a pointwise comparison between the stress required by mechanical equilibrium and the stress predicted by the assumed constitutive model. Both governing equations enter the probabilistic learning objective as virtual observables with separate precision hyperparameters: the conservation law precision is set a priori to a small value reflecting its undisputed validity, while the constitutive precision is inferred under a sparsity-promoting prior. The resulting constitutive precision field provides an uncertainty-aware map of where the assumed model is supported by the data and where it is not. Inference is carried out via stochastic variational inference and is forward-model-free. We validate the framework on synthetic harmonic elastography experiments on a brain-slice geometry with an anisotropic inclusion. The inferred precision field identifies the inclusion with a five-order-of-magnitude precision contrast against the valid domain, robustly across 25-35 dB noise and four-fold sparser observations. A phantom experiment with ultrasound measurements on a linear elastic material yields no false-positive violations and recovers the true stiffness contrast. Comments: 29 pages, 12 figures Subjects: Machine Learning (stat.ML) ; Machine Learning (cs.LG) Cite as: arXiv:2502.07415 [stat.ML] (or arXiv:2502.07415v2 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2502.07415 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Vincent C. Scholz [ view email ] [v1] Tue, 11 Feb 2025 09:52:06 UTC (352 KB) [v2] Mon, 13 Apr 2026 12:45:08 UTC (4,987 KB) Full-text links: Access Paper: View a PDF of the paper titled The Illusion of Fit: Spatially Resolved Assessment of Constitutive Model Validity in Elastography and Physics-Based Inverse Problems, by Vincent C. Scholz and P.S. 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